Daily Papers

In continuous diffusion language models (DLMs), latents generated by the diffusion prior are mapped almost deterministically to tokens, either by a decoder or through a token embedding matrix. Unlike in image generation, where visual details can vary continuously, the diffusion prior must capture fine-grained discrete token choices in continuous space, which can make the joint latent distribution difficult to model. We argue that generative roles should instead be divided: the diffusion prior should generate high-level predictive information, while the decoder should resolve the remaining token-level choices. Based on this view, we introduce Predictive-State Flows (PSF), which partitions a sequence into blocks and associates each block with a predictive state computed solely from the preceding context. A rectified-flow prior generates the sequence of predictive states, after which a block-causal decoder generates all blocks in parallel, autoregressively only within each block. This design reduces diffusion from L token-level states to K << L predictive states and reduces token-level sequential depth to L/K. On unconditional OpenWebText generation, a 197M-parameter model with K=8 achieves a generative perplexity of 22.8 at entropy 5.16 using 0.31 TFLOPs per 1024-token document, versus 24.0 and 7.2 TFLOPs for ELF-B with 32 sampling steps. The corresponding measured operating points yield MAUVE@512 of 0.93 and 0.73, respectively. Controlled comparisons further show that content states, which additionally encode their own blocks, yield 8-16% higher generative perplexity than predictive states, and that replacing sampled predictive-state trajectories with a shared mean lowers MAUVE@512 by 0.11. These results suggest that latent design for continuous DLMs should consider not only how compactly text is represented, but also how generative roles are divided between the prior and the decoder.

A user's movie, news, and dialogue histories differ in their native actions and outputs, yet each interaction supplies evidence that can update user memory. We study whether these histories can train one reusable update mechanism. An action-on-item schema pairs a mapped interaction role with a content embedding, allowing shared update parameters to operate on separate user states. We establish invariance to native relabeling, bounded state changes under item-embedding perturbations, and a pooled-training bound under explicit compatibility conditions. The Multi-Timescale State Hypothesis (MTSH) specifies how this evidence enters, persists, and is consumed; PerTIDE implements it with action gating, three state-space traces, fusion, and command-conditioned readout. On PENS, the same history encoder supports both next-news prediction and personalized headline generation. In a controlled PENS-to-MovieLens experiment, a frozen source-trained core exceeds an identically structured random core by 15.23 MRR points after fitting the same target consumer. On MIND, PerTIDE retains a 4.12-point MRR advantage over a same-input three-branch state-space control. Action, readout, and trace interventions identify complementary contributions to these gains. Together, the theory and experiments support learning history updates across compatible sources and reusing them through predictive and generative consumers.

Autonomous vehicles operate in highly dynamic environments necessitating an accurate assessment of which aspects of a scene are moving and where they are moving to. A popular approach to 3D motion estimation, termed scene flow, is to employ 3D point cloud data from consecutive LiDAR scans, although such approaches have been limited by the small size of real-world, annotated LiDAR data. In this work, we introduce a new large-scale dataset for scene flow estimation derived from corresponding tracked 3D objects, which is sim1,000times larger than previous real-world datasets in terms of the number of annotated frames. We demonstrate how previous works were bounded based on the amount of real LiDAR data available, suggesting that larger datasets are required to achieve state-of-the-art predictive performance. Furthermore, we show how previous heuristics for operating on point clouds such as down-sampling heavily degrade performance, motivating a new class of models that are tractable on the full point cloud. To address this issue, we introduce the FastFlow3D architecture which provides real time inference on the full point cloud. Additionally, we design human-interpretable metrics that better capture real world aspects by accounting for ego-motion and providing breakdowns per object type. We hope that this dataset may provide new opportunities for developing real world scene flow systems.

World models in robot learning predict future states from visual observations and actions, enabling agents to reason about the consequences of their controls. However, many action-conditioned models are evaluated in settings where motion is dominated by immediate control, whereas aquatic surface vehicles and other real-world objects continue moving under inertia and are displaced by hidden ambient drift, such as water currents or wind. We propose FlowMo-WM, an end-to-end trainable visual world model that infers object-centric motion state and a predictive long-history context associated with hidden drift from image-action histories without direct supervision of flow fields. FlowMo-WM factorizes image-action history into a short-history latent state, trained to summarize object-centric motion, and a longer-history context, trained to summarize slowly varying exogenous influences. A zero-context residual transition separates action-conditioned base dynamics from context-dependent drift effects during latent rollout. In simulated aquatic surface-vehicle environments with diverse hidden flows, disturbances, and randomized vehicle dynamics, FlowMo-WM improves long-horizon rollout accuracy over representative action-conditioned latent world models. Prediction-time context ablations, in which the inferred context is zeroed or shuffled during rollout, show that the ambient context is important for stable prediction under hidden drift, while frozen linear probes characterize information encoded in the learned factors.

Accurate uncertainty quantification is critical for many time series forecasting applications, and recent studies have increasingly adopted generative models to capture predictive uncertainty. Existing approaches often combine deterministic forecasting with generative modeling to improve predictive performance. However, their joint training is typically unstable because the deterministic model is embedded within the generative process, resulting in deep computational graphs and changing the probability transport path. In this work, we propose DV-Flow, a unified flow-matching formulation that incorporates the deterministic predictor as a parallel velocity component rather than as the endpoint of the transport path. This design enables stable end-to-end optimization while subsuming several existing formulations as special cases, allowing direct comparisons among them. Extensive experiments on six real-world datasets demonstrate that DV-Flow consistently improves probabilistic forecasting performance over strong baselines. Our code is available at https://github.com/tufts-ml/dv-flow-time-series.

Closed-loop human-AI systems generate high-dimensional behavioural trajectories whose collective dynamics remain obscure. Using 297,915 learners' adaptive-tutoring histories, we define semantic order variables before model fitting and test them in user-disjoint cohorts. The state exhibits reproducible basin-like flow and operationally defined, state-heterogeneous metastable-like kinetics. A construction-matched null distinguishes normalised-memory relaxation from a reproducible excess field. A four-term conditional mechanism recovers population drift (r = 0.946; learner-bootstrap 95% CI, 0.935-0.955). Predictive event-level self-supervised learning recovers the state and learned-plane flow; null-referenced corrections retain directional, partial-amplitude excess-field structure without full calibration. Shuffled-order training reverses learned-plane flow on ordered trajectories; support-alignment randomisation selectively reduces inward transport. Both axes remain linearly accessible without state supervision. Without cross-model fitting, the models share leading population drift (r = 0.866; learner-bootstrap 95% CI, 0.857-0.875) and persistence ordering; residual directions remain model-specific. These results identify an externally anchored leading-order effective field linking empirical dynamics, an interpretable mechanism and neural computation.

We present Probabilistic Structure Integration (PSI), a system for learning richly controllable and flexibly promptable world models from data. PSI consists of a three-step cycle. The first step, Probabilistic prediction, involves building a probabilistic graphical model Psi of the data, in the form of a random-access autoregressive sequence model. Psi supports a complete set of learned conditional distributions describing the dependence of any variables in the data on any other set of variables. In step 2, Structure extraction, we show how to extract underlying low-dimensional properties in the data, corresponding to a diverse set of meaningful "intermediate structures", in a zero-shot fashion via causal inference on Psi. Step 3, Integration, completes the cycle by converting these structures into new token types that are then continually mixed back into the training diet as conditioning signals and prediction targets. Each such cycle augments the capabilities of Psi, both allowing it to model the underlying data better, and creating new control handles -- akin to an LLM-like universal prompting language. We train an instance of Psi on 1.4 trillion tokens of internet video data; we use it to perform a variety of useful video prediction and understanding inferences; we extract state-of-the-art optical flow, self-supervised depth and object segmentation; and we use these structures to support a full cycle of predictive improvements.

Vision-Language-Action (VLA) models commonly generate robot actions token by token through Large Language Model (LLM) decoders, causing inference latency to grow with action sequence length and limiting closed-loop control frequency. We present Goal-Conditioned Vision-Predictor-Action (VPA), which replaces autoregressive decoders with a lightweight latent control loop. A shared vision encoder and a frozen text encoder embed observations, goal images, and instructions; a neuro-symbolic selector chooses a discrete skill; a Joint-Embedding Predictive Architecture (JEPA) predictor forecasts the next latent state; and a flow-matching solver generates an entire action chunk in a few integration steps, so that sequential network evaluations per decision step do not depend on the action horizon. We analyze inference complexity, regularization against representation collapse, and conditions under which latent sub-goal thresholding limits error accumulation across task phases. As an initial proof of concept, we evaluated VPA on the LIBERO-10 suite. The trainable model has under 20M parameters (checkpoint under 75 MB, excluding a frozen 63.4M-parameter CLIP text encoder); a decision step of a single-camera reference configuration takes 10-14 ms on an Apple M4; and trained only on LIBERO-10 demonstrations in under three hours on a single GPU, a two-camera policy succeeded in 40.0% of 200 evaluation episodes. These preliminary results from a single training run suggest the approach is workable. Code and weights are available at https://github.com/ylee-sling/Vision-Predictor-Action and https://huggingface.co/ylee-sling/vpa-libero10, and archived at https://doi.org/10.5281/zenodo.22960920.

Flow- and diffusion-based generative models have recently emerged as flexible and highly efficient forecasting models for dynamical systems. When combined with inference-time guidance, they offer a promising route to high-dimensional non-Gaussian data assimilation (DA), the problem of combining forecasts with observations to estimate latent system states. Existing filters, however, condition on a fixed history and assimilate only the most recent observation, leaving them unable to revise past states when new observations arrive. Estimates then stay tethered to a history that later observations may contradict, and errors accumulate over the assimilation run. To this end, we introduce **DAWIS**, a unified DA method covering filtering, fixed-lag smoothing, and block smoothing within a single framework. DAWIS replaces the single flow time of a state-level prior with a multitask stochastic interpolant over a window of consecutive states, assigning a separate flow time to each. An assimilation cycle inverts the window to a vector of per-state turning points and regenerates it under observation guidance, with the turning points controlling how strongly each state is held fixed, revised, or generated from scratch. The same construction can also absorb the forecast into the assimilation cycle, removing the need for a separate forecasting model. Experiments on challenging nonlinear systems show that DAWIS improves on both filtering and smoothing baselines under sparse, noisy, and nonlinear observations. The code for DAWIS is available at https://github.com/Erik-Wikingsson/DAWIS

World models construct latent states that support prediction, planning, and reasoning about an underlying system. Joint-embedding predictive architectures (JEPAs) offer a direct way to learn such states by predicting targets in representation space instead of reconstructing every detail of the observation. Standard JEPAs, however, organize all predictable content through one target embedding and one prediction pathway. In complex systems, this monolithic state can allocate redundant capacity to dominant signals while providing weak or conflicting gradients to less dominant predictive structure. We introduce \method, a latent world-modeling framework based on orthogonal predictive factorization. Learned basis matrices analyze each target state into multiple components, and a dedicated prediction branch estimates each component from a shared context representation. Predictive regression preserves the factor magnitudes required for state synthesis, an orthogonality objective discourages repeated directions, factor-activity regularization maintains variation in projected targets, and online variance regularization discourages coordinate-wise encoder collapse. Predicted components are synthesized into a complete latent state that can be used by a readout, decoder, planner, or autoregressive rollout. The same predictive-state mechanism applies when the target is temporally future, spatially hidden, or another partial observation of the same system. Experiments on controlled vision, single-cell transcriptomics, longitudinal health records, continuous control, and molecular dynamics evaluate representation quality, forecasting, planning, and long-horizon stability.

Large-scale pre-training has fundamentally changed how machine learning research is done today: large foundation models are trained once, and then can be used by anyone in the community (including those without data or compute resources to train a model from scratch) to adapt and fine-tune to specific tasks. Applying this same framework to reinforcement learning (RL) is appealing because it offers compelling avenues for addressing core challenges in RL, including sample efficiency and robustness. However, there remains a fundamental challenge to pre-train large models in the context of RL: actions have long-term dependencies, so training a foundation model that reasons across time is important. Recent advances in generative AI have provided new tools for modeling highly complex distributions. In this paper, we build a probabilistic model to predict which states an agent will visit in the temporally distant future (i.e., an occupancy measure) using flow matching. As large datasets are often constructed by many distinct users performing distinct tasks, we include in our model a latent variable capturing the user intention. This intention increases the expressivity of our model, and enables adaptation with generalized policy improvement. We call our proposed method intention-conditioned flow occupancy models (InFOM). Comparing with alternative methods for pre-training, our experiments on 36 state-based and 4 image-based benchmark tasks demonstrate that the proposed method achieves 1.8 times median improvement in returns and increases success rates by 36%. Website: https://chongyi-zheng.github.io/infom Code: https://github.com/chongyi-zheng/infom

In this paper, we address the problem of human trajectory forecasting, which aims to predict the inherently multi-modal future movements of humans based on their past trajectories and other contextual cues. We propose a novel motion prediction conditional flow matching model, termed MoFlow, to predict K-shot future trajectories for all agents in a given scene. We design a novel flow matching loss function that not only ensures at least one of the K sets of future trajectories is accurate but also encourages all K sets of future trajectories to be diverse and plausible. Furthermore, by leveraging the implicit maximum likelihood estimation (IMLE), we propose a novel distillation method for flow models that only requires samples from the teacher model. Extensive experiments on the real-world datasets, including SportVU NBA games, ETH-UCY, and SDD, demonstrate that both our teacher flow model and the IMLE-distilled student model achieve state-of-the-art performance. These models can generate diverse trajectories that are physically and socially plausible. Moreover, our one-step student model is 100 times faster than the teacher flow model during sampling. The code, model, and data are available at our project page: https://moflow-imle.github.io

Recent work on the sequence universality of State Space Models (SSMs) has introduced efficient, maximally expressive continuous-time approaches for time-series modelling. While these works focus on discriminative settings, we extend this perspective to generative time-series modelling by proving that maximally expressive Structured Linear Controlled Differential Equations (SLiCEs) are universal time-series generators, in the sense that they can approximate the induced path laws of continuous causal pushforwards on compact latent sets in W_infty. Building on these theoretical results, we propose Generative SLiCEs (G-SLiCEs), a maximally expressive continuous-time model for flow matching on path-space. Empirically, we show that expressivity improves performance in probabilistic forecasting and downstream tasks, while retaining the advantages of continuous-time models such as generalising to arbitrary observation grids. This is particularly beneficial for irregular grids, where fixed-grid models often struggle.

Long-horizon search requires agents to acquire relevant evidence and integrate it into an evolving research state. Existing methods maintain research states to guide exploration or assign turn-level progress signals, yet grounding these signals in explicit, attributable state changes remains underexplored. We introduce ClueFlow, which learns long-horizon search from attributed research-state transitions. ClueFlow constructs Source-State-Final attribution chains that connect evidence-acquiring browser actions, Evidence and Candidate updates, and the final answer supported by those updates. During search, ClueFlow records typed state changes and potentially supporting browser actions, then applies gold-conditioned semantic validation and source tracing after execution. We use this attribution to guide both supervised fine-tuning and reinforcement learning. During SFT, attribution selects which decisions receive supervision with their original interaction contexts. During Turn-PPO, the same attribution augments outcome-based turn advantages with credit assigned along the Source-State-Final chains. Transition-level validation also recovers useful supervision from gold-consistent state changes in trajectories with incorrect final answers. We evaluate ClueFlow across two Qwen backbones and four search benchmarks spanning live-web and fixed-corpus settings, observing consistent gains from SFT and further improvements from PPO. With Qwen3.5-35B-A3B, ClueFlow achieves 60.0% accuracy on BrowseComp and 72.0% on BrowseComp-Plus. In controlled BrowseComp-Plus experiments, attribution-guided SFT matches all-turn exact-context SFT using about 30% of the training tokens, while attribution-guided PPO outperforms outcome-only PPO by 4.1 pp. These results demonstrate that state-transition attribution enables efficient supervision and effective credit assignment for long-horizon search agents.

We propose a unified, few-step generative modeling framework based on cumulative flow maps for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a cumulative-flow abstraction that connects local, instantaneous updates with finite-time transport, enabling generative models to reason about global state transitions. This perspective yields a unified few-step framework built on cumulative transport and cumulative parameterization that applies broadly to existing diffusion- and flow-based models without being tied to a specific prediction instantiation. Our formulation supports few-step and even one-step generation while preserving synthesis quality, requiring only minimal changes to time embeddings and training objectives, and no increase in model capacity. We demonstrate its effectiveness across diverse tasks, including image generation, geometric distribution modeling, joint prediction, and SDF generation, with reduced inference cost.

In the physical world we inhabit, space and time are fundamentally continuous. However, existing machine learning paradigms for world modeling are largely confined to discrete-time prediction, thereby exhibiting significant inefficiency in capturing the dynamics of physical world. We introduce Physical-Time Flow (PT-Flow), a novel approach that learns a continuous latent velocity field operating in physical time. Crucially, the underlying dynamics of sequential data are parameterized by an ordinary differential equation (ODE) embedded in a well-structured representation space. Under this paradigm, the prediction of future can be recast as temporal integration via an ODE solver in the compressed latent space. Building upon PT-Flow, we construct ODEWorld, a continuous-time latent world model that is both efficient and versatile. By extracting time-variant features and enforcing ODE properties on both the dynamical representation space and the latent velocity field, ODEWorld effectively addresses the long-standing representation collapse issue in latent world model literature. This also enables high-quality image reconstruction even after long-horizon prediction. Moreover, its continuous nature allows for arbitrary temporal resolution and even backward prediction, which is impossible for most discrete-time models. Lastly, ODEWorld can provide rich planning-oriented information to facilitate downstream policy learning. Comprehensive experiments demonstrate that ODEWorld successfully reconciles planning-conducive dynamics abstraction with visual realism, excelling in both video generation and robotic control. https://dstate.github.io/odeworld_website/{Project Website}.

It is a notable trend to use Large Language Models (LLMs) to tackle complex tasks, e.g., tasks that require a sequence of actions and dynamic interaction with tools and external environments. In this paper, we propose StateFlow, a novel LLM-based task-solving paradigm that conceptualizes complex task-solving processes as state machines. In StateFlow, we distinguish between "process grounding" (via state and state transitions) and "sub-task solving" (through actions within a state), enhancing control and interpretability of the task-solving procedure. A state represents the status of a running process. The transitions between states are controlled by heuristic rules or decisions made by the LLM, allowing for a dynamic and adaptive progression. Upon entering a state, a series of actions is executed, involving not only calling LLMs guided by different prompts, but also the utilization of external tools as needed. Our results show that StateFlow significantly enhances LLMs' efficiency. For instance, StateFlow achieves 13% and 28% higher success rates compared to ReAct in InterCode SQL and ALFWorld benchmark, with 5x and 3x less cost respectively. We also show that StateFlow can be combined with iterative refining methods like Reflexion to further improve performance.

Flow matching (FM) has emerged as a powerful framework for learning dynamic transport maps between two empirical distributions. However, less explored is the setting with intermediate observed marginals that can help constrain the flows between the endpoints. This "multimarginal" regime is central to modeling temporal evolution in dynamical systems in many scientific domains that can sample sequential distributions. We tackle this problem with a novel approach that leverages the connection between FM and dynamic optimal transport (OT), softly steering the flow towards the intermediate marginals through potential terms in the dynamic OT action. By extending the conditional FM learning target to incorporate these potentials, we derive an efficient, simulation-free algorithm for multimarginal FM that offers considerable flexibility in the spatiotemporal dynamics of the learned flows. We demonstrate state-of-the-art performance and training efficiency of OT-potential FM (OTP-FM) on diverse single-cell RNA sequencing, oceanographic, and meteorological datasets. Our code is available at https://github.com/Bexorg-Inc/OTP-FM.

Diffusion and flow-based models have enabled significant progress in generation tasks across various modalities and have recently found applications in world modeling. However, unlike typical generation tasks that encourage sample diversity, world models entail different sources of uncertainty and require consistent samples aligned with the ground-truth trajectory, which is a limitation we empirically observe in diffusion models. We argue that a key bottleneck in learning consistent diffusion-based world models lies in the suboptimal predictive ability, which we attribute to the entanglement of condition understanding and target denoising within shared architectures and co-training schemes. To address this, we propose Foresight Diffusion (ForeDiff), a diffusion-based world modeling framework that enhances consistency by decoupling condition understanding from target denoising. ForeDiff incorporates a separate deterministic predictive stream to process conditioning inputs independently of the denoising stream, and further leverages a pretrained predictor to extract informative representations that guide generation. Extensive experiments on robot video prediction and scientific spatiotemporal forecasting show that ForeDiff improves both predictive accuracy and sample consistency over strong baselines, offering a promising direction for diffusion-based world models.

We study the learning dynamics of self-predictive learning for reinforcement learning, a family of algorithms that learn representations by minimizing the prediction error of their own future latent representations. Despite its recent empirical success, such algorithms have an apparent defect: trivial representations (such as constants) minimize the prediction error, yet it is obviously undesirable to converge to such solutions. Our central insight is that careful designs of the optimization dynamics are critical to learning meaningful representations. We identify that a faster paced optimization of the predictor and semi-gradient updates on the representation, are crucial to preventing the representation collapse. Then in an idealized setup, we show self-predictive learning dynamics carries out spectral decomposition on the state transition matrix, effectively capturing information of the transition dynamics. Building on the theoretical insights, we propose bidirectional self-predictive learning, a novel self-predictive algorithm that learns two representations simultaneously. We examine the robustness of our theoretical insights with a number of small-scale experiments and showcase the promise of the novel representation learning algorithm with large-scale experiments.

Few-step diffusion or flow-based generative models typically distill a velocity-predicting teacher into a student that predicts a shortcut towards denoised data. This format mismatch has led to complex distillation procedures that often suffer from a quality-diversity trade-off. To address this, we propose policy-based flow models (pi-Flow). pi-Flow modifies the output layer of a student flow model to predict a network-free policy at one timestep. The policy then produces dynamic flow velocities at future substeps with negligible overhead, enabling fast and accurate ODE integration on these substeps without extra network evaluations. To match the policy's ODE trajectory to the teacher's, we introduce a novel imitation distillation approach, which matches the policy's velocity to the teacher's along the policy's trajectory using a standard ell_2 flow matching loss. By simply mimicking the teacher's behavior, pi-Flow enables stable and scalable training and avoids the quality-diversity trade-off. On ImageNet 256^2, it attains a 1-NFE FID of 2.85, outperforming MeanFlow of the same DiT architecture. On FLUX.1-12B and Qwen-Image-20B at 4 NFEs, pi-Flow achieves substantially better diversity than state-of-the-art few-step methods, while maintaining teacher-level quality.

Probabilistic weather forecasting requires not only accurate trajectories, but calibrated distributions over plausible atmospheric futures. Recent data-driven systems have achieved remarkable deterministic skill, and diffusion-based ensemble forecasters have substantially improved sample realism and uncertainty quantification. However, their inference cost scales with forecast horizon, ensemble size, and the number of denoising steps required for each transition, making large operational ensembles expensive. To address this, we present Tyche, a one-step conditional flow model for efficient probabilistic weather forecasting. Tyche models the conditional forecast distribution with a destination-aware average-velocity flow that maps Gaussian noise directly to future weather states in a single function evaluation (1-NFE). To make this one-step transport learnable in high-dimensional geophysical fields, we derive a JVP-regularized rectification objective that enforces temporal self-consistency across source and destination flow timesteps without explicitly forming Jacobians. The transport field is parameterized by an isotropic Swin-style transformer that preserves fine-scale spatial structure while remaining scalable on global grids. To improve ensemble reliability under autoregressive forecasting, we further introduce a rollout-based finetuning stage with curriculum CRPS calibration supervision. Experiments on ERA5 at 1.5^circ and 6-hour resolution show that our Tyche, using merely a single NFE, matches or exceeds the forecast skill and calibration of state-of-the-art multi-step generative baselines and the operational ECMWF IFS ensemble.

Long-horizon tasks require LLM agents to continually draw on information from earlier interactions. However, retaining the full history increases context costs, while compressing it risks losing details needed later, and the relevance of historical information often becomes apparent as the task progresses. To address these challenges, we propose FlowState, which treats execution state as memory that can be retained and revisited across requests, unifying current decision-making with the reuse of historical information. FlowState preserves semantically typed state nodes, their relations, and references to raw tool observations, separating persistent retention from on-demand access. Within a single execution loop, Incremental State Update (ISU) maintains the current state based on new inputs and feedback, while Progressive State Access (PSA) progressively reveals historical states and supporting evidence as needed during reasoning. Together, these mechanisms enable agents to reassess prior decisions in light of new information and guide subsequent actions. Compared with a full-context baseline using the same DeepSeek-V4-Flash model, FlowState improves the average success rate on MemoryArena and the average pass rate on τ^3-Bench by 4.55 and 13.95 percentage points, respectively, while reducing total token consumption by 43.2% and 40.6%. These results demonstrate the performance and efficiency advantages of FlowState on long-horizon tasks.

High-dimensional count data are common in scientific applications, but most diffusion and flow models are designed for continuous or categorical data, and generation often requires many sequential model evaluations. We propose Count Flow Map, a generative model that learns finite-time transitions directly in count space for one- or few-step generation. Our model directly learns stochastic transitions over finite time intervals, using Poisson births and Binomial deaths to preserve nonnegative integer counts without a predefined maximum. These transition models are trained to match the underlying local birth--death dynamics and to maintain consistency across step sizes. We characterize the connection between local dynamics and finite-time transition consistency and derive a bound on the generation error. After validating Count Flow Map in several simulations, including a high-dimensional, high-count setting, we apply it to single-cell drug perturbation prediction and neural population forecasting, where it captures perturbation responses and supports forecasts of high-activity events with only one or a few model evaluations. Together, these experiments demonstrate that Count Flow Map enables high-quality generation directly in count space across inference budgets, from one-step to few-step generation, using a single trained model.

We conjecture that hidden state vectors corresponding to individual input tokens encode information sufficient to accurately predict several tokens ahead. More concretely, in this paper we ask: Given a hidden (internal) representation of a single token at position t in an input, can we reliably anticipate the tokens that will appear at positions geq t + 2? To test this, we measure linear approximation and causal intervention methods in GPT-J-6B to evaluate the degree to which individual hidden states in the network contain signal rich enough to predict future hidden states and, ultimately, token outputs. We find that, at some layers, we can approximate a model's output with more than 48% accuracy with respect to its prediction of subsequent tokens through a single hidden state. Finally we present a "Future Lens" visualization that uses these methods to create a new view of transformer states.

Generative Flow Networks or GFlowNets are related to Monte-Carlo Markov chain methods (as they sample from a distribution specified by an energy function), reinforcement learning (as they learn a policy to sample composed objects through a sequence of steps), generative models (as they learn to represent and sample from a distribution) and amortized variational methods (as they can be used to learn to approximate and sample from an otherwise intractable posterior, given a prior and a likelihood). They are trained to generate an object x through a sequence of steps with probability proportional to some reward function R(x) (or exp(-E(x)) with E(x) denoting the energy function), given at the end of the generative trajectory. Like for other RL settings where the reward is only given at the end, the efficiency of training and credit assignment may suffer when those trajectories are longer. With previous GFlowNet work, no learning was possible from incomplete trajectories (lacking a terminal state and the computation of the associated reward). In this paper, we consider the case where the energy function can be applied not just to terminal states but also to intermediate states. This is for example achieved when the energy function is additive, with terms available along the trajectory. We show how to reparameterize the GFlowNet state flow function to take advantage of the partial reward already accrued at each state. This enables a training objective that can be applied to update parameters even with incomplete trajectories. Even when complete trajectories are available, being able to obtain more localized credit and gradients is found to speed up training convergence, as demonstrated across many simulations.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

Efficient and accurate motion prediction is crucial for ensuring safety and informed decision-making in autonomous driving, particularly under dynamic real-world conditions that necessitate multi-modal forecasts. We introduce TrajFlow, a novel flow matching-based motion prediction framework that addresses the scalability and efficiency challenges of existing generative trajectory prediction methods. Unlike conventional generative approaches that employ i.i.d. sampling and require multiple inference passes to capture diverse outcomes, TrajFlow predicts multiple plausible future trajectories in a single pass, significantly reducing computational overhead while maintaining coherence across predictions. Moreover, we propose a ranking loss based on the Plackett-Luce distribution to improve uncertainty estimation of predicted trajectories. Additionally, we design a self-conditioning training technique that reuses the model's own predictions to construct noisy inputs during a second forward pass, thereby improving generalization and accelerating inference. Extensive experiments on the large-scale Waymo Open Motion Dataset (WOMD) demonstrate that TrajFlow achieves state-of-the-art performance across various key metrics, underscoring its effectiveness for safety-critical autonomous driving applications. The code and other details are available on the project website https://traj-flow.github.io/.

Predictive process monitoring is a process mining task aimed at forecasting information about a running process trace, such as the most correct next activity to be executed. In medical domains, predictive process monitoring can provide valuable decision support in atypical and nontrivial situations. Decision support and quality assessment in medicine cannot ignore domain knowledge, in order to be grounded on all the available information (which is not limited to data) and to be really acceptable by end users. In this paper, we propose a predictive process monitoring approach relying on the use of a {\em transformer}, a deep learning architecture based on the attention mechanism. A major contribution of our work lies in the incorporation of ontological domain-specific knowledge, carried out through a graph positional encoding technique. The paper presents and discusses the encouraging experimental result we are collecting in the domain of stroke management.

Diffusion models operate in a reflexive System 1 mode, constrained by a fixed, content-agnostic sampling schedule. This rigidity arises from the curse of state dimensionality, where the combinatorial explosion of possible states in the high-dimensional noise manifold renders explicit trajectory planning intractable and leads to systematic computational misallocation. To address this, we introduce Chain-of-Trajectories (CoTj), a train-free framework enabling System 2 deliberative planning. Central to CoTj is Diffusion DNA, a low-dimensional signature that quantifies per-stage denoising difficulty and serves as a proxy for the high-dimensional state space, allowing us to reformulate sampling as graph planning on a directed acyclic graph. Through a Predict-Plan-Execute paradigm, CoTj dynamically allocates computational effort to the most challenging generative phases. Experiments across multiple generative models demonstrate that CoTj discovers context-aware trajectories, improving output quality and stability while reducing redundant computation. This work establishes a new foundation for resource-aware, planning-based diffusion modeling. The code is available at https://github.com/UnicomAI/CoTj.

Extracting optical flow from videos remains a core computer vision problem. Motivated by the success of large general-purpose models, we ask whether frozen self-supervised video models trained only for future frame prediction can be prompted, without fine-tuning, to output flow. Prior work reading out depth or illumination from video generators required fine-tuning, which is impractical for flow where labels are scarce and synthetic datasets suffer from a sim-to-real gap. Inspired by the Counterfactual World Model (CWM) paradigm, which can obtain point-wise correspondences by injecting a small tracer perturbation into a next-frame predictor and tracking its propagation, we extend this idea to generative video models. We explore several popular architectures and find that successful zero-shot flow extraction in this manner is aided by three model properties: (1) distributional prediction of future frames (avoiding blurry or noisy outputs); (2) factorized latents that treat each spatio-temporal patch independently; and (3) random-access decoding that can condition on any subset of future pixels. These properties are uniquely present in the recent Local Random Access Sequence (LRAS) architecture. Building on LRAS, we propose KL-tracing: a novel test-time procedure that injects a localized perturbation into the first frame, rolls out the model one step, and computes the Kullback-Leibler divergence between perturbed and unperturbed predictive distributions. Without any flow-specific fine-tuning, our method outperforms state-of-the-art models on real-world TAP-Vid DAVIS dataset (16.6% relative improvement for endpoint error) and synthetic TAP-Vid Kubric (4.7% relative improvement). Our results indicate that counterfactual prompting of controllable generative video models is a scalable and effective alternative to supervised or photometric-loss approaches for high-quality flow.

World models must predict how an environment evolves under sequences of actions, enabling agents to compare possible futures and reason about counterfactual actions before acting. Long-horizon prediction is commonly obtained by recursively applying a one-step transition model, but intermediate errors can compound over time. Multi-step dynamics models instead condition on a sequence of future actions and predict their consequences directly, but become harder to learn as horizon grows: the model must track interacting state changes across the trajectory, endpoint supervision provides weak credit assignment, and intermediate predictions can remain plausible while losing information needed for later states. We show that these challenges can be addressed by casting the internal evolution of a multi-step transition as structured reasoning over textual world states: reasoning over sparse state changes reduces the burden of state tracking, a predictive-gain objective rewards the learned state for improving over a matched predictor that conditions on raw history instead, and intermediate predictive rewards supervise each state along the trajectory. Because these intermediate states are explicit textual representations of the world, they provide semantically meaningful targets that can be inspected, scored, and corrected during training. Across ScienceWorld, Jericho, and CEO-Bench, our approach achieves the strongest average long-horizon performance against recursive and non-recursive baselines that condition directly on raw history, with gains increasing at longer horizons. In a controlled counterfactual study, our model is also the only one with statistically significant sensitivity to future actions.

Foundation models (FMs) have transformed natural language processing, but their success has not yet translated to time series forecasting. Existing time series foundation models (TSFMs), often based on transformer variants, struggle with generalization across varying context and target lengths, lack adaptability to different sampling rates, and are computationally inefficient. We introduce FlowState, a novel TSFM architecture that addresses these challenges through two key innovations: a state space model (SSM) based encoder and a functional basis decoder. This design enables continuous-time modeling and dynamic time-scale adjustment, allowing FlowState to inherently generalize across all possible temporal resolutions, and dynamically adjust the forecasting horizons. In contrast to other state-of-the-art TSFMs, which require training data across all possible sampling rates to memorize patterns at each scale, FlowState inherently adapts its internal dynamics to the input scale, enabling smaller models, reduced data requirements, and improved efficiency. We further propose an efficient pretraining strategy that improves robustness and accelerates training. Despite being the smallest model, FlowState outperforms all other models and is state-of-the-art for the GIFT-ZS and the Chronos-ZS benchmarks. Ablation studies confirm the effectiveness of its components, and we demonstrate its unique ability to adapt online to varying input sampling rates.

Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental challenge, as existing approaches face a critical speed-fidelity trade-off. In this work, we introduce Recursive Flow Matching (RecFM), a generative framework for forecasting complex spatiotemporal dynamics. RecFM enforces self-consistency to align trajectories across discretization scales, reducing discretization errors and improving performance across metrics for physics-based tasks. To our knowledge, this is the first method to achieve high-fidelity one- and few-step (2-4 step) dynamic generation for scientific systems with performance comparable to state-of-the-art multi-step solvers. Across challenging scientific benchmarks, RecFM achieves up to a 20times speedup over leading diffusion-based emulators while improving predictive accuracy. Furthermore, RecFM reduces mean squared error by over 15% compared to vanilla flow matching, offering a scalable and efficient solution for real-time scientific emulation.

Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help us predict which type of event will happen next and when. We model streams of discrete events in continuous time, by constructing a neurally self-modulating multivariate point process in which the intensities of multiple event types evolve according to a novel continuous-time LSTM. This generative model allows past events to influence the future in complex and realistic ways, by conditioning future event intensities on the hidden state of a recurrent neural network that has consumed the stream of past events. Our model has desirable qualitative properties. It achieves competitive likelihood and predictive accuracy on real and synthetic datasets, including under missing-data conditions.

A central puzzle for the behavioural sciences and for human-facing artificial intelligence is the persistence of within-person variability. The same individual, presented with the same observable input, produces different outcomes on different occasions, and different individuals produce divergent outcomes that no observable covariate fully predicts. We argue that this variability belongs in the dynamic latent state of the person, and that human outcomes are controllable in a precise and operational sense through interventions that target the state and its weighting at the moment a decision is being formed. We define a state as the time-indexed weighting vector over the dimensions that govern how an individual's biology, physiology, and neuropsychology process the next event into a decision and an outcome. The relationship between state, decision, and outcome is causal rather than correlational. The weighting vector is dynamic at sub-daily timescales. The conscious channel through which outcomes are reportable is a narrow attentional bottleneck whose contents are themselves state-dependent. Taken together, these claims imply that the outcome of a given event is controllable, conditionally, on the state-trajectory at the time of intervention. We motivate the framework with six strands of established evidence (causal inference, predictive processing, allostasis, attentional bottleneck, chronobiology, computational psychiatry) and a 24-month observational base from a deployed behavioural platform spanning more than 200,000 consented users across four occupational personas (research period 2023 to 2026). We derive seven testable predictions, list six operational requirements for state-aware systems, and discuss implications for digital health, education, AI personalisation, and personal agency.

There is growing interest in utilizing flow-based models as decision-making policies in reinforcement learning due to their high expressive capacity. However, effectively leveraging this expressivity for value maximization remains challenging, as naive gradient-based optimization requires backpropagating through numerical solvers and often leads to instability. Existing approaches typically address this issue by restricting the expressive capacity of flow-based policies, resulting in a trade-off between optimization stability and representational flexibility. To resolve this, we introduce Q-Flow, a framework that leverages the deterministic nature of flow dynamics to explicitly propagate terminal trajectory value to intermediate latent states along the policy-induced flow. This formulation enables stable policy optimization using intermediate value gradients without unrolling the numerical solver, effectively bridging the gap between stability and expressivity. We evaluate Q-Flow in the offline learning setting on the challenging OGBench suite, where it consistently outperforms state-of-the-art baselines by an average of 10.6 percentage points, while also enabling stable online adaptation within the same framework.

Predicting cellular responses to perturbations is a central problem in cellular biology, with broad applications in systems biology and drug discovery. This task is challenging because cellular responses can be complex and cell-state dependent, intrinsic cell-to-cell variability can be confounded with perturbation effects, and destructive single-cell RNA sequencing precludes paired measurements of the same cell before and after treatment. Flow matching transports control cells to perturbed states flexibly, but acting on the full cell state can confound perturbation effects with pre-existing cell-to-cell variability. Disentangled approaches separate responsive from invariant components, but model perturbations through prescribed mechanisms, such as latent shifts or graph edits, limiting their flexibility. We address both limitations in a unified framework. A variational encoder disentangles each cell into an invariant block, capturing state unaffected by the perturbation, and a responsive block, capturing state it changes, through conditional priors and an information-theoretic invariance constraint. Conditional flow matching transports only the responsive block, conditioned on the perturbation and invariant state, yielding a flexible, data-driven model of perturbation effects without confounding pre-existing variability. Across several benchmarks, our method outperforms the strongest published method in settings involving combinatorial and unseen perturbation prediction.

Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs demonstrate outstanding performance across a diverse set of domains, at a reduced training and inference cost compared to attention-based transformers. Recent developments show that if the linear recurrence powering SSMs allows for multiplicative interactions between inputs and hidden states (e.g. GateLoop, Mamba, GLA), then the resulting architecture can surpass in both in accuracy and efficiency attention-powered foundation models trained on text, at scales of billion parameters. In this paper, we give theoretical grounding to this recent finding using tools from Rough Path Theory: we show that when random linear recurrences are equipped with simple input-controlled transitions (selectivity mechanism), then the hidden state is provably a low-dimensional projection of a powerful mathematical object called the signature of the input -- capturing non-linear interactions between tokens at distinct timescales. Our theory not only motivates the success of modern selective state-space models such as Mamba but also provides a solid framework to understand the expressive power of future SSM variants.

This is an extended version of our publication Learning state machines from data streams: A generic strategy and an improved heuristic, International Conference on Grammatical Inference (ICGI) 2023, Rabat, Morocco. It has been extended with a formal proof on PAC-bounds, and the discussion and analysis of a similar approach has been moved from the appendix and now has a full dedicated section. State machine models are models that simulate the behavior of discrete event systems, capable of representing systems such as software systems, network interactions, and control systems, and have been researched extensively. The nature of most learning algorithms however is the assumption that all data be available at the beginning of the algorithm, and little research has been done in learning state machines from streaming data. In this paper, we want to close this gap further by presenting a generic method for learning state machines from data streams, as well as a merge heuristic that uses sketches to account for incomplete prefix trees. We implement our approach in an open-source state merging library and compare it with existing methods. We show the effectiveness of our approach with respect to run-time, memory consumption, and quality of results on a well known open dataset. Additionally, we provide a formal analysis of our algorithm, showing that it is capable of learning within the PAC framework, and show a theoretical improvement to increase run-time, without sacrificing correctness of the algorithm in larger sample sizes.

Forecasting from partial observations is central to world modeling. Many recent methods represent the world through images, and reduce forecasting to stochastic video generation. Although such methods excel at realism and visual fidelity, predicting pixels is computationally intensive and not directly useful in many applications, as it requires translating RGB into signals useful for decision making. An alternative approach uses features from vision foundation models (VFMs) as world representations, performing deterministic regression to predict future world states. These features can be directly translated into actionable signals such as semantic segmentation and depth, while remaining computationally efficient. However, deterministic regression averages over multiple plausible futures, undermining forecast accuracy by failing to capture uncertainty. To address this crucial limitation, we introduce a generative forecaster that performs autoregressive flow matching in VFM feature space. Our key insight is that generative modeling in this space requires encoding VFM features into a compact latent space suitable for diffusion. We show that this latent space preserves information more effectively than previously used PCA-based alternatives, both for forecasting and other applications, such as image generation. Our latent predictions can be easily decoded into multiple useful and interpretable output modalities: semantic segmentation, depth, surface normals, and even RGB. With matched architecture and compute, our method produces sharper and more accurate predictions than regression across all modalities. Our results suggest that stochastic conditional generation of VFM features offers a promising and scalable foundation for future world models.

Safety-critical applications such as autonomous vehicles and social robots require fast computation and accurate probability density estimation on trajectory prediction. To address both requirements, this paper presents a new normalizing flow-based trajectory prediction model named FlowChain. FlowChain is a stack of conditional continuously-indexed flows (CIFs) that are expressive and allow analytical probability density computation. This analytical computation is faster than the generative models that need additional approximations such as kernel density estimation. Moreover, FlowChain is more accurate than the Gaussian mixture-based models due to fewer assumptions on the estimated density. FlowChain also allows a rapid update of estimated probability densities. This update is achieved by adopting the newest observed position and reusing the flow transformations and its log-det-jacobians that represent the motion trend. This update is completed in less than one millisecond because this reuse greatly omits the computational cost. Experimental results showed our FlowChain achieved state-of-the-art trajectory prediction accuracy compared to previous methods. Furthermore, our FlowChain demonstrated superiority in the accuracy and speed of density estimation. Our code is available at https://github.com/meaten/FlowChain-ICCV2023

Critical transitions - abrupt, often irreversible changes in system dynamics - arise across human and natural systems, often with catastrophic consequences. Real-world observations of such shifts remain scarce, preventing the development of reliable early warning systems. Conventional statistical and spectral indicators, such as increasing variance, tend to fail under realistic conditions of limited data and correlated noise, whereas existing deep learning classifiers do not extrapolate beyond their training data distribution. In this work, we introduce TipPFN, an in-context learning (ICL) framework that uses a prior-data fitted network to infer a system's proximity to a critical transition. Trained on our novel synthetic data generator, which is based on canonical bifurcation scenarios coupled to diverse, randomized stochastic dynamics, TipPFN flexibly capitalizes on contexts of various sizes, complexity and dimensionalities. We demonstrate robust, state-of-the-art early detection of critical transitions in previously unseen tipping regimes, sim-to-real examples, and real-world observations in both ICL and zero-shot settings.

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models.

Time series foundation models are becoming increasingly popular for general-purpose forecasting. However, most leading models predict marginal quantiles, leaving the dependence structure of future trajectories unspecified. This distinction matters for trajectory-dependent quantities such as cumulative demand, peak load, and event timing, yet point and marginal scores do not reveal it. To model this dependence, we introduce PathFM, a trajectory-based forecasting model that uses flow matching to generate complete future paths. We further distill the model to one or two steps and share history attention cache across draws. Together, these enable PathFM to generate multiple paths for a single series in roughly the time needed for one query to a quantile model. The distilled sampler also makes it practical to optimize a calibration loss directly. PathFM achieves competitive marginal accuracy on the established forecasting benchmarks fev-bench and TIME. To complement these evaluations, we introduce Forecast Path Score Bench (fps-bench), which augments fev-bench tasks with energy and variogram scores and downstream metrics. PathFM achieves a higher aggregate path score on fps-bench than all evaluated external baselines. Experiments on chaotic systems further show that our flow model sustains long-run variability, while strong baselines rapidly collapse. PathFM makes generative time series forecasting both competitive and practical, enabling diverse downstream applications.

The high cost of fine-tuning LLMs poses a significant economic barrier; pre-hoc performance prediction offers a critical solution to substantially reduce this expense. However, the theoretical limits of pre-hoc performance prediction remain unexplored. We formulate it as a stochastic estimation problem under information constraints, decomposing prediction risk into two components: an intrinsic limit (static data-model compatibility) and a reducible optimization variance. We prove that optimization variance admits a necessary lower bound on its decay rate, implying fundamental constraints on how quickly uncertainty dissipates, regardless of the predictor used. Based on these dynamics, we derive a budget-optimal probing principle and introduce a predictability phase diagram that organizes tasks into three distinct regimes: Static-Sufficient, Dynamic-Critical, and Noise-Dominant. Extensive experiments on synthetic and real-world benchmarks validate these theoretical regimes and demonstrate the efficiency of our probing strategy.

Representations are at the core of all deep reinforcement learning (RL) methods for both Markov decision processes (MDPs) and partially observable Markov decision processes (POMDPs). Many representation learning methods and theoretical frameworks have been developed to understand what constitutes an effective representation. However, the relationships between these methods and the shared properties among them remain unclear. In this paper, we show that many of these seemingly distinct methods and frameworks for state and history abstractions are, in fact, based on a common idea of self-predictive abstraction. Furthermore, we provide theoretical insights into the widely adopted objectives and optimization, such as the stop-gradient technique, in learning self-predictive representations. These findings together yield a minimalist algorithm to learn self-predictive representations for states and histories. We validate our theories by applying our algorithm to standard MDPs, MDPs with distractors, and POMDPs with sparse rewards. These findings culminate in a set of preliminary guidelines for RL practitioners.

Predictive Coding (PC) is a theoretical framework in cognitive science suggesting that the human brain processes cognition through spatiotemporal prediction of the visual world. Existing studies have developed spatiotemporal prediction neural networks based on the PC theory, emulating its two core mechanisms: Correcting predictions from residuals and hierarchical learning. However, these models do not show the enhancement of prediction skills on real-world forecasting tasks and ignore the Precision Weighting mechanism of PC theory. The precision weighting mechanism posits that the brain allocates more attention to signals with lower precision, contributing to the cognitive ability of human brains. This work introduces the Cognitive Diffusion Probabilistic Models (CogDPM), which demonstrate the connection between diffusion probabilistic models and PC theory. CogDPM features a precision estimation method based on the hierarchical sampling capabilities of diffusion models and weight the guidance with precision weights estimated by the inherent property of diffusion models. We experimentally show that the precision weights effectively estimate the data predictability. We apply CogDPM to real-world prediction tasks using the United Kindom precipitation and ERA surface wind datasets. Our results demonstrate that CogDPM outperforms both existing domain-specific operational models and general deep prediction models by providing more proficient forecasting.

Representation learning and exploration are among the key challenges for any deep reinforcement learning agent. In this work, we provide a singular value decomposition based method that can be used to obtain representations that preserve the underlying transition structure in the domain. Perhaps interestingly, we show that these representations also capture the relative frequency of state visitations, thereby providing an estimate for pseudo-counts for free. To scale this decomposition method to large-scale domains, we provide an algorithm that never requires building the transition matrix, can make use of deep networks, and also permits mini-batch training. Further, we draw inspiration from predictive state representations and extend our decomposition method to partially observable environments. With experiments on multi-task settings with partially observable domains, we show that the proposed method can not only learn useful representation on DM-Lab-30 environments (that have inputs involving language instructions, pixel images, and rewards, among others) but it can also be effective at hard exploration tasks in DM-Hard-8 environments.

Recent 3D world models increasingly use features from geometry foundation models (GFMs) as predictive world states, benefiting from their rich geometric priors. However, the view dependence of these features entangles scene dynamics with camera-induced variation, making the resulting state evolution harder to predict. We propose GeoState, a view-decoupled geometry representation for predictive 3D world modeling that separates scene-state evolution from camera-dependent observation. Specifically, a scene tokenizer aggregates multi-view GFM features into a view-decoupled scene state, which a geometry decoder queries using camera rays. An autoregressive world model then predicts future scene states, while camera motion is modeled separately. The predicted states can therefore be decoded under either predicted or externally specified cameras, while retaining a single context-derived scale throughout the rollout without per-frame scale alignment. Experiments show that GeoState outperforms prior 3D world models on Waymo, supports geometrically consistent cross-view querying, and generalizes zero-shot to KITTI and nuScenes. Project page: https://hongchang-liu.github.io/GeoState-project-page/

Modeling dynamical systems and unraveling their underlying structural dependencies is central to many domains in the natural sciences. Various physical systems, such as those arising in cell biology, are inherently high-dimensional and stochastic in nature, and admit only partial, noisy state measurements. Our primary motivating setting is single-cell biology, where destructive measurements yield unpaired population snapshots rather than longitudinal trajectories of the same cells. This poses a significant challenge for addressing the problems of modeling the underlying dynamics and inferring the network structure of these systems. Existing methods are typically tailored either for structure learning or modeling dynamics at the population level, but are limited in their ability to address both problems together. In this work, we address both problems simultaneously: we present StructureFlow, a novel and principled simulation-free training approach for jointly learning the structure and stochastic population dynamics of physical systems. We showcase the utility of StructureFlow for the tasks of structure learning from interventions and dynamical (trajectory) inference of conditional population dynamics. We empirically evaluate our approach on high-dimensional synthetic systems, a set of biologically plausible simulated systems, and an experimental single-cell dataset. We show that StructureFlow can learn the structure of underlying systems while simultaneously modeling their conditional population dynamics --- a key step toward model-based mechanistic understanding of systems behavior.

Temporal point processes are the dominant paradigm for modeling sequences of events happening at irregular intervals. The standard way of learning in such models is by estimating the conditional intensity function. However, parameterizing the intensity function usually incurs several trade-offs. We show how to overcome the limitations of intensity-based approaches by directly modeling the conditional distribution of inter-event times. We draw on the literature on normalizing flows to design models that are flexible and efficient. We additionally propose a simple mixture model that matches the flexibility of flow-based models, but also permits sampling and computing moments in closed form. The proposed models achieve state-of-the-art performance in standard prediction tasks and are suitable for novel applications, such as learning sequence embeddings and imputing missing data.

Neural Flows efficiently model irregular multivariate time series by directly learning ODE solution trajectories with neural networks, bypassing step-by-step numerical solvers. Despite their efficiency, many existing approaches treat variables independently, leaving inter-variable interactions underexplored. Moreover, their one-step mapping makes interaction modeling inherently challenging, as it removes the iterative refinement of interactions during learning. To address this challenge, we propose one-step Graph-Structured Neural Flows (GSNF), which introduce two auxiliary-trajectory self-supervision strategies to strengthen interaction learning: (i) interaction-aware trajectory generation via re-initialization, which induces trajectory divergence to expose graph-induced interactions, with a theoretically derived lower bound on divergence; and (ii) reverse-time trajectory generation, which enforces forward-backward consistency to regularize graph learning, enabled by flow invertibility. Experiments on five real-world datasets show that GSNF achieves state-of-the-art classification performance with highly competitive training time and memory usage.

Generative planners based on diffusion/flow matching can learn to synthesize long-horizon trajectories from demonstrations. However, real-world deployment requires (i) enforcing safety constraints during execution and (ii) tight online replanning at fast execution rates. Prior safe diffusion/flow planners generate the agent's full trajectory at once, while repeatedly perturbing intermediate states to satisfy safety constraints. This approach is not only computationally intensive, but also introduces distribution shift since the learned sampling dynamics is distinct from the system's execution dynamics. We propose SafeStreamingFlow, a goal-conditioned planner that aligns flow sampling dynamics with execution dynamics by sequentially integrating a learned state vector field with hierarchical state prediction. Importantly, we need to enforce safety constraints only for the executed step via high order control barrier functions. Across navigation, racing, and locomotion benchmarks, SafeStreamingFlow reduces planning latency and improves safety compared to existing methods, while maintaining competitive goal-reaching success.

In recent years, trace generation has emerged as a significant challenge within the Process Mining community. Deep Learning (DL) models have demonstrated accuracy in reproducing the features of the selected processes. However, current DL generative models are limited in their ability to adapt the learned distributions to generate data samples based on specific conditions or attributes. This limitation is particularly significant because the ability to control the type of generated data can be beneficial in various contexts, enabling a focus on specific behaviours, exploration of infrequent patterns, or simulation of alternative 'what-if' scenarios. In this work, we address this challenge by introducing a conditional model for process data generation based on a conditional variational autoencoder (CVAE). Conditional models offer control over the generation process by tuning input conditional variables, enabling more targeted and controlled data generation. Unlike other domains, CVAE for process mining faces specific challenges due to the multiperspective nature of the data and the need to adhere to control-flow rules while ensuring data variability. Specifically, we focus on generating process executions conditioned on control flow and temporal features of the trace, allowing us to produce traces for specific, identified sub-processes. The generated traces are then evaluated using common metrics for generative model assessment, along with additional metrics to evaluate the quality of the conditional generation

In reinforcement learning and imitation learning, an object of central importance is the state distribution induced by the policy. It plays a crucial role in the policy gradient theorem, and references to it--along with the related state-action distribution--can be found all across the literature. Despite its importance, the state distribution is mostly discussed indirectly and theoretically, rather than being modeled explicitly. The reason being an absence of appropriate density estimation tools. In this work, we investigate applications of a normalizing flow-based model for the aforementioned distributions. In particular, we use a pair of flows coupled through the optimality point of the Donsker-Varadhan representation of the Kullback-Leibler (KL) divergence, for distribution matching based imitation learning. Our algorithm, Coupled Flow Imitation Learning (CFIL), achieves state-of-the-art performance on benchmark tasks with a single expert trajectory and extends naturally to a variety of other settings, including the subsampled and state-only regimes.

Predicting phenotypic and transcriptional responses to perturbations at single-cell resolution provides a powerful tool for probing biological systems. However, existing methods typically rely on fixed mappings learned during training, making it challenging to calibrate distribution shifts or adapt to novel perturbation conditions during inference. Here, we present scEGFlow, an energy-guided flow matching framework that dynamically bridges control and perturbed cellular states. scEGFlow models continuous transitions from control cell populations to perturbed states using conditional flow matching. It then applies condition-specific energy gradients to correct and steer these predictions, enabling flexible adjustments without retraining the flow model. Evaluations across benchmarks spanning imaging phenotypes and transcriptomic profiles show that scEGFlow outperforms existing methods in reconstructing response distributions under both seen and unseen perturbation conditions, faithfully preserving cellular manifold geometry and population heterogeneity. This advantage is notable when adapting to new conditions with only a few measured cells, consistently improving prediction accuracy. Furthermore, scEGFlow accurately recapitulates perturbation-induced up- and down-regulation patterns across consensus gene expression signatures, where energy guidance improves the agreement between predicted and observed regulatory directions. Ultimately, these findings demonstrate that scEGFlow provides a modular, generalizable, and steerable solution for single-cell perturbation modeling. By grounding generative flows in learned biological landscapes, this architecture establishes a new computational paradigm for navigating and manipulating cellular behavior in silico.

As large language model (LLM) agents increasingly learn from experience, they primarily rely on trajectory-level reflection to extract insights. Viewed through the lens of predictive knowledge, we argue that this approach operates on episodic hindsight rather than predictive foresight, yielding brittle, path-dependent heuristics. To address this, we propose Stateful Knowledge Learning (SKL). SKL shifts the agent's focus from trajectory-level summarization to maintaining Stateful Knowledge: explicit, declarative predictive assessments anchored to state. We first demonstrate a motivating example showing how stateful knowledge provides granularity, enhances generalization, and enables knowledge bootstrapping. To further scale up the idea, we introduce two algorithms via self-distillation (SKL-SD) and reinforcement learning (SKL-RL), training agents to autonomously extract state-grounded predictive knowledge from experience and learn to leverage it for policy making. Experiments on interactive environments (WebShop, ScienceWorld) and a complex reasoning task (ChessPuzzles) demonstrate that equipping models with the inherent ability to learn stateful predictive knowledge significantly outpaces current reflection-based training paradigms.

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

The theory of state tracking in recurrent architectures has predominantly focused on expressive capacity: whether a fixed architecture can theoretically realize a set of symbolic transition rules. We argue that equally important is error control, the dynamics governing hidden-state drift along the directions that distinguish symbolic states. We prove that affine recurrent networks, a class of models encompassing State-Space Models and Linear Attention, cannot correct errors along state-separating subspaces once they preserve state representations. Consequently, practical affine trackers do not learn robust state tracking; rather, they learn finite horizon solutions governed by accumulated state-relevant error. We characterize the mechanics of this failure, showing that tracking remains readable only while the accumulating within-class spread remains small relative to the initial between-class separation. We demonstrate empirically on group state-tracking tasks that this breakdown is predictable: tracking collapses when the distinguishability ratio crosses the readability threshold of the trained decoder. Across trained models, the point of this crossing predicts the horizon at which downstream accuracy fails. These results establish that robust state tracking is determined not only by an architecture's theoretical expressivity but crucially by its error control.

Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). Conditional flow matching (CFM) exploits the fact that the marginal vector field of a CNF can be learned by fitting least-squares regression to the conditional vector field specified given one or both ends of the flow path. In this paper, we extend the CFM algorithm by defining conditional probability paths along ``streams'', instances of latent stochastic paths that connect data pairs of source and target, which are modeled with Gaussian process (GP) distributions. The unique distributional properties of GPs help preserve the ``simulation-free" nature of CFM training. We show that this generalization of the CFM can effectively reduce the variance in the estimated marginal vector field at a moderate computational cost, thereby improving the quality of the generated samples under common metrics. Additionally, adopting the GP on the streams allows for flexibly linking multiple correlated training data points (e.g., time series). We empirically validate our claim through both simulations and applications to image and neural time series data.

Conditional generative modeling aims to learn a conditional data distribution from samples containing data-condition pairs. For this, diffusion and flow-based methods have attained compelling results. These methods use a learned (flow) model to transport an initial standard Gaussian noise that ignores the condition to the conditional data distribution. The model is hence required to learn both mass transport and conditional injection. To ease the demand on the model, we propose Condition-Aware Reparameterization for Flow Matching (CAR-Flow) -- a lightweight, learned shift that conditions the source, the target, or both distributions. By relocating these distributions, CAR-Flow shortens the probability path the model must learn, leading to faster training in practice. On low-dimensional synthetic data, we visualize and quantify the effects of CAR. On higher-dimensional natural image data (ImageNet-256), equipping SiT-XL/2 with CAR-Flow reduces FID from 2.07 to 1.68, while introducing less than 0.6% additional parameters.

Precipitation nowcasting aims to forecast short-term radar echo sequences for extreme weather warning, where both prediction fidelity and inference efficiency are critical for real-world deployment. However, diffusion-based models, despite their strong generative capability, suffer from slow inference due to multi-step sampling trajectories, limiting their practical usability. Conditional Flow Matching (CFM) improves efficiency via straightened trajectories, but relies on latent space compression, which inevitably discards high-frequency physical details and degrades fine-grained prediction quality. To address these limitations, we propose PixelFlowCast, a two-stage probabilistic forecasting framework that achieves both high-efficiency and high-fidelity prediction without latent compression. Specifically, in the first stage, a deterministic model first produces coarse forecasts to capture global evolution trends. In the subsequent stage, the proposed KANCondNet extracts deep spatiotemporal evolution features to provide accurate conditional guidance. Based on this, a latent-free, few-step Pixel Mean Flows (PMF) predictor employs an x-prediction mechanism to generate high-quality predictions, effectively preserving fine-grained structures while maintaining fast inference. Experiments on the publicly available SEVIR dataset demonstrate that PixelFlowCast outperforms existing mainstream methods in both prediction accuracy and inference efficiency, particularly for long sequence forecasting, highlighting its strong potential for real-world operational deployment.

Recently, large language models (LLMs) have shown great promise in time series forecasting. However, most existing LLM-based forecasting methods still follow a static generative paradigm that directly maps historical observations to future values in a single pass. Under this paradigm, forecasting is constrained by limited temporal pattern extraction, single-round acquisition of contextual features, one-shot forecast generation, and lack of support from ensemble forecasts. To address these limitations, in this work, we propose CastFlow, a dynamic agentic forecasting framework that enables multi-view temporal pattern extraction, multi-round contextual features acquisition, iterative forecast refinement, and forecasting with ensemble forecasts. First, CastFlow organizes the forecasting process into planning, action, forecasting, and reflection, establishing an agentic workflow. Second, this workflow is supported by a memory module that retrieves prior experience and a multi-view toolkit that constructs diagnostic evidence and provides a reliable ensemble forecast baseline. Third, CastFlow adopts a role-specialized design that combines general-purpose reasoning with specialized numerical forecasting. Under this design, a frozen LLM preserves general-purpose reasoning, while a fine-tuned domain-specific LLM performs evidence-guided numerical forecasting based on the ensemble forecast baseline, rather than from scratch. To optimize a fine-tuned domain-specific LLM, we further develop a two-stage workflow-oriented training that combines supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). To evaluate the effectiveness of CastFlow, we conduct extensive experiments on diverse datasets and show that it achieves superior overall results against strong baselines. We hope that this work can serve as a step toward more adaptive and accurate time series forecasting.

Flow matching models excel at generative modeling, and many downstream applications require their samples to satisfy prescribed constraints, such as observed measurements and physical laws. However, existing constrained samplers often face a trade-off: enforcing constraints can substantially displace samples from the pretrained data distribution. To address this trade-off, we introduce MintFlow, a training-free constrained sampling framework that formulates constraint enforcement as a minimal intervention on the pretrained flow trajectory. MintFlow seeks the minimal perturbation of an intermediate flow state such that its subsequent evolution under the pretrained flow field satisfies the target constraint. By minimally perturbing the flow state while keeping the pretrained flow field unchanged, MintFlow enforces the constraint while minimizing unnecessary deviation from the pretrained distribution. An adjoint formulation yields a closed-form expression for this perturbation, eliminating expensive iterative optimization. Furthermore, MintFlow adaptively selects the intervention time to balance the required perturbation magnitude with its amplification by the remaining flow. Across a range of tasks in generative vision and physical system modeling, MintFlow achieves competitive constraint satisfaction while preserving the pretrained generative distribution substantially better than state-of-the-art constrained methods.

World models learn to predict future states of an environment, enabling planning and mental simulation. Current approaches default to Transformer-based predictors operating in learned latent spaces. This comes at a cost: O(N^2) computation and no explicit spatial inductive bias. This paper asks a foundational question: is self-attention necessary for predictive world modeling, or can alternative computational substrates achieve comparable or superior results? I introduce FluidWorld, a proof-of-concept world model whose predictive dynamics are governed by partial differential equations (PDEs) of reaction-diffusion type. Instead of using a separate neural network predictor, the PDE integration itself produces the future state prediction. In a strictly parameter-matched three-way ablation on unconditional UCF-101 video prediction (64x64, ~800K parameters, identical encoder, decoder, losses, and data), FluidWorld is compared against both a Transformer baseline (self-attention) and a ConvLSTM baseline (convolutional recurrence). While all three models converge to comparable single-step prediction loss, FluidWorld achieves 2x lower reconstruction error, produces representations with 10-15% higher spatial structure preservation and 18-25% more effective dimensionality, and critically maintains coherent multi-step rollouts where both baselines degrade rapidly. All experiments were conducted on a single consumer-grade PC (Intel Core i5, NVIDIA RTX 4070 Ti), without any large-scale compute. These results establish that PDE-based dynamics, which natively provide O(N) spatial complexity, adaptive computation, and global spatial coherence through diffusion, are a viable and parameter-efficient alternative to both attention and convolutional recurrence for world modeling.

This paper studies generative flow networks (GFlowNets) to sample objects from the Boltzmann energy distribution via a sequence of actions. In particular, we focus on improving GFlowNet with partial inference: training flow functions with the evaluation of the intermediate states or transitions. To this end, the recently developed forward-looking GFlowNet reparameterizes the flow functions based on evaluating the energy of intermediate states. However, such an evaluation of intermediate energies may (i) be too expensive or impossible to evaluate and (ii) even provide misleading training signals under large energy fluctuations along the sequence of actions. To resolve this issue, we propose learning energy decompositions for GFlowNets (LED-GFN). Our main idea is to (i) decompose the energy of an object into learnable potential functions defined on state transitions and (ii) reparameterize the flow functions using the potential functions. In particular, to produce informative local credits, we propose to regularize the potential to change smoothly over the sequence of actions. It is also noteworthy that training GFlowNet with our learned potential can preserve the optimal policy. We empirically verify the superiority of LED-GFN in five problems including the generation of unstructured and maximum independent sets, molecular graphs, and RNA sequences.

Prompt engineering is crucial for deploying LLMs but is poorly understood mathematically. We formalize LLM systems as a class of discrete stochastic dynamical systems to explore prompt engineering through the lens of control theory. We investigate the reachable set of output token sequences R_y(mathbf x_0) for which there exists a control input sequence mathbf u for each mathbf y in R_y(mathbf x_0) that steers the LLM to output mathbf y from initial state sequence mathbf x_0. We offer analytic analysis on the limitations on the controllability of self-attention in terms of reachable set, where we prove an upper bound on the reachable set of outputs R_y(mathbf x_0) as a function of the singular values of the parameter matrices. We present complementary empirical analysis on the controllability of a panel of LLMs, including Falcon-7b, Llama-7b, and Falcon-40b. Our results demonstrate a lower bound on the reachable set of outputs R_y(mathbf x_0) w.r.t. initial state sequences mathbf x_0 sampled from the Wikitext dataset. We find that the correct next Wikitext token following sequence mathbf x_0 is reachable over 97% of the time with prompts of kleq 10 tokens. We also establish that the top 75 most likely next tokens, as estimated by the LLM itself, are reachable at least 85% of the time with prompts of kleq 10 tokens. Intriguingly, short prompt sequences can dramatically alter the likelihood of specific outputs, even making the least likely tokens become the most likely ones. This control-centric analysis of LLMs demonstrates the significant and poorly understood role of input sequences in steering output probabilities, offering a foundational perspective for enhancing language model system capabilities.

Flow-based methods have achieved significant success in various generative modeling tasks, capturing nuanced details within complex data distributions. However, few existing works have exploited this unique capability to resolve fine-grained structural details beyond generation tasks. This paper presents a flow-inspired framework for representation learning. First, we demonstrate that a rectified flow trained using independent coupling is zero everywhere at t=0.5 if and only if the source and target distributions are identical. We term this property the zero-flow criterion. Second, we show that this criterion can certify conditional independence, thereby extracting sufficient information from the data. Third, we translate this criterion into a tractable, simulation-free loss function that enables learning amortized Markov blankets in graphical models and latent representations in self-supervised learning tasks. Experiments on both simulated and real-world datasets demonstrate the effectiveness of our approach. The code reproducing our experiments can be found at: https://github.com/probabilityFLOW/zfe.

Recent flow matching models for text-to-image generation have achieved remarkable quality, yet their integration with reinforcement learning for human preference alignment remains suboptimal, hindering fine-grained reward-based optimization. We observe that the key impediment to effective GRPO training of flow models is the temporal uniformity assumption in existing approaches: sparse terminal rewards with uniform credit assignment fail to capture the varying criticality of decisions across generation timesteps, resulting in inefficient exploration and suboptimal convergence. To remedy this shortcoming, we introduce TempFlow-GRPO (Temporal Flow GRPO), a principled GRPO framework that captures and exploits the temporal structure inherent in flow-based generation. TempFlow-GRPO introduces two key innovations: (i) a trajectory branching mechanism that provides process rewards by concentrating stochasticity at designated branching points, enabling precise credit assignment without requiring specialized intermediate reward models; and (ii) a noise-aware weighting scheme that modulates policy optimization according to the intrinsic exploration potential of each timestep, prioritizing learning during high-impact early stages while ensuring stable refinement in later phases. These innovations endow the model with temporally-aware optimization that respects the underlying generative dynamics, leading to state-of-the-art performance in human preference alignment and standard text-to-image benchmarks.

Forecasting future events based on evidence of current conditions is an innate skill of human beings, and key for predicting the outcome of any decision making. In artificial vision for example, we would like to predict the next human action before it happens, without observing the future video frames associated to it. Computer vision models for action anticipation are expected to collect the subtle evidence in the preamble of the target actions. In prior studies recurrence modeling often leads to better performance, the strong temporal inference is assumed to be a key element for reasonable prediction. To this end, we propose a unified recurrence modeling for video action anticipation via message passing framework. The information flow in space-time can be described by the interaction between vertices and edges, and the changes of vertices for each incoming frame reflects the underlying dynamics. Our model leverages self-attention as the building blocks for each of the message passing functions. In addition, we introduce different edge learning strategies that can be end-to-end optimized to gain better flexibility for the connectivity between vertices. Our experimental results demonstrate that our proposed method outperforms previous works on the large-scale EPIC-Kitchen dataset.

We provide an optimization-based framework to perform counterfactual analysis in a dynamic model with hidden states. Our framework is grounded in the ``abduction, action, and prediction'' approach to answer counterfactual queries and handles two key challenges where (1) the states are hidden and (2) the model is dynamic. Recognizing the lack of knowledge on the underlying causal mechanism and the possibility of infinitely many such mechanisms, we optimize over this space and compute upper and lower bounds on the counterfactual quantity of interest. Our work brings together ideas from causality, state-space models, simulation, and optimization, and we apply it on a breast cancer case study. To the best of our knowledge, we are the first to compute lower and upper bounds on a counterfactual query in a dynamic latent-state model.

Process model forecasting (PMF) aims to predict the process model that will characterize a future period, thereby providing a process-level view of how behavior is expected to evolve. Existing PMF methods, however, forecast directly-follows graphs, which cannot explicitly represent concurrency. We extend PMF to causal nets by forecasting time series of relation and binding counts and using these forecasts to reconstruct future process models with AND/XOR semantics. To evaluate the resulting models, we introduce a protocol that accounts for partial traces and constructs the workflow nets required for conformance checking. Experiments on four event logs show that the forecasted models achieve conformance levels close to those of models re-mined from observations in the corresponding future windows. They also outperform static discovery baselines, which retain high precision on the structurally stable log but exhibit substantial precision losses on the other three logs. Filtering infrequent bindings improves most conformance metrics, although it also removes much of the concurrent behavior captured by the models.

Predicting future physical states stands as a central challenge in embodied intelligence. Existing video world models leave 3D dynamics implicit, action-based formulations remain tied to specific robot configurations, and 3D motion prediction models use flow-only supervision, providing a limited learning signal for physical dynamics. To circumvent these limitations, we introduce , a generative world model that jointly predicts future video and query-based 3D trajectories. By parameterizing 3D motion as continuous displacement tokens aligned with the video grid, a unified Mixture-of-Transformers (MoT) backbone jointly denoises both modalities under a rectified-flow objective. This formulation couples explicit geometric dynamics with visual evolution, effectively unlocking the physical commonsense embedded within pretrained video models. To empirically scale and validate this unified architecture, we train on a heterogeneous mixture of 1.44 million object-level samples spanning simulated and real-world domains. We further introduce WorldFlowBench, comprising 1,678 evaluation samples from 11 data sources across simulated and real-world interactions, including spatial reasoning tasks. Across all three evaluation sets, WorldFlow achieves the lowest average displacement error (ADE) and final displacement error (FDE) among the evaluated learning-based methods. Notably, on the challenging SpatialCog set, WorldFlow achieves an ADE of 0.060 m, a 54.2\% reduction compared with the strongest external baseline. It also reduces ADE and FDE by 55.9\% and 68.5\%, respectively, compared with its flow-only variant. Project page: https://worldflow-rbs.github.io/.

Event sequences are chains of random events, each described by heterogeneous (numerical and categorical) features. The problem of event sequence forecasting occurs in finance, healthcare, business process intelligence, and other fields. In this work, we study multi-horizon forecasting of event sequences as a conditional generative modeling problem. We evaluate forecasts not only for prediction accuracy, but also for distributional realism. To this end, we present a benchmark comprising metrics for both quality aspects, strong statistical baselines, recent models adapted from adjacent fields, and curated real-world datasets. Careful evaluation reveals that no method excels at both accuracy and realism, highlighting a fundamental trade-off between the two. Finally, we introduce Wasserstein BaryBooster, an algorithm that aggregates samples from a realism-strong diffusion model into a state-of-the-art predictor, demonstrating that distributional realism can be converted into prediction accuracy. Code is available at https://github.com/xaosina/event-sequence-forecasting.

This monograph develops a unified account of training and inference in Power Law Decoder Representation language models (PLDR-LLMs). Exact finite work identities decompose changes in the absolute energy of the row-centered learned map into parameter contributions, signed interactions, and numerical observation defects. Positive affine blocking retains restarts at the row-constant face, while the augmented AdamW state supplies the complete dynamical description. Predictive renormalization acts on the complete conditional training law for a single pass over distinct corpus target blocks, retaining optimizer memory, remaining data, schedule, and numerical policy. Autonomous reductions require closure; approximate reductions carry successor and emission errors. Finite-population covariance, matched physical clocks, matrix fluxes, and signed temporal energy connect row dynamics to model-wide observations. Absolute row collapse, relative row concentration, operator stabilization, and predictive accuracy are distinguished. Experiments reveal observer and optimizer dependence, reject the tested autonomous row-state candidates, and support finite conditional prediction and state-specific operator reduction. Independent single-pass families exhibit moving finite fluctuation regions without establishing a thermodynamic critical class. Conditional symmetry, head limits, covariance flows, and readout error budgets specify assumptions needed to transfer scaling laws to inference. The theory separates exact identities, conditional dynamical claims, and finite empirical findings, with proofs, selected formal checks, and compact numerical evidence.

Stream networks, a unique class of spatiotemporal graphs, exhibit complex directional flow constraints and evolving dependencies, making uncertainty quantification a critical yet challenging task. Traditional conformal prediction methods struggle in this setting due to the need for joint predictions across multiple interdependent locations and the intricate spatio-temporal dependencies inherent in stream networks. Existing approaches either neglect dependencies, leading to overly conservative predictions, or rely solely on data-driven estimations, failing to capture the rich topological structure of the network. To address these challenges, we propose Spatio-Temporal Adaptive Conformal Inference (STACI), a novel framework that integrates network topology and temporal dynamics into the conformal prediction framework. STACI introduces a topology-aware nonconformity score that respects directional flow constraints and dynamically adjusts prediction sets to account for temporal distributional shifts. We provide theoretical guarantees on the validity of our approach and demonstrate its superior performance on both synthetic and real-world datasets. Our results show that STACI effectively balances prediction efficiency and coverage, outperforming existing conformal prediction methods for stream networks.

Flow models are effective at progressively generating realistic images, but they generally struggle to capture long-range dependencies during the generation process as they compress all the information from previous time steps into a single corrupted image. To address this limitation, we propose integrating autoregressive modeling -- known for its excellence in modeling complex, high-dimensional joint probability distributions -- into flow models. During training, at each step, we construct causally-ordered sequences by sampling multiple images from the same semantic category and applying different levels of noise, where images with higher noise levels serve as causal predecessors to those with lower noise levels. This design enables the model to learn broader category-level variations while maintaining proper causal relationships in the flow process. During generation, the model autoregressively conditions the previously generated images from earlier denoising steps, forming a contextual and coherent generation trajectory. Additionally, we design a customized hybrid linear attention mechanism tailored to our modeling approach to enhance computational efficiency. Our approach, termed ARFlow, under 400k training steps, achieves 14.08 FID scores on ImageNet at 128 * 128 without classifier-free guidance, reaching 4.34 FID with classifier-free guidance 1.5, significantly outperforming the previous flow-based model SiT's 9.17 FID. Extensive ablation studies demonstrate the effectiveness of our modeling strategy and chunk-wise attention design.

Among on-policy reinforcement learning algorithms, Proximal Policy Optimization (PPO) demonstrates is widely favored for its simplicity, numerical stability, and strong empirical performance. Standard PPO relies on surrogate objectives defined via importance ratios, which require evaluating policy likelihood that is typically straightforward when the policy is modeled as a Gaussian distribution. However, extending PPO to more expressive, high-capacity policy models such as continuous normalizing flows (CNFs), also known as flow-matching models, is challenging because likelihood evaluation along the full flow trajectory is computationally expensive and often numerically unstable. To resolve this issue, we propose PolicyFlow, a novel on-policy CNF-based reinforcement learning algorithm that integrates expressive CNF policies with PPO-style objectives without requiring likelihood evaluation along the full flow path. PolicyFlow approximates importance ratios using velocity field variations along a simple interpolation path, reducing computational overhead without compromising training stability. To further prevent mode collapse and further encourage diverse behaviors, we propose the Brownian Regularizer, an implicit policy entropy regularizer inspired by Brownian motion, which is conceptually elegant and computationally lightweight. Experiments on diverse tasks across various environments including MultiGoal, PointMaze, IsaacLab and MuJoCo Playground show that PolicyFlow achieves competitive or superior performance compared to PPO using Gaussian policies and flow-based baselines including FPO and DPPO. Notably, results on MultiGoal highlight PolicyFlow's ability to capture richer multimodal action distributions.

This paper presents two variations of a novel stochastic prediction algorithm that enables mobile robots to accurately and robustly predict the future state of complex dynamic scenes. The proposed algorithm uses a variational autoencoder to predict a range of possible future states of the environment. The algorithm takes full advantage of the motion of the robot itself, the motion of dynamic objects, and the geometry of static objects in the scene to improve prediction accuracy. Three simulated and real-world datasets collected by different robot models are used to demonstrate that the proposed algorithm is able to achieve more accurate and robust prediction performance than other prediction algorithms. Furthermore, a predictive uncertainty-aware planner is proposed to demonstrate the effectiveness of the proposed predictor in simulation and real-world navigation experiments. Implementations are open source at https://github.com/TempleRAIL/SOGMP.

Recent advances in world models have shown promise for modeling future dynamics of environmental states, enabling agents to reason and act without accessing real environments. Current methods mainly perform single-step or fixed-horizon rollouts, leaving their potential for complex task planning under-exploited. We propose Imagine-then-Plan (ITP), a unified framework for agent learning via lookahead imagination, where an agent's policy model interacts with the learned world model, yielding multi-step ``imagined'' trajectories. Since the imagination horizon may vary by tasks and stages, we introduce a novel adaptive lookahead mechanism by trading off the ultimate goal and task progress. The resulting imagined trajectories provide rich signals about future consequences, such as achieved progress and potential conflicts, which are fused with current observations, formulating a partially observable and imaginable Markov decision process to guide policy learning. We instantiate ITP with both training-free and reinforcement-trained variants. Extensive experiments across representative agent benchmarks demonstrate that ITP significantly outperforms competitive baselines. Further analyses validate that our adaptive lookahead largely enhances agents' reasoning capability, providing valuable insights into addressing broader, complex tasks.

Transformer-based models generate hidden states that are difficult to interpret. In this work, we analyze hidden states and modify them at inference, with a focus on motion forecasting. We use linear probing to analyze whether interpretable features are embedded in hidden states. Our experiments reveal high probing accuracy, indicating latent space regularities with functionally important directions. Building on this, we use the directions between hidden states with opposing features to fit control vectors. At inference, we add our control vectors to hidden states and evaluate their impact on predictions. Remarkably, such modifications preserve the feasibility of predictions. We further refine our control vectors using sparse autoencoders (SAEs). This leads to more linear changes in predictions when scaling control vectors. Our approach enables mechanistic interpretation as well as zero-shot generalization to unseen dataset characteristics with negligible computational overhead.

The growing use of language models for forecasting motivates a broader evaluation of their world-model capabilities. Such evaluation must go beyond predictive accuracy to assess hidden-state inference and intervention prediction. Real-world forecasting benchmarks offer limited access to hidden-state ground truth and controlled experiments. We introduce CivWorldBench, a benchmark built on a multi-agent strategy game engine with recorded internal states, controlled observations, and paired intervention rollouts. Its 1,900 decision points from 475 worlds support three task levels: association forecasting, belief inference, and intervention prediction. Reference predictors support attributable evaluation of capability gaps, with an expert harness and empirical ceiling estimates contextualizing scores. Stored trajectories make intermediate predictions verifiable, while agent-play experiments test whether world-model capabilities support decision-making. The main panel comprises eleven frontier language models. Composite benchmark scores correlate with real-world forecasting leaderboards on matched model panels, more closely than with a general-capability index, supporting its use as a proxy for real-world forecasting capability. Strong association forecasts do not consistently extend to belief inference or intervention prediction, and effect magnitudes remain poorly calibrated despite informative direction predictions. Process verification reveals errors missed by final-answer evaluation, and structured reasoning improves intervention prediction for the strongest model in the process study. Agent-play experiments identify useful assisted plans and motivate evaluating decision-relevant capabilities beyond association forecasting. These findings identify hidden-state inference, intermediate-state prediction, and effect calibration as priorities for world-model training.

A central hope behind process supervision is that models can expose intermediate variables that matter for their later behavior. For this to help with alignment, a scratchpad must be tied to the computation: when the model writes a state, later steps should compute from that state. To test this requirement, we use a controlled state-tracking task with a known update rule, comparing models trained to report only the final state with models trained to write intermediate states before giving the final answer. At evaluation, we edit the internal representation of one written state while leaving the visible scratchpad text fixed. Because the transition rule is known, the edit has a single correct downstream consequence. In Qwen2.5-Coder-7B, the state-writing model predicts the next phase bit implied by the edited state on 80% and 91% of held-out examples across the two task variants, while pretrained and final-answer-only controls remain near baseline. Additional controls rule out generic next-token steering and copying another continuation: the prediction depends on both the edited state and the current move. The same causal-use pattern replicates across model families. Together, these results suggest a sharper goal for scratchpad oversight: not just to make intermediate reasoning legible, but to train written states that the model uses as part of its computation.

We propose ReinFlow, a simple yet effective online reinforcement learning (RL) framework that fine-tunes a family of flow matching policies for continuous robotic control. Derived from rigorous RL theory, ReinFlow injects learnable noise into a flow policy's deterministic path, converting the flow into a discrete-time Markov Process for exact and straightforward likelihood computation. This conversion facilitates exploration and ensures training stability, enabling ReinFlow to fine-tune diverse flow model variants, including Rectified Flow [35] and Shortcut Models [19], particularly at very few or even one denoising step. We benchmark ReinFlow in representative locomotion and manipulation tasks, including long-horizon planning with visual input and sparse reward. The episode reward of Rectified Flow policies obtained an average net growth of 135.36% after fine-tuning in challenging legged locomotion tasks while saving denoising steps and 82.63% of wall time compared to state-of-the-art diffusion RL fine-tuning method DPPO [43]. The success rate of the Shortcut Model policies in state and visual manipulation tasks achieved an average net increase of 40.34% after fine-tuning with ReinFlow at four or even one denoising step, whose performance is comparable to fine-tuned DDIM policies while saving computation time for an average of 23.20%. Project webpage: https://reinflow.github.io/

Neural processes (NPs) are a class of models that learn stochastic processes directly from data and can be used for inference, sampling and conditional sampling. We introduce a new NP model based on flow matching, a generative modeling paradigm that has demonstrated strong performance on various data modalities. Following the NP training framework, the model provides amortized predictions of conditional distributions over any arbitrary points in the data. Compared to previous NP models, our model is simple to implement and can be used to sample from conditional distributions using an ODE solver, without requiring auxiliary conditioning methods. In addition, the model provides a controllable tradeoff between accuracy and running time via the number of steps in the ODE solver. We show that our model outperforms previous state-of-the-art neural process methods on various benchmarks including synthetic 1D Gaussian processes data, 2D images, and real-world weather data.

We present DEF (\ul{D}iffusion-augmented \ul{E}nsemble \ul{F}orecasting), a novel approach for generating initial condition perturbations. Modern approaches to initial condition perturbations are primarily designed for numerical weather prediction (NWP) solvers, limiting their applicability in the rapidly growing field of machine learning for weather prediction. Consequently, stochastic models in this domain are often developed on a case-by-case basis. We demonstrate that a simple conditional diffusion model can (1) generate meaningful structured perturbations, (2) be applied iteratively, and (3) utilize a guidance term to intuitivey control the level of perturbation. This method enables the transformation of any deterministic neural forecasting system into a stochastic one. With our stochastic extended systems, we show that the model accumulates less error over long-term forecasts while producing meaningful forecast distributions. We validate our approach on the 5.625^circ ERA5 reanalysis dataset, which comprises atmospheric and surface variables over a discretized global grid, spanning from the 1960s to the present. On this dataset, our method demonstrates improved predictive performance along with reasonable spread estimates.

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

Process analytics is an umbrella of data-driven techniques which includes making predictions for individual process instances or overall process models. At the instance level, various novel techniques have been recently devised, tackling next activity, remaining time, and outcome prediction. At the model level, there is a notable void. It is the ambition of this paper to fill this gap. To this end, we develop a technique to forecast the entire process model from historical event data. A forecasted model is a will-be process model representing a probable future state of the overall process. Such a forecast helps to investigate the consequences of drift and emerging bottlenecks. Our technique builds on a representation of event data as multiple time series, each capturing the evolution of a behavioural aspect of the process model, such that corresponding forecasting techniques can be applied. Our implementation demonstrates the accuracy of our technique on real-world event log data.

Diffusion Transformers have established a new state-of-the-art in image synthesis, but the high computational cost of iterative sampling severely hampers their practical deployment. While existing acceleration methods often focus on the temporal domain, they overlook the substantial spatial redundancy inherent in the generative process, where global structures emerge long before fine-grained details are formed. The uniform computational treatment of all spatial regions represents a critical inefficiency. In this paper, we introduce Just-in-Time (JiT), a novel training-free framework that addresses this challenge by acceleration in the spatial domain. JiT formulates a spatially approximated generative ordinary differential equation (ODE) that drives the full latent state evolution based on computations from a dynamically selected, sparse subset of anchor tokens. To ensure seamless transitions as new tokens are incorporated to expand the dimensions of the latent state, we propose a deterministic micro-flow, a simple and effective finite-time ODE that maintains both structural coherence and statistical correctness. Extensive experiments on the state-of-the-art FLUX.1-dev model demonstrate that JiT achieves up to a 7x speedup with nearly lossless performance, significantly outperforming existing acceleration methods and establishing a new and superior trade-off between inference speed and generation fidelity.

World modeling requires forecasting uncertain futures while preserving information useful for downstream perception. Existing visual world models often struggle to satisfy both goals: VAE-based stochastic models operate in low-dimensional reconstruction latents, which can limit perception performance, while deterministic predictors using strong pretrained features collapse multimodal futures into a single blurry mean. In this work, we propose FlowWM, a stochastic world model that performs flow matching directly within pretrained feature space (e.g., DINOv3). This is challenging because pretrained features are substantially high-dimensional, making standard diffusion recipes suboptimal. To address this, we investigate the design choices needed for feature-space flow matching and introduce a differentiable one-step projection mechanism that enables efficient training with temporal consistency and task-driven objectives. We evaluate FlowWM on two benchmarks: a synthetic benchmark for systematic evaluation of accuracy and diversity, and a real-world benchmark FuturePerception. FlowWM improves perception performance, mode coverage, and horizon robustness, validating our proposed design for stochastic world modeling in high-dimensional feature spaces.

Large language models (LLMs) increasingly act as research agents, yet their ability to track shifts in research attention is difficult to evaluate because reviews and research ideas lack uniquely verifiable outcomes. We introduce Research Attention Prediction (RAP), a rolling benchmark covering 278 AI/ML fields and 1,390 episodes. At each cut-off, an LLM agent searches a temporally restricted arXiv corpus and predicts the next six months' paper shares across eight frozen research directions. Search generally helps, but all four diagnostic models perform worse than an exact-count exponentially weighted moving average (EWMA) baseline in compositional accuracy. We identify two linked bottlenecks. Under cumulative-history access, State carry-forward outperforms direct Forecast for all four diagnostic models; frozen-evidence replay links a shared component of this reversal to Forecast-oriented policies retrieving a smaller share of recent evidence. Even with exact historical activity, future-specific updating remains limited, with only GPT-5.5 plus reopened Search slightly surpassing EWMA. Fine-tuning on realised outcomes improves Qwen3-4B's forecast Spearman correlation by 0.105 on held-out fields at later origins, with gains also on change-rich episodes.

Flow-based generative models, including diffusion models, excel at modeling continuous distributions in high-dimensional spaces. In this work, we introduce Flow Policy Optimization (FPO), a simple on-policy reinforcement learning algorithm that brings flow matching into the policy gradient framework. FPO casts policy optimization as maximizing an advantage-weighted ratio computed from the conditional flow matching loss, in a manner compatible with the popular PPO-clip framework. It sidesteps the need for exact likelihood computation while preserving the generative capabilities of flow-based models. Unlike prior approaches for diffusion-based reinforcement learning that bind training to a specific sampling method, FPO is agnostic to the choice of diffusion or flow integration at both training and inference time. We show that FPO can train diffusion-style policies from scratch in a variety of continuous control tasks. We find that flow-based models can capture multimodal action distributions and achieve higher performance than Gaussian policies, particularly in under-conditioned settings.

In this short report, we introduce joint multi-token prediction (JTP), a lightweight modification of standard next-token prediction designed to enrich hidden state representations by jointly predicting multiple future tokens. Unlike previous multi-token prediction approaches, JTP strategically employs teacher forcing of future-tokens through a carefully designed representation bottleneck, allowing the model to encode rich predictive information with minimal computational overhead during training. We show that the JTP approach achieves a short-horizon belief state representation, while popular alternatives for multi-token prediction fail to do so. We demonstrate the effectiveness of our method on the synthetic star graph navigation task from from Bachmann and Nagarajan [2024], highlighting a significant performance improvement over existing methods. This manuscript presents promising preliminary results intended to stimulate further research.

Generative flow networks (GFlowNets) are a family of algorithms that learn a generative policy to sample discrete objects x with non-negative reward R(x). Learning objectives guarantee the GFlowNet samples x from the target distribution p^*(x) propto R(x) when loss is globally minimized over all states or trajectories, but it is unclear how well they perform with practical limits on training resources. We introduce an efficient evaluation strategy to compare the learned sampling distribution to the target reward distribution. As flows can be underdetermined given training data, we clarify the importance of learned flows to generalization and matching p^*(x) in practice. We investigate how to learn better flows, and propose (i) prioritized replay training of high-reward x, (ii) relative edge flow policy parametrization, and (iii) a novel guided trajectory balance objective, and show how it can solve a substructure credit assignment problem. We substantially improve sample efficiency on biochemical design tasks.

Interactive game world models typically autoregress visual observations directly in pixel or latent space, forcing structured properties such as pose, geometry, and occlusion to be implicitly maintained by the same generative sequence. Over long horizons, errors in these latent world properties accumulate, making consistency and controllability fragile. We explicitly model the evolving world state, delegate exact geometric computation to a fixed, zero-parameter renderer, and leave the neural model to synthesize appearance. We instantiate this idea as Marionette, a world model for interactive games with articulated characters. First, a two-stage autoregressive dynamics model predicts an explicit and interpretable 276-dimensional 3D world state comprising multi-entity articulated skeletons, metric root trajectories, and rotations. Second, a zero-parameter graphics bridge converts the predicted state into pose-control videos, computing world-space geometry and occlusion in closed form. Third, a control-conditioned video-diffusion observation model synthesizes photorealistic RGB observations from the resulting structured controls. Our experiments establish two properties of Marionette. First, the predicted world state is directly controllable. Forcing a mismatched action stream changes root-aligned joint error by 31% across 48 held-out segments. Second, long-horizon behaviour is determined in the state, and can be repaired there. Left free, the two generated characters drift to 21.2 m apart (recorded sessions stay near 5 m) and a third of frames show ground penetration. Two rules imposed on the explicit state, a terrain collider and a separation cap, cut penetration by 66% and keep the pair engaged, with no change to the observation model. Routing appearance through the predicted state costs no fidelity we can detect, at an FVD of 831 against 799 for recorded pose.

Learning behavioral patterns from observational data has been a de-facto approach to motion forecasting. Yet, the current paradigm suffers from two shortcomings: brittle under distribution shifts and inefficient for knowledge transfer. In this work, we propose to address these challenges from a causal representation perspective. We first introduce a causal formalism of motion forecasting, which casts the problem as a dynamic process with three groups of latent variables, namely invariant variables, style confounders, and spurious features. We then introduce a learning framework that treats each group separately: (i) unlike the common practice mixing datasets collected from different locations, we exploit their subtle distinctions by means of an invariance loss encouraging the model to suppress spurious correlations; (ii) we devise a modular architecture that factorizes the representations of invariant mechanisms and style confounders to approximate a sparse causal graph; (iii) we introduce a style contrastive loss that not only enforces the structure of style representations but also serves as a self-supervisory signal for test-time refinement on the fly. Experiments on synthetic and real datasets show that our proposed method improves the robustness and reusability of learned motion representations, significantly outperforming prior state-of-the-art motion forecasting models for out-of-distribution generalization and low-shot transfer.

We introduce a novel generative model for video prediction based on latent flow matching, an efficient alternative to diffusion-based models. In contrast to prior work, we keep the high costs of modeling the past during training and inference at bay by conditioning only on a small random set of past frames at each integration step of the image generation process. Moreover, to enable the generation of high-resolution videos and to speed up the training, we work in the latent space of a pretrained VQGAN. Finally, we propose to approximate the initial condition of the flow ODE with the previous noisy frame. This allows to reduce the number of integration steps and hence, speed up the sampling at inference time. We call our model Random frame conditioned flow Integration for VidEo pRediction, or, in short, RIVER. We show that RIVER achieves superior or on par performance compared to prior work on common video prediction benchmarks, while requiring an order of magnitude fewer computational resources.

Modern continuous-time generative models typically induce V-shaped flows: each sample travels independently along a nearly straight trajectory from the prior to the data. Although effective, this independent movement overlooks the hierarchical structures that exist in real-world data. To address this, we introduce Y-shaped generative flows, a framework in which samples travel together along shared pathways before branching off to target-specific endpoints. Our formulation is theoretically justified, yet remains practical, requiring only minimal modifications to standard velocity-driven models. We implement this through a scalable, neural network-based training objective. Experiments on synthetic, image, and biological datasets demonstrate that our method recovers hierarchy-aware structures, improves distributional metrics over strong flow-based baselines, and reaches targets in fewer steps.

In many environments only a tiny subset of all states yield high reward. In these cases, few of the interactions with the environment provide a relevant learning signal. Hence, we may want to preferentially train on those high-reward states and the probable trajectories leading to them. To this end, we advocate for the use of a backtracking model that predicts the preceding states that terminate at a given high-reward state. We can train a model which, starting from a high value state (or one that is estimated to have high value), predicts and sample for which the (state, action)-tuples may have led to that high value state. These traces of (state, action) pairs, which we refer to as Recall Traces, sampled from this backtracking model starting from a high value state, are informative as they terminate in good states, and hence we can use these traces to improve a policy. We provide a variational interpretation for this idea and a practical algorithm in which the backtracking model samples from an approximate posterior distribution over trajectories which lead to large rewards. Our method improves the sample efficiency of both on- and off-policy RL algorithms across several environments and tasks.

Autoregressive foundation models offer state-of-the-art capabilities to simulate the market by generating the message flow of limit order books (LOBs). Yet, without understanding their inner workings, research directions are hard to narrow and practical use in real-world trading environments remains uncertain. This study therefore asks what these models actually learn about market microstructure. We find that, similarly to games where sequence models build an internal representation of the board, an 8.2M-parameter Mamba-3 state-space model trained autoregressively on the tokenized message stream of eight large-cap US equities learns an internal representation of the market and its dynamics. In particular, order-flow imbalance, a central driver of short-horizon price moves, is decodable at R^2 approx 0.59, far above controls and baselines. This representation extends to unseen stocks, suggesting that these models learn general representations rather than ticker-specific patterns. The model also generalizes across metrics beyond order-flow imbalance: results hold across traded volume and volatility. Additionally, the representation is causally steerable: pushing the state along a feature's axis shifts the model's next-message beliefs as that feature implies, monotonically in dose, consistent with the emergence of a world model.

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space. Specifically, we seek to construct a projected Markov chain that optimizes various information-theoretic criteria under cardinality constraints. These criteria include entropy rate, information-theoretic distance to factorizability, independence, and stationarity. We formulate these tasks as best subset selection problems over multivariate Markov chains and leverage the submodular (or supermodular) structure of the objective functions to develop efficient greedy-based algorithms with theoretical guarantees. We extend our analysis to k-submodular settings and introduce a generalized version of the distorted greedy algorithm, which may be of independent interest. Finally, we illustrate the theory and algorithms through extensive numerical experiments with publicly available code on multivariate Markov chains associated with the Bernoulli-Laplace and Curie-Weiss model.

Probabilistic time-series forecasting requires models that simultaneously capture structured temporal dynamics, expressive uncertainty, and efficient inference, yet existing approaches fall short of this goal: latent dynamical models impose structure but rely on restrictive generation mechanisms, while modern generative methods such as diffusion and flow matching achieve flexibility at the cost of iterative and computationally expensive sampling. We introduce the Koopman Generative Operator (KGO), a probabilistic forecasting method that conceptualizes prediction as the evolution of structured uncertainty. KGO integrates three core components: (1) Koopman Patch Embedding (KoPE) for temporally consistent latent trajectory extrapolation; (2) Koopman Flow Matching (KoFM), which enables fast, single-step generation through a closed-form matrix exponential in a Koopman latent space, bypassing iterative sampling; and (3) an Adaptive Uncertainty Gate (AUG), which provides probabilistic forecasts by adapting uncertainty per-variable and per-horizon, corresponding to a learned decomposition of aleatoric uncertainty without manual tuning. By unifying these components, KGO achieves state-of-the-art accuracy on 13/17 ProbTS benchmarks in CRPS and 16/17 in NMAE. Further, by eliminating iterative sampling, KGO delivers at least a 25times reduction in inference time compared to iterative generative models. These results position KGO as a practical and principled framework that advances the accuracy-efficiency trade-off in probabilistic time-series forecasting, combining leading accuracy on the evaluated benchmarks with fast, single-step generation.

Previsualization is an intermediate layer between ideas and production in film, games, architecture, and urban design. It lets creators iteratively refine scenes, actions, cameras, and spatial-temporal dynamics. Yet existing generative methods rely on simple prompts to jointly control all of these factors through one-shot image or video synthesis, offering weak controllability and limited support for iterative editing. Fundamentally, a world comprises multiple elements with geometry, appearance, and other attributes, together with cameras. Different frames are produced through local modifications or recombinations of this shared state, which is otherwise largely reused. Therefore, we argue that the missing component is an explicit and persistent working state. To address this, we present StateFlow, a state-centric framework for generative previsualization. Rather than generating videos in one shot, StateFlow uses an editable 3D world to organize scene structure, evolution, and cameras, while off-the-shelf video models enhance visual quality when higher fidelity is desired. This world is maintained as a persistent structured 3D state of scene elements and camera configurations, serving as the core working representation for previsualization. Built on this insight, StateFlow has three stages to construct, evolve, and access the world state. State construction lifts generated 2D content into a coherent 3D world through prior-guided, conflict-aware dual-view initialization, while State evolution translates user intent into structured state transitions while preserving world memory, avoiding full-scene regeneration for each edit. State access uses render-feedback reflection to refine camera plans into visually feasible trajectories, avoiding reliance on VLM semantics alone. Experiments show that StateFlow produces high-quality 3D worlds for video creation and game-like prototyping.

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

Building accurate decision-support tools for next-generation air traffic control requires robust trajectory prediction models. We present a flow-matching architecture trained exclusively on historical aircraft trajectories, with no route labels or chart supervision. Trained on 1.15 million Automatic Dependent Surveillance-Broadcast trajectory windows collected over the San Francisco Bay Area, the model generates aircraft trajectory distributions that closely match historical traffic, reproducing known airspace structure around San Francisco Airport such as the shape of SFO's published NIITE FOUR departure procedure. Our model is trained directly on the native, irregular ADS-B sampling interval. Trajectory prediction is cast as sequence inpainting using a block-causal Transformer that denoises future state tokens conditioned on the observed history using Conditional Flow Matching or Denoising Diffusion Probabilistic Models. We compare our architecture against constant-velocity, deterministic-Long Short Term Memory, and Conditional Variational Autoencoders baselines. At matched parameter count, CFM outperforms DDPM by 11-26% in minADE@20, and both generative objectives surpass the CVAE baseline by 31-41%. We further show that the error degrades gracefully with prediction horizon, and the architecture remains effective when retrained on temporally decimated feeds. Lastly, we sample K independent completions, yielding spatial probabilistic occupancy estimates that can serve as input to downstream conflict-risk estimation.

Motion behaviour is driven by several factors -- goals, presence and actions of neighbouring agents, social relations, physical and social norms, the environment with its variable characteristics, and further. Most factors are not directly observable and must be modelled from context. Trajectory prediction, is thus a hard problem, and has seen increasing attention from researchers in the recent years. Prediction of motion, in application, must be realistic, diverse and controllable. In spite of increasing focus on multimodal trajectory generation, most methods still lack means for explicitly controlling different modes of the data generation. Further, most endeavours invest heavily in designing special mechanisms to learn the interactions in latent space. We present Conditional Speed GAN (CSG), that allows controlled generation of diverse and socially acceptable trajectories, based on user controlled speed. During prediction, CSG forecasts future speed from latent space and conditions its generation based on it. CSG is comparable to state-of-the-art GAN methods in terms of the benchmark distance metrics, while being simple and useful for simulation and data augmentation for different contexts such as fast or slow paced environments. Additionally, we compare the effect of different aggregation mechanisms and show that a naive approach of concatenation works comparable to its attention and pooling alternatives.

Diffusion-based imitation learning improves Behavioral Cloning (BC) on multi-modal decision-making, but comes at the cost of significantly slower inference due to the recursion in the diffusion process. It urges us to design efficient policy generators while keeping the ability to generate diverse actions. To address this challenge, we propose AdaFlow, an imitation learning framework based on flow-based generative modeling. AdaFlow represents the policy with state-conditioned ordinary differential equations (ODEs), which are known as probability flows. We reveal an intriguing connection between the conditional variance of their training loss and the discretization error of the ODEs. With this insight, we propose a variance-adaptive ODE solver that can adjust its step size in the inference stage, making AdaFlow an adaptive decision-maker, offering rapid inference without sacrificing diversity. Interestingly, it automatically reduces to a one-step generator when the action distribution is uni-modal. Our comprehensive empirical evaluation shows that AdaFlow achieves high performance with fast inference speed.

Cellular automata (CA) provide a minimal formalism for investigating how simple local interactions generate rich spatiotemporal behavior in domains as diverse as traffic flow, ecology, tissue morphogenesis and crystal growth. However, automatically discovering the local update rules for a given phenomenon and using them for quantitative prediction remains challenging. Here we present AutomataGPT, a decoder-only transformer pretrained on around 1 million simulated trajectories that span 100 distinct two-dimensional binary deterministic CA rules on toroidal grids. When evaluated on previously unseen rules drawn from the same CA family, AutomataGPT attains 98.5% perfect one-step forecasts and reconstructs the governing update rule with up to 96% functional (application) accuracy and 82% exact rule-matrix match. These results demonstrate that large-scale pretraining over wider regions of rule space yields substantial generalization in both the forward (state forecasting) and inverse (rule inference) problems, without hand-crafted priors. By showing that transformer models can faithfully infer and execute CA dynamics from data alone, our work lays the groundwork for abstracting real-world dynamical phenomena into data-efficient CA surrogates, opening avenues in biology, tissue engineering, physics and AI-driven scientific discovery.

This paper is about the problem of learning a stochastic policy for generating an object (like a molecular graph) from a sequence of actions, such that the probability of generating an object is proportional to a given positive reward for that object. Whereas standard return maximization tends to converge to a single return-maximizing sequence, there are cases where we would like to sample a diverse set of high-return solutions. These arise, for example, in black-box function optimization when few rounds are possible, each with large batches of queries, where the batches should be diverse, e.g., in the design of new molecules. One can also see this as a problem of approximately converting an energy function to a generative distribution. While MCMC methods can achieve that, they are expensive and generally only perform local exploration. Instead, training a generative policy amortizes the cost of search during training and yields to fast generation. Using insights from Temporal Difference learning, we propose GFlowNet, based on a view of the generative process as a flow network, making it possible to handle the tricky case where different trajectories can yield the same final state, e.g., there are many ways to sequentially add atoms to generate some molecular graph. We cast the set of trajectories as a flow and convert the flow consistency equations into a learning objective, akin to the casting of the Bellman equations into Temporal Difference methods. We prove that any global minimum of the proposed objectives yields a policy which samples from the desired distribution, and demonstrate the improved performance and diversity of GFlowNet on a simple domain where there are many modes to the reward function, and on a molecule synthesis task.

Many scientific questions require reasoning about what was never observed: What if the conditions, interventions, or history had been different? Models can predict accurately on observed data yet fail on such what-if queries when correlated inputs are varied independently. A common remedy is to add controlled simulation data in which these factors are explicitly disentangled, but this requires access to a simulator, can be computationally expensive, and inherits the simulator's modeling assumptions. We introduce ReRoute, a framework for targeted scientific what-if prediction that combines factual data with partial mechanistic knowledge, without requiring controlled intervention data for adaptation. ReRoute fixes the queried input of a pretrained backbone to a reference value, reintroduces its variation through a known mechanistic pathway, and fine-tunes on the original factual data, while leaving downstream effects to the learned dynamics. We provide a causal identification result for this construction under explicit structural assumptions, with the core argument machine-checked in Lean. After showing that ReRoute achieves highly accurate counterfactual predictions in a controlled advection-diffusion system where exact responses are available, we turn to state-of-the-art climate emulation. On held-out coupled-climate interventions, ReRoute reduces aggregate climate error by 18.2-31.8% under severe CO_2 distribution shifts while preserving skill under standard conditions, at a small fraction of the cost of retraining on additional controlled simulations, without even accounting for the substantial expense of generating such data. Finally, on an emulator trained from historical ERA5 reanalysis, where no counterfactual reference exists, ReRoute preserves substantially more of the surface warming implied by the observed boundary conditions under a fixed-CO_2 counterfactual.

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is computationally and statistically challenging due to the large number of latent variables in the model and the strong temporal dependencies between them. In this paper, we propose a new method for inference in Bayesian GPSSMs, which overcomes the drawbacks of previous approaches, namely over-simplified assumptions, and high computational requirements. Our method is based on free-form variational inference via stochastic gradient Hamiltonian Monte Carlo within the inducing-variable formalism. Furthermore, by exploiting our proposed variational distribution, we provide a collapsed extension of our method where the inducing variables are marginalized analytically. We also showcase results when combining our framework with particle MCMC methods. We show that, on six real-world datasets, our approach can learn transition dynamics and latent states more accurately than competing methods.

Deep learning has emerged as a promising paradigm for spatio-temporal modeling of fluid dynamics. However, existing approaches often suffer from limited generalization to unseen flow conditions and typically require retraining when applied to new scenarios. In this paper, we present LLM4Fluid, a spatio-temporal prediction framework that leverages Large Language Models (LLMs) as generalizable neural solvers for fluid dynamics. The framework first compresses high-dimensional flow fields into a compact latent space via reduced-order modeling enhanced with a physics-informed disentanglement mechanism, effectively mitigating spatial feature entanglement while preserving essential flow structures. A pretrained LLM then serves as a temporal processor, autoregressively predicting the dynamics of physical sequences with time series prompts. To bridge the modality gap between prompts and physical sequences, which can otherwise degrade prediction accuracy, we propose a dedicated modality alignment strategy that resolves representational mismatch and stabilizes long-term prediction. Extensive experiments across diverse flow scenarios demonstrate that LLM4Fluid functions as a robust and generalizable neural solver without retraining, achieving state-of-the-art accuracy while exhibiting powerful zero-shot and in-context learning capabilities. Code and datasets are publicly available at https://github.com/qisongxiao/LLM4Fluid.

Living systems face both environmental complexity and limited access to free-energy resources. Survival under these conditions requires a control system that can activate, or deploy, available perception and action resources in a context specific way. We show here that when systems are described as executing active inference driven by the free-energy principle (and hence can be considered Bayesian prediction-error minimizers), their control flow systems can always be represented as tensor networks (TNs). We show how TNs as control systems can be implmented within the general framework of quantum topological neural networks, and discuss the implications of these results for modeling biological systems at multiple scales.

Accurately anticipating how complex, diverse scenes will evolve requires models that represent uncertainty, simulate along extended interaction chains, and efficiently explore many plausible futures. Yet most existing approaches rely on dense video or latent-space prediction, expending substantial capacity on dense appearance rather than on the underlying sparse trajectories of points in the scene. This makes large-scale exploration of future hypotheses costly and limits performance when long-horizon, multi-modal motion is essential. We address this by formulating the prediction of open-set future scene dynamics as step-wise inference over sparse point trajectories. Our autoregressive diffusion model advances these trajectories through short, locally predictable transitions, explicitly modeling the growth of uncertainty over time. This dynamics-centric representation enables fast rollout of thousands of diverse futures from a single image, optionally guided by initial constraints on motion, while maintaining physical plausibility and long-range coherence. We further introduce OWM, a benchmark for open-set motion prediction based on diverse in-the-wild videos, to evaluate accuracy and variability of predicted trajectory distributions under real-world uncertainty. Our method matches or surpasses dense simulators in predictive accuracy while achieving orders-of-magnitude higher sampling speed, making open-set future prediction both scalable and practical. Project page: http://compvis.github.io/myriad.

Existing approaches to controllable generation typically rely on fine-tuning, auxiliary networks, or test-time search. We show that flow matching admits a different control interface: adaptation through examples. For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself. This yields a simple principle for controllable generation: steer a pretrained model by changing the reference set it follows. We instantiate this idea in two forms. Reference-Mean Guidance is training-free: it computes a closed-form endpoint-mean correction from a reference bank and applies it to a frozen FLUX.2-klein (4B) model, enabling control of color, identity, style, and structure while keeping the prompt, seed, and weights fixed. Semi-Parametric Guidance amortizes the same idea through an explicit mean anchor and learned residual refiner, matching unconditional DiT-B/4 quality on AFHQv2 while allowing the reference set to be swapped at inference time. These results point to a broader direction: generative models that adapt through data, not parameter updates.

Long-context training is increasingly important for large language models, and linear attention and state space models have become popular for improving long-context efficiency. However, efficiently parallelizing long-sequence training for recurrent and hybrid models remains challenging. We present StateFlow, a sequence pipeline parallelism system for models with linear recurrence. StateFlow partitions each sequence into chunks and schedules their execution while propagating boundary states and gradients across chunks, thereby reducing activation lifetimes and improving training throughput. StateFlow further uses profile-guided nonuniform chunking to balance recurrence and softmax attention computation in hybrid models, and overlaps state transitions that expose limited parallelism with surrounding computation. Applying StateFlow to models with up to 32B parameters and 256K context length, we achieve up to \(2.22\times\) throughput improvements and \(2.45\times\) memory reduction compared to conventional pipeline parallelism, enabling otherwise infeasible configurations.

Aligning generative flow models on continuous spaces via online reinforcement learning is constrained by intractable trajectory likelihoods. Existing density-approximated policy gradient methods rely on stochastic SDE samplers to construct tractable transition kernels, which introduce training-inference inconsistencies and necessitates Classifier-Free Guidance (CFG). While implicit frameworks such as DiffusionNFT directly optimize forward-process velocity fields, its heuristic fixed-magnitude corrections prevent optimization strength from relative intra-group quality. We propose Flow Advantage-Weighted Rectification (FlowAWR), a paradigm that recasts continuous generative policy optimization as supervised regression toward a theoretically optimal velocity field. Starting from the optimal policy of a KL-constrained reward maximization, FlowAWR derives the optimal velocity field that admits a magnitude-aware, advantage-weighted rectification form, yielding SDE-free optimization and CFG-free generation. In comparative evaluations on SD3.5-Medium, FlowAWR achieves improved alignment performance alongside a 2times to 5times convergence acceleration over DiffusionNFT (e.g., reaching a 24.12 PickScore in 1.2k steps, versus 23.82 in 2.0k steps for DiffusionNFT and 23.50 in >4k steps for FlowGRPO). Under multi-reward constraints, FlowAWR sustains generation quality, satisfying structural rules while maintaining stable out-of-domain performance.

Predicting the motion of multiple traffic participants has always been one of the most challenging tasks in autonomous driving. The recently proposed occupancy flow field prediction method has shown to be a more effective and scalable representation compared to general trajectory prediction methods. However, in complex multi-agent traffic scenarios, it remains difficult to model the interactions among various factors and the dependencies among prediction outputs at different time steps. In view of this, we propose a transformer-based hierarchical feature guided network (HGNET), which can efficiently extract features of agents and map information from visual and vectorized inputs, modeling multimodal interaction relationships. Second, we design the Feature-Guided Attention (FGAT) module to leverage the potential guiding effects between different prediction targets, thereby improving prediction accuracy. Additionally, to enhance the temporal consistency and causal relationships of the predictions, we propose a Time Series Memory framework to learn the conditional distribution models of the prediction outputs at future time steps from multivariate time series. The results demonstrate that our model exhibits competitive performance, which ranks 3rd in the 2024 Waymo Occupancy and Flow Prediction Challenge.