Daily Papers

While few-step generative models have enabled powerful image and video generation at significantly lower cost, generic reinforcement learning (RL) paradigms for few-step models remain an unsolved problem. Existing RL approaches for few-step diffusion models strongly rely on back-propagating through differentiable reward models, thereby excluding the majority of important real-world reward signals, e.g., non-differentiable rewards such as humans' binary likeness, object counts, etc. To properly incorporate non-differentiable rewards to improve few-step generative models, we introduce TDM-R1, a novel reinforcement learning paradigm built upon a leading few-step model, Trajectory Distribution Matching (TDM). TDM-R1 decouples the learning process into surrogate reward learning and generator learning. Furthermore, we developed practical methods to obtain per-step reward signals along the deterministic generation trajectory of TDM, resulting in a unified RL post-training method that significantly improves few-step models' ability with generic rewards. We conduct extensive experiments ranging from text-rendering, visual quality, and preference alignment. All results demonstrate that TDM-R1 is a powerful reinforcement learning paradigm for few-step text-to-image models, achieving state-of-the-art reinforcement learning performances on both in-domain and out-of-domain metrics. Furthermore, TDM-R1 also scales effectively to the recent strong Z-Image model, consistently outperforming both its 100-NFE and few-step variants with only 4 NFEs. Project page: https://github.com/Luo-Yihong/TDM-R1

Score distillation sampling (SDS) and its variants have greatly boosted the development of text-to-3D generation, but are vulnerable to geometry collapse and poor textures yet. To solve this issue, we first deeply analyze the SDS and find that its distillation sampling process indeed corresponds to the trajectory sampling of a stochastic differential equation (SDE): SDS samples along an SDE trajectory to yield a less noisy sample which then serves as a guidance to optimize a 3D model. However, the randomness in SDE sampling often leads to a diverse and unpredictable sample which is not always less noisy, and thus is not a consistently correct guidance, explaining the vulnerability of SDS. Since for any SDE, there always exists an ordinary differential equation (ODE) whose trajectory sampling can deterministically and consistently converge to the desired target point as the SDE, we propose a novel and effective "Consistent3D" method that explores the ODE deterministic sampling prior for text-to-3D generation. Specifically, at each training iteration, given a rendered image by a 3D model, we first estimate its desired 3D score function by a pre-trained 2D diffusion model, and build an ODE for trajectory sampling. Next, we design a consistency distillation sampling loss which samples along the ODE trajectory to generate two adjacent samples and uses the less noisy sample to guide another more noisy one for distilling the deterministic prior into the 3D model. Experimental results show the efficacy of our Consistent3D in generating high-fidelity and diverse 3D objects and large-scale scenes, as shown in Fig. 1. The codes are available at https://github.com/sail-sg/Consistent3D.

We present TrajectoryCrafter, a novel approach to redirect camera trajectories for monocular videos. By disentangling deterministic view transformations from stochastic content generation, our method achieves precise control over user-specified camera trajectories. We propose a novel dual-stream conditional video diffusion model that concurrently integrates point cloud renders and source videos as conditions, ensuring accurate view transformations and coherent 4D content generation. Instead of leveraging scarce multi-view videos, we curate a hybrid training dataset combining web-scale monocular videos with static multi-view datasets, by our innovative double-reprojection strategy, significantly fostering robust generalization across diverse scenes. Extensive evaluations on multi-view and large-scale monocular videos demonstrate the superior performance of our method.

Score Distillation Sampling (SDS) and its variants have been widely used for text-to-3D generation by distilling 2D image diffusion priors. However, the standard SDS objective is prone to severe mode collapse, frequently yielding over-smoothed and over-saturated results. Although recent advancements, such as Score Distillation via Inversion (SDI), mitigate these artifacts and produce visually sharper models, they ultimately fail to faithfully capture the full target distribution. In this work, we show that the bottleneck limiting the sampling capacity of SDI stems from its reliance on the posterior mean estimator, which is mathematically equivalent to a single-step Euler approximation of the deterministic reverse DDIM trajectory. To address this, we propose a naturally motivated extension termed Probability-Flow Distillation (PFD). We establish that PFD corresponds exactly to a Wasserstein gradient flow, thereby inducing principled distribution-matching dynamics. Finally, we show that PFD can synthesize 3D assets with fine-grained, high-fidelity details and achieve improved quality compared to existing methods.

Recent advances in text-to-image diffusion models enable photorealistic image generation, but they also risk producing malicious content, such as NSFW images. To mitigate risk, concept erasure methods are studied to facilitate the model to unlearn specific concepts. However, current studies struggle to fully erase malicious concepts implicitly embedded in prompts (e.g., metaphorical expressions or adversarial prompts) while preserving the model's normal generation capability. To address this challenge, our study proposes TRCE, using a two-stage concept erasure strategy to achieve an effective trade-off between reliable erasure and knowledge preservation. Firstly, TRCE starts by erasing the malicious semantics implicitly embedded in textual prompts. By identifying a critical mapping objective(i.e., the [EoT] embedding), we optimize the cross-attention layers to map malicious prompts to contextually similar prompts but with safe concepts. This step prevents the model from being overly influenced by malicious semantics during the denoising process. Following this, considering the deterministic properties of the sampling trajectory of the diffusion model, TRCE further steers the early denoising prediction toward the safe direction and away from the unsafe one through contrastive learning, thus further avoiding the generation of malicious content. Finally, we conduct comprehensive evaluations of TRCE on multiple malicious concept erasure benchmarks, and the results demonstrate its effectiveness in erasing malicious concepts while better preserving the model's original generation ability. The code is available at: http://github.com/ddgoodgood/TRCE. CAUTION: This paper includes model-generated content that may contain offensive material.

Developing multi-turn interactive tool-use agents is challenging because real-world user needs are often complex and ambiguous, yet agents must execute deterministic actions to satisfy them. To address this gap, we introduce CoVe (Constraint-Verification), a post-training data synthesis framework designed for training interactive tool-use agents while ensuring both data complexity and correctness. CoVe begins by defining explicit task constraints, which serve a dual role: they guide the generation of complex trajectories and act as deterministic verifiers for assessing trajectory quality. This enables the creation of high-quality training trajectories for supervised fine-tuning (SFT) and the derivation of accurate reward signals for reinforcement learning (RL). Our evaluation on the challenging τ^2-bench benchmark demonstrates the effectiveness of the framework. Notably, our compact CoVe-4B model achieves success rates of 43.0\% and 59.4\% in the Airline and Retail domains, respectively; its overall performance significantly outperforms strong baselines of similar scale and remains competitive with models up to 17times its size. These results indicate that CoVe provides an effective and efficient pathway for synthesizing training data for state-of-the-art interactive tool-use agents. To support future research, we open-source our code, trained model, and the full set of 12K high-quality trajectories used for training.

The recent advancements in text-to-3D generation mark a significant milestone in generative models, unlocking new possibilities for creating imaginative 3D assets across various real-world scenarios. While recent advancements in text-to-3D generation have shown promise, they often fall short in rendering detailed and high-quality 3D models. This problem is especially prevalent as many methods base themselves on Score Distillation Sampling (SDS). This paper identifies a notable deficiency in SDS, that it brings inconsistent and low-quality updating direction for the 3D model, causing the over-smoothing effect. To address this, we propose a novel approach called Interval Score Matching (ISM). ISM employs deterministic diffusing trajectories and utilizes interval-based score matching to counteract over-smoothing. Furthermore, we incorporate 3D Gaussian Splatting into our text-to-3D generation pipeline. Extensive experiments show that our model largely outperforms the state-of-the-art in quality and training efficiency.

Modeling Lagrangian turbulence remains a fundamental challenge due to its multiscale, intermittent, and non-Gaussian nature. Recent advances in data-driven diffusion models have enabled the generation of realistic Lagrangian velocity trajectories that accurately reproduce statistical properties across scales and capture rare extreme events. This study investigates three key aspects of diffusion-based modeling for Lagrangian turbulence. First, we assess architectural robustness by comparing a U-Net backbone with a transformer-based alternative, finding strong consistency in generated trajectories, with only minor discrepancies at small scales. Second, leveraging a deterministic variant of diffusion model formulation, namely the deterministic denoising diffusion implicit model (DDIM), we identify structured features in the initial latent noise that align consistently with extreme acceleration events. Third, we explore accelerated generation by reducing the number of diffusion steps, and find that DDIM enables substantial speedups with minimal loss of statistical fidelity. These findings highlight the robustness of diffusion models and their potential for interpretable, scalable modeling of complex turbulent systems.

Extending the generation horizon of video diffusion models to long sequences remains a long-standing and important challenge. Existing training-free approaches fall into two categories: extensions of bidirectional models, which are tightly coupled to specific architectures and suffer from quality degradation over long horizons, and autoregressive models, which accumulate drift errors due to exposure bias and tend to produce repetitive motion patterns. To address these issues, we propose a novel but simple inference-time approach for long video generation that is architecture-agnostic and requires no additional training. Our method generates long videos via overlapping sliding windows, where predicted clean samples from adjacent windows are blended via Tweedie matching to enforce both manifold constraint and temporal consistency across overlap regions. Stochastic early-phase sampling then synchronizes per-window trajectories by injecting fresh noise after each Tweedie matching correction in the high-noise phase, before transitioning to deterministic ODE sampling to preserve fine-grained visual fidelity. Applied to various video generation models, our method generates videos several times longer than the native window length while outperforming both training-free and autoregressive baselines in temporal consistency and visual quality, and further extends to audio-video joint generation and text-to-3DGS without any fine-tuning.

Retrieval-Augmented Generation (RAG) has become a standard approach for knowledge-intensive question answering, but existing systems remain brittle on multi-hop questions, where solving the task requires chaining multiple retrieval and reasoning steps. Key challenges are that current methods represent reasoning through free-form natural language, where intermediate states are implicit, retrieval queries can drift from intended entities, and errors are detected by the same model that produces them making self-reflection an unreliable, ungrounded signal. We observe that multi-hop question answering is a typical form of step-by-step computation, and that this structured process aligns closely with how code-specialized language models are trained to operate. Motivated by this, we introduce \pyrag, a framework that reformulates multi-hop RAG as program synthesis and execution. Instead of free-form reasoning trajectories, \pyrag represents the reasoning process as an executable Python program over retrieval and QA tools, exposing intermediate states as variables, producing deterministic feedback through execution, and yielding an inspectable trace of the entire reasoning process. This formulation further enables compiler-grounded self-repair and execution-driven adaptive retrieval without any additional training. Experiments on five QA benchmarks (PopQA, HotpotQA, 2WikiMultihopQA, MuSiQue, and Bamboogle) show that \pyrag consistently outperforms strong baselines under both training-free and RL-trained settings, with especially large gains on compositional multi-hop datasets. Our code, data and models are publicly available at https://github.com/GasolSun36/PyRAG.

Recent work in Video Frame Interpolation (VFI) tries to formulate VFI as a diffusion-based conditional image generation problem, synthesizing the intermediate frame given a random noise and neighboring frames. Due to the relatively high resolution of videos, Latent Diffusion Models (LDMs) are employed as the conditional generation model, where the autoencoder compresses images into latent representations for diffusion and then reconstructs images from these latent representations. Such a formulation poses a crucial challenge: VFI expects that the output is deterministically equal to the ground truth intermediate frame, but LDMs randomly generate a diverse set of different images when the model runs multiple times. The reason for the diverse generation is that the cumulative variance (variance accumulated at each step of generation) of generated latent representations in LDMs is large. This makes the sampling trajectory random, resulting in diverse rather than deterministic generations. To address this problem, we propose our unique solution: Frame Interpolation with Consecutive Brownian Bridge Diffusion. Specifically, we propose consecutive Brownian Bridge diffusion that takes a deterministic initial value as input, resulting in a much smaller cumulative variance of generated latent representations. Our experiments suggest that our method can improve together with the improvement of the autoencoder and achieve state-of-the-art performance in VFI, leaving strong potential for further enhancement.

Future Frame Synthesis (FFS), the task of generating subsequent video frames from context, represents a core challenge in machine intelligence and a cornerstone for developing predictive world models. This survey provides a comprehensive analysis of the FFS landscape, charting its critical evolution from deterministic algorithms focused on pixel-level accuracy to modern generative paradigms that prioritize semantic coherence and dynamic plausibility. We introduce a novel taxonomy organized by algorithmic stochasticity, which not only categorizes existing methods but also reveals the fundamental drivers--advances in architectures, datasets, and computational scale--behind this paradigm shift. Critically, our analysis identifies a bifurcation in the field's trajectory: one path toward efficient, real-time prediction, and another toward large-scale, generative world simulation. By pinpointing key challenges and proposing concrete research questions for both frontiers, this survey serves as an essential guide for researchers aiming to advance the frontiers of visual dynamic modeling.

Reasoning about human motion is an important prerequisite to safe and socially-aware robotic navigation. As a result, multi-agent behavior prediction has become a core component of modern human-robot interactive systems, such as self-driving cars. While there exist many methods for trajectory forecasting, most do not enforce dynamic constraints and do not account for environmental information (e.g., maps). Towards this end, we present Trajectron++, a modular, graph-structured recurrent model that forecasts the trajectories of a general number of diverse agents while incorporating agent dynamics and heterogeneous data (e.g., semantic maps). Trajectron++ is designed to be tightly integrated with robotic planning and control frameworks; for example, it can produce predictions that are optionally conditioned on ego-agent motion plans. We demonstrate its performance on several challenging real-world trajectory forecasting datasets, outperforming a wide array of state-of-the-art deterministic and generative methods.

Deterministic inference is a comforting ideal in classical software: the same program on the same input should always produce the same output. As large language models move into real-world deployment, this ideal has been imported wholesale into inference stacks. Recent work from the Thinking Machines Lab has presented a detailed analysis of nondeterminism in LLM inference, showing how batch-invariant kernels and deterministic attention can enforce bitwise-identical outputs, positioning deterministic inference as a prerequisite for reproducibility and enterprise reliability. In this paper, we take the opposite stance. We argue that, for LLMs, deterministic inference kills. It kills the ability to model uncertainty, suppresses emergent abilities, collapses reasoning into a single brittle path, and weakens safety alignment by hiding tail risks. LLMs implement conditional distributions over outputs, not fixed functions. Collapsing these distributions to a single canonical completion may appear reassuring, but it systematically conceals properties central to artificial cognition. We instead advocate Stochastic CHAOS, treating distributional variability as a signal to be measured and controlled. Empirically, we show that deterministic inference is systematically misleading. Single-sample deterministic evaluation underestimates both capability and fragility, masking failure probability under paraphrases and noise. Phase-like transitions associated with emergent abilities disappear under greedy decoding. Multi-path reasoning degrades when forced onto deterministic backbones, reducing accuracy and diagnostic insight. Finally, deterministic evaluation underestimates safety risk by hiding rare but dangerous behaviors that appear only under multi-sample evaluation.

Current diffusion-based super-resolution (SR) approaches achieve commendable performance at the cost of high inference overhead. Therefore, distillation techniques are utilized to accelerate the multi-step teacher model into one-step student model. Nevertheless, these methods significantly raise training costs and constrain the performance of the student model by the teacher model. To overcome these tough challenges, we propose Consistency Trajectory Matching for Super-Resolution (CTMSR), a distillation-free strategy that is able to generate photo-realistic SR results in one step. Concretely, we first formulate a Probability Flow Ordinary Differential Equation (PF-ODE) trajectory to establish a deterministic mapping from low-resolution (LR) images with noise to high-resolution (HR) images. Then we apply the Consistency Training (CT) strategy to directly learn the mapping in one step, eliminating the necessity of pre-trained diffusion model. To further enhance the performance and better leverage the ground-truth during the training process, we aim to align the distribution of SR results more closely with that of the natural images. To this end, we propose to minimize the discrepancy between their respective PF-ODE trajectories from the LR image distribution by our meticulously designed Distribution Trajectory Matching (DTM) loss, resulting in improved realism of our recovered HR images. Comprehensive experimental results demonstrate that the proposed methods can attain comparable or even superior capabilities on both synthetic and real datasets while maintaining minimal inference latency.

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the interpolation argument. Unfortunately, these techniques give vacuous bounds when applied to deterministic samplers. We give a new operational interpretation for deterministic sampling by showing that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs gradient ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current iterate. This perspective allows us to extend denoising diffusion implicit models to general, non-linear forward processes. We then develop the first polynomial convergence bounds for these samplers under mild conditions on the data distribution.

How should future neural reasoning systems implement extended computation? Recursive Reasoning Models (RRMs) offer a promising alternative to autoregressive sequence extension by performing iterative latent-state refinement with shared transition functions. Yet existing RRMs are largely deterministic, following a single latent trajectory and converging to a single prediction. We introduce Generative Recursive reAsoning Models (GRAM), a framework that turns recursive latent reasoning into probabilistic multi-trajectory computation. GRAM models reasoning as a stochastic latent trajectory, enabling multiple hypotheses, alternative solution strategies, and inference-time scaling through both recursive depth and parallel trajectory sampling. This yields a latent-variable generative model supporting conditional reasoning via p_θ(y mid x) and, with fixed or absent inputs, unconditional generation via p_θ(x). Trained with amortized variational inference, GRAM improves over deterministic recurrent and recursive baselines on structured reasoning and multi-solution constraint satisfaction tasks, while demonstrating an unconditional generation capability. https://ahn-ml.github.io/gram-website

Modeling open-play soccer tactics is a formidable challenge due to the stochastic, multi-agent nature of the game. Existing computational approaches typically produce single, deterministic trajectory forecasts or focus on highly structured set-pieces, fundamentally failing to capture the inherent variance and branching possibilities of real-world match evolution. Here, we introduce GenTac, a diffusion-based generative framework that conceptualizes soccer tactics as a stochastic process over continuous multi-player trajectories and discrete semantic events. By learning the underlying distribution of player movements from historical tracking data, GenTac samples diverse, plausible, long-horizon future trajectories. The framework supports rich contextual conditioning, including opponent behavior, specific team or league playing styles, and strategic objectives, while grounding continuous spatial dynamics into a 15-class tactical event space. Extensive evaluations on our proposed benchmark, TacBench, demonstrate four key capabilities: (1) GenTac achieves high geometric accuracy while strictly preserving the collective structural consistency of the team; (2) it accurately simulates stylistic nuances, distinguishing between specific teams (e.g., Auckland FC) and leagues (e.g., A-League versus German leagues); (3) it enables controllable counterfactual simulations, demonstrably altering spatial control and expected threat metrics based on offensive or defensive guidance; and (4) it reliably anticipates future tactical outcomes directly from generated rollouts. Finally, we demonstrate that GenTac can be successfully trained to generalize to other dynamic team sports, including basketball, American football, and ice hockey.

Pixel-space generative models are often more difficult to train and generally underperform compared to their latent-space counterparts, leaving a persistent performance and efficiency gap. In this paper, we introduce a novel two-stage training framework that closes this gap for pixel-space diffusion and consistency models. In the first stage, we pre-train encoders to capture meaningful semantics from clean images while aligning them with points along the same deterministic sampling trajectory, which evolves points from the prior to the data distribution. In the second stage, we integrate the encoder with a randomly initialized decoder and fine-tune the complete model end-to-end for both diffusion and consistency models. Our training framework demonstrates strong empirical performance on ImageNet dataset. Specifically, our diffusion model reaches an FID of 2.04 on ImageNet-256 and 2.35 on ImageNet-512 with 75 number of function evaluations (NFE), surpassing prior pixel-space methods by a large margin in both generation quality and efficiency while rivaling leading VAE-based models at comparable training cost. Furthermore, on ImageNet-256, our consistency model achieves an impressive FID of 8.82 in a single sampling step, significantly surpassing its latent-space counterpart. To the best of our knowledge, this marks the first successful training of a consistency model directly on high-resolution images without relying on pre-trained VAEs or diffusion models.

We present a Learning from Demonstration method for teaching robots to perform search strategies imitated from humans in scenarios where alignment tasks fail due to position uncertainty. The method utilizes human demonstrations to learn both a state invariant dynamics model and an exploration distribution that captures the search area covered by the demonstrator. We present two alternative algorithms for computing a search trajectory from the exploration distribution, one based on sampling and another based on deterministic ergodic control. We augment the search trajectory with forces learnt through the dynamics model to enable searching both in force and position domains. An impedance controller with superposed forces is used for reproducing the learnt strategy. We experimentally evaluate the method on a KUKA LWR4+ performing a 2D peg-in-hole and a 3D electricity socket task. Results show that the proposed method can, with only few human demonstrations, learn to complete the search task.

In LLM inference, the same prompt may yield different outputs across different runs. At the system level, this non-determinism arises from floating-point non-associativity combined with dynamic batching and GPU kernels whose reduction orders vary with batch size. A straightforward way to eliminate non-determinism is to disable dynamic batching during inference, but doing so severely degrades throughput. Another approach is to make kernels batch-invariant; however, this tightly couples determinism to kernel design, requiring new implementations. This coupling also imposes fixed runtime overheads, regardless of how much of the workload actually requires determinism. Inspired by ideas from speculative decoding, we present LLM-42, a scheduling-based approach to enable determinism in LLM inference. Our key observation is that if a sequence is in a consistent state, the next emitted token is likely to be consistent even with dynamic batching. Moreover, most GPU kernels use shape-consistent reductions. Leveraging these insights, LLM-42 decodes tokens using a non-deterministic fast path and enforces determinism via a lightweight verify-rollback loop. The verifier replays candidate tokens under a fixed-shape reduction schedule, commits those that are guaranteed to be consistent across runs, and rolls back those violating determinism. LLM-42 mostly re-uses existing kernels unchanged and incurs overhead only in proportion to the traffic that requires determinism.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

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.

We present a novel approach for generating motion primitives for kinodynamic motion planning using diffusion models. The motions generated by our approach are adapted to each problem instance by utilizing problem-specific parameters, allowing for finding solutions faster and of better quality. The diffusion models used in our approach are trained on randomly cut solution trajectories. These trajectories are created by solving randomly generated problem instances with a kinodynamic motion planner. Experimental results show significant improvements up to 30 percent in both computation time and solution quality across varying robot dynamics such as second-order unicycle or car with trailer.

This paper presents a continuous-time optimal control framework for the generation of reference trajectories in driving scenarios with uncertainty. A previous work presented a discrete-time stochastic generator for autonomous vehicles; those results are extended to continuous time to ensure the robustness of the generator in a real-time setting. We show that the stochastic model in continuous time can capture the uncertainty of information by producing better results, limiting the risk of violating the problem's constraints compared to a discrete approach. Dynamic solvers provide faster computation and the continuous-time model is more robust to a wider variety of driving scenarios than the discrete-time model, as it can handle further time horizons, which allows trajectory planning outside the framework of urban driving scenarios.

Generative sequence models are often trained to plan motion in physical domains, from robotics to mechanical simulations. When constructing a dataset to train such a model, engineers may curate demonstrations to specify how trajectories should be distributed over a physical quantity like travel distance or mechanical energy. For example, a roboticist building a maze navigation agent might choose demonstrations whose travel distances cover a fixed range uniformly, hoping to constrain the agent's expected power usage. We find that standard deep learning can violate this intent: each generated trajectory can seem plausible on its own, but the aggregate distribution over the physical quantity is wrong. We call this failure physical misgeneralization, and develop an account of its mechanism. Using controlled synthetic tasks, we show that physical misgeneralization arises when local errors typical of the model class propagate through the physical measurement to shift the recovered distribution. We estimate these errors with a data deviation kernel, and we use it to predict which physical quantities gain or lose mass in both our synthetic and more applied maze navigation and double-pendulum motion tasks. Finally, our mechanistic interpretation helps identify which mitigation strategies are structurally promising, and we use it to propose a kernel-informed intervention.

Masked Diffusion Models (MDMs) offer flexible, non-autoregressive generation, but this freedom introduces a challenge: final output quality is highly sensitive to the decoding order. We are the first to formalize this issue, attributing the variability in output quality to the cumulative predictive uncertainty along a generative path. To quantify this uncertainty, we introduce Denoising Entropy, a computable metric that serves as an internal signal for evaluating generative process. Leveraging this metric, we propose two algorithms designed to optimize the decoding path: a post-hoc selection method and a real-time guidance strategy. Experiments demonstrate that our entropy-guided methods significantly improve generation quality, consistently boosting accuracy on challenging reasoning, planning, and code benchmarks. Our work establishes Denoising Entropy as a principled tool for understanding and controlling generation, effectively turning the uncertainty in MDMs from a liability into a key advantage for discovering high-quality solutions.

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.

We present a novel data-driven simulation environment for modeling traffic in metropolitan street intersections. Using real-world tracking data collected over an extended period of time, we train trajectory forecasting models to learn agent interactions and environmental constraints that are difficult to capture conventionally. Trajectories of new agents are first coarsely generated by sampling from the spatial and temporal generative distributions, then refined using state-of-the-art trajectory forecasting models. The simulation can run either autonomously, or under explicit human control conditioned on the generative distributions. We present the experiments for a variety of model configurations. Under an iterative prediction scheme, the way-point-supervised TrajNet++ model obtained 0.36 Final Displacement Error (FDE) in 20 FPS on an NVIDIA A100 GPU.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Effective trajectory stitching for long-horizon planning is a significant challenge in robotic decision-making. While diffusion models have shown promise in planning, they are limited to solving tasks similar to those seen in their training data. We propose CompDiffuser, a novel generative approach that can solve new tasks by learning to compositionally stitch together shorter trajectory chunks from previously seen tasks. Our key insight is modeling the trajectory distribution by subdividing it into overlapping chunks and learning their conditional relationships through a single bidirectional diffusion model. This allows information to propagate between segments during generation, ensuring physically consistent connections. We conduct experiments on benchmark tasks of various difficulties, covering different environment sizes, agent state dimension, trajectory types, training data quality, and show that CompDiffuser significantly outperforms existing methods.

Generative models have gained significant traction in offline reinforcement learning (RL) due to their ability to model complex trajectory distributions. However, existing generation-based approaches still struggle with long-horizon tasks characterized by sparse rewards. Some hierarchical generation methods have been developed to mitigate this issue by decomposing the original problem into shorter-horizon subproblems using one policy and generating detailed actions with another. While effective, these methods often overlook the multi-scale temporal structure inherent in trajectories, resulting in suboptimal performance. To overcome these limitations, we propose MAGE, a Multi-scale Autoregressive GEneration-based offline RL method. MAGE incorporates a condition-guided multi-scale autoencoder to learn hierarchical trajectory representations, along with a multi-scale transformer that autoregressively generates trajectory representations from coarse to fine temporal scales. MAGE effectively captures temporal dependencies of trajectories at multiple resolutions. Additionally, a condition-guided decoder is employed to exert precise control over short-term behaviors. Extensive experiments on five offline RL benchmarks against fifteen baseline algorithms show that MAGE successfully integrates multi-scale trajectory modeling with conditional guidance, generating coherent and controllable trajectories in long-horizon sparse-reward settings.

Diffusion and flow-based generative models produce strong images, yet their controllability remains largely endpoint-centric: users specify conditions and receive final outputs, while the intermediate generative dynamics remain hidden. Recent methods have begun to exploit generation order and process decomposition to improve sample quality, but still treat intermediate states as internal computation rather than objects for interaction. We propose Trajectory Forcing (TF), a trajectory-centric framework that makes the generation path explicit, semantic, and editable. TF organizes synthesis as a sequence of semantically structured stages, progressing from global layout to object-, part-, and detail-level representations. Each stage produces a decodable latent state that can be inspected, evaluated, and locally edited before the next stage begins. To instantiate this path, we derive coarse-to-fine teacher hierarchies by clustering pretrained visual representations such as DINOv2, and train a hierarchy-conditioned one-step flow-matching model at each level. We further introduce trajectory-aware metrics that measure structural consistency and local controllability beyond endpoint quality metrics such as FID. Experiments show that TF achieves competitive sample quality while exposing coherent intermediate states and supporting localized edits across semantic levels. By shifting the focus from final images to the generative path itself, TF opens a route toward controllable, trajectory-aware image synthesis.

We introduce a learning-guided motion planning framework that generates seed trajectories using a diffusion model for trajectory optimization. Given a workspace, our method approximates the configuration space (C-space) obstacles through an environment representation consisting of a sparse set of task-related key configurations, which is then used as a conditioning input to the diffusion model. The diffusion model integrates regularization terms that encourage smooth, collision-free trajectories during training, and trajectory optimization refines the generated seed trajectories to correct any colliding segments. Our experimental results demonstrate that high-quality trajectory priors, learned through our C-space-grounded diffusion model, enable the efficient generation of collision-free trajectories in narrow-passage environments, outperforming previous learning- and planning-based baselines. Videos and additional materials can be found on the project page: https://kiwi-sherbet.github.io/PRESTO.

Imitation learning (IL) algorithms have shown promising results for robots to learn skills from expert demonstrations. However, they need multi-task demonstrations to be provided at once for acquiring diverse skills, which is difficult in real world. In this work we study how to realize continual imitation learning ability that empowers robots to continually learn new tasks one by one, thus reducing the burden of multi-task IL and accelerating the process of new task learning at the same time. We propose a novel trajectory generation model that employs both a generative adversarial network and a dynamics-aware prediction model to generate pseudo trajectories from all learned tasks in the new task learning process. Our experiments on both simulation and real-world manipulation tasks demonstrate the effectiveness of our method.

Large reasoning models achieve strong performance on complex tasks through long chain-of-thought (CoT) trajectories, but directly transferring such reasoning processes to smaller models remains challenging. A key difficulty is that not all teacher-generated reasoning trajectories are suitable for student learning. Existing approaches typically rely on post-hoc filtering, selecting trajectories after full generation based on heuristic criteria. However, such methods cannot control the generation process itself and may still produce reasoning paths that lie outside the student's learning capacity. To address this limitation, we propose Gen-SSD (Generation-time Self-Selection Distillation), a student-in-the-loop framework that performs generation-time selection. Instead of passively consuming complete trajectories, the student evaluates candidate continuations during the teacher's sampling process, guiding the expansion of only learnable reasoning paths and enabling early pruning of unhelpful branches. Experiments on mathematical reasoning benchmarks demonstrate that Gen-SSD consistently outperforms standard knowledge distillation and recent baselines, with improvements of around 5.9 points over Standard KD and up to 4.7 points over other baselines. Further analysis shows that Gen-SSD produces more stable and learnable reasoning trajectories, highlighting the importance of incorporating supervision during generation for effective distillation.

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative trajectories, and results in costly inference for diffusion models. To address these limitations, we introduce Neural Flow Diffusion Models (NFDM), a novel framework that enhances diffusion models by supporting a broader range of forward processes beyond the fixed linear Gaussian. We also propose a novel parameterization technique for learning the forward process. Our framework provides an end-to-end, simulation-free optimization objective, effectively minimizing a variational upper bound on the negative log-likelihood. Experimental results demonstrate NFDM's strong performance, evidenced by state-of-the-art likelihood estimation. Furthermore, we investigate NFDM's capacity for learning generative dynamics with specific characteristics, such as deterministic straight lines trajectories. This exploration underscores NFDM's versatility and its potential for a wide range of applications.

Most offline reinforcement learning (RL) algorithms return a target policy maximizing a trade-off between (1) the expected performance gain over the behavior policy that collected the dataset, and (2) the risk stemming from the out-of-distribution-ness of the induced state-action occupancy. It follows that the performance of the target policy is strongly related to the performance of the behavior policy and, thus, the trajectory return distribution of the dataset. We show that in mixed datasets consisting of mostly low-return trajectories and minor high-return trajectories, state-of-the-art offline RL algorithms are overly restrained by low-return trajectories and fail to exploit high-performing trajectories to the fullest. To overcome this issue, we show that, in deterministic MDPs with stochastic initial states, the dataset sampling can be re-weighted to induce an artificial dataset whose behavior policy has a higher return. This re-weighted sampling strategy may be combined with any offline RL algorithm. We further analyze that the opportunity for performance improvement over the behavior policy correlates with the positive-sided variance of the returns of the trajectories in the dataset. We empirically show that while CQL, IQL, and TD3+BC achieve only a part of this potential policy improvement, these same algorithms combined with our reweighted sampling strategy fully exploit the dataset. Furthermore, we empirically demonstrate that, despite its theoretical limitation, the approach may still be efficient in stochastic environments. The code is available at https://github.com/Improbable-AI/harness-offline-rl.

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

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.

Applying diffusion models in reinforcement learning for long-term planning has gained much attention recently. Several diffusion-based methods have successfully leveraged the modeling capabilities of diffusion for arbitrary distributions. These methods generate subsequent trajectories for planning and have demonstrated significant improvement. However, these methods are limited by their plain base distributions and their overlooking of the diversity of samples, in which different states have different returns. They simply leverage diffusion to learn the distribution of offline dataset, generate the trajectories whose states share the same distribution with the offline dataset. As a result, the probability of these models reaching the high-return states is largely dependent on the dataset distribution. Even equipped with the guidance model, the performance is still suppressed. To address these limitations, in this paper, we propose a novel method called CDiffuser, which devises a return contrast mechanism to pull the states in generated trajectories towards high-return states while pushing them away from low-return states to improve the base distribution. Experiments on 14 commonly used D4RL benchmarks demonstrate the effectiveness of our proposed method.

Recent image generators have demonstrated impressive photorealism and instruction-following capabilities in single-image generation and editing. However, constrained by their architectures, they cannot achieve interleaved generation (text-image sequence), which has crucial applications in visual narratives, guidance, and embodied manipulation. Even the latest open-source Unified Multimodal Models (UMMs) exhibit limited performance in this regard. In this paper, we introduce InterleaveThinker, the first multi-agent pipeline designed to endow any existing image generator with interleaved generation capabilities. Specifically, we employ a planner agent to organize the image-text input sequence, instructing the image generator on the required execution at each step. Subsequently, we introduce a critic agent to evaluate the generator's outputs, identify samples that deviate from the planned instructions, and refine the instructions for regeneration. To implement this pipeline, we construct the Interleave-Planner-SFT-80k and Interleave-Critic-SFT-112k to perform a format cold-start. Then we develop Interleave-Critic-RL-13k to reinforce the step-wise instruction correction capability within a generation trajectory using GRPO. Since a single interleaved generation trajectory may involve over 25 generator calls, optimizing the entire trajectory is computationally impractical. Therefore, we propose accuracy reward and step-wise reward, allowing single-step RL to effectively guide the entire generation trajectory. The results show that InterleaveThinker improves performance across various image generators. On interleaved generation benchmarks, it achieves performance comparable to Nano Banana and GPT-5. Surprisingly, it also significantly enhances the base model on reasoning-based benchmarks; for example, on 4-step FLUX.2-klein, we observe substantial gains on WISE and RISE.

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.

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point. When driven by stochastic input, trajectories instead exhibit noise-sustained dynamics along closed orbits. Rotation along these orbits modulates the emission probabilities and is governed by transitions between regions of slow, noise-driven dynamics connected by fast, deterministic transitions. The trained RNNs develop highly structured connectivity, with a small set of "kick neurons" initiating transitions between these regions. This mechanism emerges during training as the network shifts into a regime of stochastic resonance, enabling it to perform probabilistic computations. Analyses across multiple HMM architectures - fully connected, cyclic, and linear-chain - reveal that this solution generalizes through the modular reuse of the same dynamical motif, suggesting a compositional principle by which RNNs can emulate complex discrete latent dynamics.

LLMs are widely used for code generation and mathematical reasoning tasks where they are required to generate structured output. They either need to reason about code, generate code for a given specification, or reason using programs of thought. The typical approach to code generation is to prompt the model and generate samples until an appropriate program is obtained. Within this process, sampling n programs from the language model requires n GPU compute-intensive generations which becomes prohibitively expensive for larger values of n. In this work, we address this limitation by exposing the LLM's distribution within the generated programs themselves. We propose a novel test-time framework we dub probabilistic programs of thought to obtain more samples from the model with fewer LLM generations. Given a program generated by a model and the associated next-token probabilities, we build a probabilistic program that compactly represents exponentially many deterministic programs. Since performing probabilistic reasoning in this probabilistic program is much cheaper, our approach allows sampling new programs without any additional GPU compute and little CPU overhead. We instantiate our approach on benchmarks for code generation, code understanding and mathematical reasoning and report improvements in performance with fewer generations from the LLM.

During the last decade, sampling-based path planning algorithms, such as Probabilistic RoadMaps (PRM) and Rapidly-exploring Random Trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g., as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g., showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e., such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.

Executing complex terminal tasks remains a significant challenge for open-weight LLMs, constrained by two fundamental limitations. First, high-fidelity, executable training environments are scarce: environments synthesized from real-world repositories are not diverse and scalable, while trajectories synthesized by LLMs suffer from hallucinations. Second, standard instruction tuning uses expert trajectories that rarely exhibit simple mistakes common to smaller models. This creates a distributional mismatch, leaving student models ill-equipped to recover from their own runtime failures. To bridge these gaps, we introduce TermiGen, an end-to-end pipeline for synthesizing verifiable environments and resilient expert trajectories. Termi-Gen first generates functionally valid tasks and Docker containers via an iterative multi-agent refinement loop. Subsequently, we employ a Generator-Critic protocol that actively injects errors during trajectory collection, synthesizing data rich in error-correction cycles. Fine-tuned on this TermiGen-generated dataset, our TermiGen-Qwen2.5-Coder-32B achieves a 31.3% pass rate on TerminalBench. This establishes a new open-weights state-of-the-art, outperforming existing baselines and notably surpassing capable proprietary models such as o4-mini. Dataset is avaiable at https://github.com/ucsb-mlsec/terminal-bench-env.

Video generation models have shown strong potential as world models for autonomous driving simulation. However, existing approaches are primarily trained on real-world driving datasets, which mostly contain natural and safe driving scenarios. As a result, current models often fail when conditioned on challenging or counterfactual trajectories-such as imperfect trajectories generated by simulators or planning systems-producing videos with severe physical inconsistencies and artifacts. To address this limitation, we propose PhyGenesis, a world model designed to generate driving videos with high visual fidelity and strong physical consistency. Our framework consists of two key components: (1) a physical condition generator that transforms potentially invalid trajectory inputs into physically plausible conditions, and (2) a physics-enhanced video generator that produces high-fidelity multi-view driving videos under these conditions. To effectively train these components, we construct a large-scale, physics-rich heterogeneous dataset. Specifically, in addition to real-world driving videos, we generate diverse challenging driving scenarios using the CARLA simulator, from which we derive supervision signals that guide the model to learn physically grounded dynamics under extreme conditions. This challenging-trajectory learning strategy enables trajectory correction and promotes physically consistent video generation. Extensive experiments demonstrate that PhyGenesis consistently outperforms state-of-the-art methods, especially on challenging trajectories. Our project page is available at: https://wm-research.github.io/PhyGenesis/.

LLM agents struggle with regulatory audit replay: when asked to reproduce a flagged transaction decision with identical inputs, many deployments fail to return consistent results. We introduce the Determinism-Faithfulness Assurance Harness (DFAH), a framework for measuring trajectory determinism, decision determinism, and evidence-conditioned faithfulness in tool-using agents deployed in financial services. Across 4,700+ agentic runs (7 models, 4 providers, 3 financial benchmarks with 50 cases each at T=0.0), we find that decision determinism and task accuracy are not detectably correlated (r = -0.11, 95% CI [-0.49, 0.31], p = 0.63, n = 21 configurations): models can be deterministic without being accurate, and accurate without being deterministic. Because neither metric predicts the other in our sample, both must be measured independently, which is precisely what DFAH provides. Small models (7-20B) achieve near-perfect determinism through rigid pattern matching at the cost of accuracy (20-42%), while frontier models show moderate determinism (50-96%) with variable accuracy. No model achieves both perfect determinism and high accuracy, supporting DFAH's multi-dimensional measurement approach. We provide three financial benchmarks (compliance triage, portfolio constraints, and DataOps exceptions; 50 cases each) together with an open-source stress-test harness. Across these benchmarks and DFAH evaluation settings, Tier 1 models with schema-first architectures achieved determinism levels consistent with audit replay requirements.

Latent Consistency Model (LCM) extends the Consistency Model to the latent space and leverages the guided consistency distillation technique to achieve impressive performance in accelerating text-to-image synthesis. However, we observed that LCM struggles to generate images with both clarity and detailed intricacy. To address this limitation, we initially delve into and elucidate the underlying causes. Our investigation identifies that the primary issue stems from errors in three distinct areas. Consequently, we introduce Trajectory Consistency Distillation (TCD), which encompasses trajectory consistency function and strategic stochastic sampling. The trajectory consistency function diminishes the distillation errors by broadening the scope of the self-consistency boundary condition and endowing the TCD with the ability to accurately trace the entire trajectory of the Probability Flow ODE. Additionally, strategic stochastic sampling is specifically designed to circumvent the accumulated errors inherent in multi-step consistency sampling, which is meticulously tailored to complement the TCD model. Experiments demonstrate that TCD not only significantly enhances image quality at low NFEs but also yields more detailed results compared to the teacher model at high NFEs.

Intelligent systems across physics, language and perception often exhibit factorisable structure, yet are typically modelled by monolithic neural architectures that do not explicitly exploit this structure. The separable neural architecture (SNA) addresses this by formalising a representational class that unifies additive, quadratic and tensor-decomposed neural models. By constraining interaction order and tensor rank, SNAs impose a structural inductive bias that factorises high-dimensional mappings into low-arity components. Separability need not be a property of the system itself: it often emerges in the coordinates or representations through which the system is expressed. Crucially, this coordinate-aware formulation reveals a structural analogy between chaotic spatiotemporal dynamics and linguistic autoregression. By treating continuous physical states as smooth, separable embeddings, SNAs enable distributional modelling of chaotic systems. This approach mitigates the nonphysical drift characteristics of deterministic operators whilst remaining applicable to discrete sequences. The compositional versatility of this approach is demonstrated across four domains: autonomous waypoint navigation via reinforcement learning, inverse generation of multifunctional microstructures, distributional modelling of turbulent flow and neural language modelling. These results establish the separable neural architecture as a domain-agnostic primitive for predictive and generative intelligence, capable of unifying both deterministic and distributional representations.

Graphical User Interface (GUI) agents powered by Vision-Language Models (VLMs) have demonstrated human-like computer control capability. Despite their utility in advancing digital automation, a critical bottleneck persists: collecting high-quality trajectory data for training. Common practices for collecting such data rely on human supervision or synthetic data generation through executing pre-defined tasks, which are either resource-intensive or unable to guarantee data quality. Moreover, these methods suffer from limited data diversity and significant gaps between synthetic data and real-world environments. To address these challenges, we propose OS-Genesis, a novel GUI data synthesis pipeline that reverses the conventional trajectory collection process. Instead of relying on pre-defined tasks, OS-Genesis enables agents first to perceive environments and perform step-wise interactions, then retrospectively derive high-quality tasks to enable trajectory-level exploration. A trajectory reward model is then employed to ensure the quality of the generated trajectories. We demonstrate that training GUI agents with OS-Genesis significantly improves their performance on highly challenging online benchmarks. In-depth analysis further validates OS-Genesis's efficiency and its superior data quality and diversity compared to existing synthesis methods. Our codes, data, and checkpoints are available at https://qiushisun.github.io/OS-Genesis-Home/{OS-Genesis Homepage}.

Generating high-fidelity synthetic GPS trajectories is increasingly important for applications in transportation, urban planning, and what-if scenario simulation, especially as privacy concerns limit access to real-world mobility data. Existing trajectory generation models face a trade-off between efficiency and faithfulness to road network topology: continuous-space methods enable fast generation but ignore the road network, while topology-aware approaches rely on search-based autoregressive decoding that limits generation speed. We propose TrajDLM, a topology-aware trajectory generation framework based on block diffusion language models that bridges this gap. TrajDLM models trajectories as sequences of discrete road segments, combining a block diffusion backbone for efficient denoising, topology-aware embeddings from a road network encoder, and topology-constrained sampling to ensure coherent and realistic trajectories. Across three city-scale datasets, TrajDLM achieves strong performance on fine-grained local similarity metrics while being up to 2.8times faster than prior work, and demonstrates strong zero-shot transfer across domains, including unseen transportation modes. These results highlight the effectiveness of block-wise discrete diffusion as a scalable approach to accurate and efficient trajectory generation. Our code is available at https://github.com/cruiseresearchgroup/TrajDLM/

P. Kabamba developed generation theory as a tool for studying self-reproducing systems. We provide an alternative definition of a generation system and give a complete solution to the problem of finding optimal seeds for a finite self-replicating system. We also exhibit examples illustrating a connection between self-replication and fixed-point theory.

A fundamental dilemma in generative modeling persists: iterative diffusion models achieve outstanding fidelity, but at a significant computational cost, while efficient few-step alternatives are constrained by a hard quality ceiling. This conflict between generation steps and output quality arises from restrictive training objectives that focus exclusively on either infinitesimal dynamics (PF-ODEs) or direct endpoint prediction. We address this challenge by introducing an exact, continuous-time dynamics equation that analytically defines state transitions across any finite time interval. This leads to a novel generative paradigm, Transition Models (TiM), which adapt to arbitrary-step transitions, seamlessly traversing the generative trajectory from single leaps to fine-grained refinement with more steps. Despite having only 865M parameters, TiM achieves state-of-the-art performance, surpassing leading models such as SD3.5 (8B parameters) and FLUX.1 (12B parameters) across all evaluated step counts. Importantly, unlike previous few-step generators, TiM demonstrates monotonic quality improvement as the sampling budget increases. Additionally, when employing our native-resolution strategy, TiM delivers exceptional fidelity at resolutions up to 4096x4096.

Multi-agent LLM systems share state through memory stores, vector indices, and tool registries. We model such sharing as long-running read-generate-write operations under deterministic-generation semantics -- the regime durable-execution engines enforce by deterministic replay -- and formalize four concurrency anomalies in TLA+: stale-generation, phantom-tool, causal-cascade, and tool-effect reordering, structural analogues of classical isolation anomalies, each with a TLC counter-example. The exclusion lattice over these anomalies is trivial; the contribution is the mechanically verified realizability and strict separation of one maximal chain within it, L_0 subsetneq cdots subsetneq L_4, to our knowledge the first machine-checked consistency hierarchy for such runtimes. A development of 274 Verus obligations (zero assume, zero admit; trust base: two structural axioms and a mutex correspondence) proves the detectors sound and complete against the specifications and each runtime its avoidance set. Three deployed Rust runtimes realize L0-L1 (pessimistic locking, serializable snapshot isolation, default-SI), each verified against stale-generation and refined to its state machine; L2-L4 are exec-mode-verified with dependency-free prevention twins (A3, A6, A2: 0/1000 versus 1000/1000), and L2 is run live across three model families (A3 prevented in all 120 retracted sessions). We reproduce a silent lost update in ByteDance's deer-flow, formalizing its fix as a verified L_0 to L_1 refinement, and exhibit tool-effect reordering in LangGraph's ToolNode on unmodified output, removed by an L3 commit-order sequencer. The verified detector, refinements, and realizability artifacts are the contribution; the phenomena and lattice are classical.

We study the right to be forgotten (GDPR Art. 17) for large language models and frame unlearning as a reproducible systems problem. Our approach treats training as a deterministic program and logs a minimal per-microbatch record (ordered ID hash, RNG seed, learning-rate value, optimizer-step counter, and accumulation boundary). Under a pinned stack and deterministic kernels, replaying the training tail while filtering only the forget closure yields the same parameters as training on the retain set (bit-identical in the training dtype) when preconditions hold. To meet latency and availability constraints, we add complementary paths: (i) exact reverts of recent steps via micro-checkpoints or dense per-step deltas, (ii) cohort-scoped adapter deletion when the base is frozen, and (iii) a curvature-guided anti-update followed by a short retain-tune, audit-gated with escalation to exact replay. We report storage/latency budgets and a toy artifact validating mechanics; in a controlled run that satisfies the preconditions we demonstrate byte-identical equality of model and optimizer states.

Probabilistic completeness is an important property in motion planning. Although it has been established with clear assumptions for geometric planners, the panorama of completeness results for kinodynamic planners is still incomplete, as most existing proofs rely on strong assumptions that are difficult, if not impossible, to verify on practical systems. In this paper, we focus on an important class of kinodynamic planners, namely those that interpolate trajectories in the state space. We provide a proof of probabilistic completeness for these planners under assumptions that can be readily verified from the system's equations of motion and the user-defined interpolation function. Our proof relies crucially on a property of interpolated trajectories, termed second-order continuity (SOC), which we show is tightly related to the ability of a planner to benefit from denser sampling. We analyze the impact of this property in simulations on a low-torque pendulum. Our results show that a simple RRT using a second-order continuous interpolation swiftly finds solution, while it is impossible for the same planner using standard Bezier curves (which are not SOC) to find any solution.

High-level autonomous driving requires motion planners capable of modeling multimodal future uncertainties while remaining robust in closed-loop interactions. Although diffusion-based planners are effective at modeling complex trajectory distributions, they often suffer from stochastic instabilities and the lack of corrective negative feedback when trained purely with imitation learning. To address these issues, we propose RAD-2, a unified generator-discriminator framework for closed-loop planning. Specifically, a diffusion-based generator is used to produce diverse trajectory candidates, while an RL-optimized discriminator reranks these candidates according to their long-term driving quality. This decoupled design avoids directly applying sparse scalar rewards to the full high-dimensional trajectory space, thereby improving optimization stability. To further enhance reinforcement learning, we introduce Temporally Consistent Group Relative Policy Optimization, which exploits temporal coherence to alleviate the credit assignment problem. In addition, we propose On-policy Generator Optimization, which converts closed-loop feedback into structured longitudinal optimization signals and progressively shifts the generator toward high-reward trajectory manifolds. To support efficient large-scale training, we introduce BEV-Warp, a high-throughput simulation environment that performs closed-loop evaluation directly in Bird's-Eye View feature space via spatial warping. RAD-2 reduces the collision rate by 56% compared with strong diffusion-based planners. Real-world deployment further demonstrates improved perceived safety and driving smoothness in complex urban traffic.

Collaborative generation, which coordinates multiple diffusion trajectories to extend the capabilities of pretrained priors, has emerged as a powerful paradigm for extending the applicability of diffusion models. Among existing approaches, diffusion synchronization provides a scenario-agnostic solution by introducing general guidance mechanisms. However, current synchronization approaches rely heavily on heuristics and still require task-specific tailoring, which limits their generalizability and performance. In this work, we mathematically derive a synchronization framework based on optimal control, providing a principled explanation of diffusion synchronization. During sampling, we optimize control variables to guide multiple trajectories toward coherent solutions while remaining close to the underlying diffusion prior. Our method operates entirely at test-time without additional training, thereby enabling broad applicability across diverse generation scenarios when combined with strong pretrained priors. We demonstrate consistent improvements over baselines on three representative collaborative generation tasks, covering a wide range of modalities and applications. Beyond performance gains, our work establishes a novel foundation for collaborative generation, opening a principled path toward extending pretrained generative models to new collaborative generation settings.

World generative models are typically used through what they produce: a rendered future, a video-conditioned action, or latent context computed by a costly generative branch. We argue that their more reusable asset is the computation that constructs a future. As a generator transforms a corrupted future into a coherent trajectory, its intermediate states organize appearance, spatial layout, and interaction across levels of abstraction. Can this future-generative computation be internalized in a representation inferred from the present alone? We present Enfold, which transfers this computation into a representation predicted from the current visual context and language instruction. During training, multi-level states exposed as the generator processes the observed future supervise a current-only encoder. The learned representation is fed back to condition future generation and is read by task heads without allowing task gradients to reshape the encoder. At deployment, action prediction no longer executes the generator. Across LIBERO, RoboTwin2.0, and real-robot tasks, Enfold supports strong control while reducing action latency by 3.7times relative to Fast--WAM, Enfold-Flash reaches 10.1times. Representation analyses show that it suppresses nuisance variation and preferentially captures changes that emerge over longer horizons. When the current scene is altered by human intervention, both the generated continuation and the executed actions adapt, which is inconsistent with fixed trajectory replay. These results recast a world generator as a source of predictive control representations: its future need not be materialized at every step if its internal structure can be enfolded into the present.

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.

Maritime vessel maneuvers, characterized by their inherent complexity and indeterminacy, requires vessel trajectory prediction system capable of modeling the multi-modality nature of future motion states. Conventional stochastic trajectory prediction methods utilize latent variables to represent the multi-modality of vessel motion, however, tends to overlook the complexity and dynamics inherent in maritime behavior. In contrast, we explicitly simulate the transition of vessel motion from uncertainty towards a state of certainty, effectively handling future indeterminacy in dynamic scenes. In this paper, we present a novel framework (DiffuTraj) to conceptualize the trajectory prediction task as a guided reverse process of motion pattern uncertainty diffusion, in which we progressively remove uncertainty from maritime regions to delineate the intended trajectory. Specifically, we encode the previous states of the target vessel, vessel-vessel interactions, and the environment context as guiding factors for trajectory generation. Subsequently, we devise a transformer-based conditional denoiser to capture spatio-temporal dependencies, enabling the generation of trajectories better aligned for particular maritime environment. Comprehensive experiments on vessel trajectory prediction benchmarks demonstrate the superiority of our method.

Diffusion models have shown strong competitiveness in offline reinforcement learning tasks by formulating decision-making as sequential generation. However, the practicality of these methods is limited due to the lengthy inference processes they require. In this paper, we address this problem by decomposing the sampling process of diffusion models into two decoupled subprocesses: 1) generating a feasible trajectory, which is a time-consuming process, and 2) optimizing the trajectory. With this decomposition approach, we are able to partially separate efficiency and quality factors, enabling us to simultaneously gain efficiency advantages and ensure quality assurance. We propose the Trajectory Diffuser, which utilizes a faster autoregressive model to handle the generation of feasible trajectories while retaining the trajectory optimization process of diffusion models. This allows us to achieve more efficient planning without sacrificing capability. To evaluate the effectiveness and efficiency of the Trajectory Diffuser, we conduct experiments on the D4RL benchmarks. The results demonstrate that our method achieves it 3-it 10 times faster inference speed compared to previous sequence modeling methods, while also outperforming them in terms of overall performance. https://github.com/RenMing-Huang/TrajectoryDiffuser Keywords: Reinforcement Learning and Efficient Planning and Diffusion Model

Reasoning-trained language models often spend more tokens on harder problems, but longer chains of thought do not show whether a model is merely computing for more steps or following a different internal trajectory. We study this distinction through hidden-state trajectories during chain-of-thought generation across competitive programming, mathematics, and Boolean satisfiability. Raw trajectory geometry is strongly shaped by generation length: longer generations mechanically alter path statistics, so difficulty-dependent comparisons are misleading without adjustment. After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines. Corrected difficulty-geometry coupling is weaker, but still present, in mathematics and Boolean satisfiability. Prompt-stage linear probes do not mirror the code-domain separation, and behavioral annotations show that stronger corrected coupling co-occurs with strategy shifts and uncertainty monitoring. Together, these findings establish length correction as a prerequisite for generation-time trajectory analysis and show that reasoning training can be associated with distinct corrected trajectory geometry, with the strength of the effect depending on the domain.

Large Language Models (LLMs) have demonstrated a powerful ability for text generation. However, achieving optimal results with a given prompt or instruction can be challenging, especially for billion-sized models. Additionally, undesired behaviors such as toxicity or hallucinations can manifest. While much larger models (e.g., ChatGPT) may demonstrate strength in mitigating these issues, there is still no guarantee of complete prevention. In this work, we propose formalizing text generation as a future-constrained generation problem to minimize undesirable behaviors and enforce faithfulness to instructions. The estimation of future constraint satisfaction, accomplished using LLMs, guides the text generation process. Our extensive experiments demonstrate the effectiveness of the proposed approach across three distinct text generation tasks: keyword-constrained generation (Lin et al., 2020), toxicity reduction (Gehman et al., 2020), and factual correctness in question-answering (Gao et al., 2023).

Modern generative models typically rely on an adversarial critic, a prescribed noise-to-data path, or an autoregressive factorization. Instead, we show that a proper distributional energy can induce sample-level motion and provide direct regression supervision for a one-step generator. Three-Body Scattering Modeling (TBSM) for generation turns the energy distance into a constant-size per-projectile interaction: each projectile is attracted toward one real source and repelled from one independently generated source. Conditioned on the projectile and its condition, its expectation equals the 2-Wasserstein gradient-flow velocity of frac12D_E^2(P_θ,Q). A batch of B frozen-target events yields O(B) sample-level losses, each using one reference for its condition instead of the minibatch-wide all-pairs field used by methods such as Drifting Models. Tracking this conditional expectation online can reduce field noise. Using scattering in frozen image features, TBSM trains one-step generators on ImageNet-256, achieving FID{}=2.23 with pixel-space PixelDiT-XL and FID{}=1.63 with latent-space DiT-XL at NFE{}=1. We provide a design map relating diffusion-related supervision, Drift-like dynamics, and GAN-like objectives. These results establish tracked scattering as a route to high-dimensional one-step generation. Code: https://github.com/sp12138/TBSM.

The evolution of Large Language Models (LLMs) from static instruction-followers to autonomous agents necessitates operating within complex, stateful environments to achieve precise state-transition objectives. However, this paradigm is bottlenecked by data scarcity, as existing tool-centric reverse-synthesis pipelines fail to capture the rigorous logic of real-world applications. We introduce LOGIGEN, a logic-driven framework that synthesizes verifiable training data based on three core pillars: Hard-Compiled Policy Grounding, Logic-Driven Forward Synthesis, and Deterministic State Verification. Specifically, a Triple-Agent Orchestration is employed: the Architect compiles natural-language policy into database constraints to enforce hard rules; the Set Designer initializes boundary-adjacent states to trigger critical policy conflicts; and the Explorer searches this environment to discover causal solution paths. This framework yields a dataset of 20,000 complex tasks across 8 domains, where validity is strictly guaranteed by checking exact state equivalence. Furthermore, we propose a verification-based training protocol where Supervised Fine-Tuning (SFT) on verifiable trajectories establishes compliance with hard-compiled policy, while Reinforcement Learning (RL) guided by dense state-rewards refines long-horizon goal achievement. On τ^2-Bench, LOGIGEN-32B(RL) achieves a 79.5\% success rate, substantially outperforming the base model (40.7\%). These results demonstrate that logic-driven synthesis combined with verification-based training effectively constructs the causally valid trajectories needed for next-generation agents.

Open-ended image generation is no longer a simple prompt-to-image problem. High-quality generation often requires an agent to combine a model's internal generative ability with external resources. As requests become more diverse and demanding, we aim to develop a general image-generation agent that can self-evolve through trajectories and use tools more effectively across varied generation challenges. To this end, we propose GenEvolve, a self-evolving framework based on Tool-Orchestrated Visual Experience Distillation. In GenEvolve, each generation attempt is modeled as a tool-orchestrated trajectory, where the agent gathers evidence, selects references, invokes generation skills, and composes them into a prompt-reference program. Unlike existing agentic generation methods that mainly rely on image-level scalar rewards, GenEvolve compares multiple trajectories for the same request and abstracts best-worst differences into structured visual experience, provided only to a privileged teacher branch. Inspired by on-policy self-distillation, Visual Experience Distillation provides dense token-level supervision, helping the student internalize better search, knowledge activation, reference selection, and prompt construction. We further construct GenEvolve-Data and GenEvolve-Bench. Experiments on public benchmarks and GenEvolve-Bench show substantial gains over strong baselines, achieving state-of-the-art performance among current image-generation frameworks. Our website is as follows: https://ephemeral182.github.io/GenEvolve/

Data-driven embodied AI is rapidly transitioning into a paradigm that scales training through massively parallel simulation, where GPU-accelerated simulators serve as the foundational data infrastructure. However, as computational throughput scales, the underlying trade-offs between parallel efficiency, physical fidelity, and execution determinism remain largely unexamined, hindering the development of reliable robot learning. In this paper, we expose the hidden limits of mainstream GPU-based robotic simulators (e.g., Isaac Lab, Genesis) by introducing GPUSimBench, which focuses on scalability, physical consistency, and computational determinism. First, GPUSimBench establishes a physical grounding evaluation with a controlled inclined-plane task, quantifying the distributional alignment between simulated dynamics and their real-world counterparts. Second, we benchmark parallel scalability by measuring throughput and memory footprints across scaling environment counts. Crucially, beyond standard performance metrics, we unveil and quantify the inherent non-determinism introduced by GPU-batched execution, characterized by significant run-to-run and inter-environment variability even under identical initial conditions. Finally, we identify four empirical regimes of stochasticity within current simulator stacks, highlighting that unbounded scaling can compromise reproducibility without explicit constraints.

Agentic applications based on large language models increasingly rely on multi-step interaction loops involving planning, action execution, and environment feedback. While such systems are now deployed at scale, improving them post-deployment remains challenging. Agent trajectories are voluminous and non-deterministic, and reviewing each one, whether through human review or auxiliary LLMs, is slow and cost-prohibitive. We propose a lightweight, signal-based framework for triaging agentic interaction trajectories. Our approach computes cheap, broadly applicable signals from live interactions and attaches them as structured attributes for trajectory triage, identifying interactions likely to be informative without affecting online agent behavior. We organize signals into a coarse-grained taxonomy spanning interaction (misalignment, stagnation, disengagement, satisfaction), execution (failure, loop), and environment (exhaustion), designed for computation without model calls. In a controlled annotation study on τ-bench, a widely used benchmark for tool-augmented agent evaluation, we show that signal-based sampling achieves an 82\% informativeness rate compared to 74\% for heuristic filtering and 54\% for random sampling, with a 1.52x efficiency gain per informative trajectory. The advantage is robust across reward strata and task domains, confirming that signals provide genuine per-trajectory informativeness gains rather than merely oversampling obvious failures. These results show that lightweight signals can serve as practical sampling infrastructure for agentic systems, and suggest a path toward preference data construction and post-deployment optimization.

The recent paradigm shift toward large reasoning models (LRMs) as autonomous agents has intensified the demand for sophisticated, multi-turn tool-use capabilities. Yet, existing datasets and data-generation approaches are limited by static, predefined toolsets that cannot scale to the complexity of open-ended human-agent collaboration. To address this, we initially developed a framework for automated task-oriented multi-turn dialogue generation at scale, utilizing an LRM-based simulator to dynamically generate high-value, domain-specific tools to solve specified tasks. However, we observe that a purely task-oriented design often results in "solely task-solving" trajectories, where the agent completes the objective with minimal interaction, failing to generate the high turn-count conversations seen in realistic scenarios. To bridge this gap, we shift toward a user-oriented simulation paradigm. By decoupling task generation from a dedicated user simulator that mimics human behavioral rules - such as incremental request-making and turn-by-turn feedback - we facilitate more authentic, extended multi-turn dialogues that reflect the iterative nature of real-world problem solving. Our generation pipeline operates as a versatile, plug-and-play module capable of initiating generation from any state, ensuring high scalability in producing extended tool-use data. Furthermore, by facilitating multiple task completions within a single trajectory, it yields a high-density dataset that reflects the multifaceted demands of real-world human-agent interaction.

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are however difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended beta-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables for the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.

Modeling human mobility is vital for extensive applications such as transportation planning and epidemic modeling. With the rise of the Artificial Intelligence Generated Content (AIGC) paradigm, recent works explore synthetic trajectory generation using autoregressive and diffusion models. While these methods show promise for generating single-day trajectories, they remain limited by inefficiencies in long-term generation (e.g., weekly trajectories) and a lack of explicit spatiotemporal multi-scale modeling. This study proposes Multi-Scale Spatio-Temporal AutoRegression (M-STAR), a new framework that generates long-term trajectories through a coarse-to-fine spatiotemporal prediction process. M-STAR combines a Multi-scale Spatiotemporal Tokenizer that encodes hierarchical mobility patterns with a Transformer-based decoder for next-scale autoregressive prediction. Experiments on two real-world datasets show that M-STAR outperforms existing methods in fidelity and significantly improves generation speed. The data and codes are available at https://github.com/YuxiaoLuo0013/M-STAR.

Tool-using LLM agents can violate the very policies they are deployed to enforce while appearing to complete the task successfully. In policy-permissive environments, a tool may execute any well-formed call even when the corresponding state transition is forbidden by domain policy. The result is a silent wrong state (a booking cancelled, a passenger count changed, a claim acted on without verification) that neither the tool nor the agent's self-report exposes. We study this failure mode in the τ^2-bench airline domain. On a budget agent, 78% of observed failures are silent wrong-state failures with no tool error, and the aggregate failure rate is reproducible across disjoint seeds, not sampling noise. We then evaluate a lightweight intervention: deterministic, read-only pre-execution gates that inspect the proposed call and current state before allowing a write. A four-gate suite raises full-benchmark success from 29.6% to 42.0% on gpt-4o-mini (+12.4pp; paired task-level bootstrap P=0.0012), and the lift reproduces on a disjoint 15-seed set (+12.3pp; P=0.0008). The effect is concentrated where the gates fire: on the 26/50 firing tasks, success rises by +19.2pp, while movement on the 24 non-firing tasks does not exclude zero. Two negative controls (a self-enforcing retail domain and BFCL) bound the mechanism: gates help when tools are policy-permissive and add little where tools already self-enforce. As suggestive evidence, not a central claim, the same failure mode persists at the frontier: gpt-5.2 at default reasoning still attempts policy-violating writes, and the same suite improves success from 61.2% to 71.6% (+10.4pp; P=0.020; n=5, no replication). The contribution is a bounded evaluation and reliability result: deterministic gates do not guarantee task success, but they can deterministically prevent a known class of silent policy-violating writes at the action boundary.

Majorities of distillation methods on pre-trained diffusion models or on pre-trained rectified flow, focus on either the distillation outputs or the trajectories between random noises and clean images to speed up sample generations from pre-trained models. In those trajectory-based distillation methods, consistency distillation requires the self-consistent trajectory projection to regulate the trajectory, which might avoid the common ODE approximation error {while still be concerning about sampling efficiencies}. At the same time, rectified flow distillations enforce straight trajectory for fast sampling, although an ODE solver is still required. In this work, we propose a trajectory distillation method, \modelname, that enjoys the benefits of both and enables few-step generations. TraFlow adopts the settings of consistency trajectory models, and further enforces the properties of self-consistency and straightness throughout the entire trajectory. These two properties are pursued by reaching a balance with following three targets: (1) reconstruct the output from pre-trained models; (2) learn the amount of changes by pre-trained models; (3) satisfy the self-consistency over its trajectory. Extensive experimental results have shown the effectiveness of our proposed method.

Large language models are increasingly trained as interactive agents for long-horizon tasks involving multi-turn interaction, tool use, and environment feedback. Outcome-based reinforcement learning (RL) provides a practical optimization paradigm, but its sparse trajectory-level rewards offer limited guidance on intermediate decisions, leaving a supervision gap between episode-level outcomes and token-level policy learning. We propose SEED (SElf-Evolving On-Policy Distillation), a self-evolving framework that converts completed on-policy trajectories into training-time hindsight skills and distills their behavioral effect back into the policy model. SEED first fine-tunes the policy to analyze completed trajectories and generate natural-language skills that capture reusable workflows, decisive observations, or failure-avoidance rules. During RL, the current policy both collects trajectories and serves as the analyzer that extracts hindsight skills from them. Policy updates therefore improve subsequent decision making and skill analysis together, allowing hindsight supervision to evolve with the policy. SEED then re-scores the sampled actions under ordinary and skill-augmented contexts, converting the skill-induced probability shift into a dense token-level on-policy distillation signal. This signal is jointly optimized with outcome-based RL, keeping the auxiliary supervision aligned with the current trajectory distribution. Extensive experiments on text-based and vision-based agentic tasks show that SEED consistently improves performance and sample efficiency, exhibiting robust generalization to unseen scenarios. Our code is available at https://github.com/jinyangwu/SEED.

Discrete flow matching generates text by iteratively transforming noise tokens into coherent language, but may require hundreds of forward passes. Distillation uses the multi-step trajectory to train a student to reproduce the process in a few steps. When the student underperforms, the usual explanation is insufficient capacity. We argue the opposite: the trajectory is the bottleneck, not the student. Each training trajectory is built through a chain of blind stochastic jumps with no evaluation of sequence quality; a single bad decision at an early midpoint propagates through subsequent steps, yet the student must imitate the result. Trajectory-Shaped Discrete Flow Matching (TS-DFM) replaces these blind jumps with guided navigation: a lightweight energy compass evaluates candidate continuations at each midpoint, selecting the most coherent. All shaping is training-only; inference cost is unchanged. On 170M-parameter language modeling, the shaped student at 8 steps achieves 32% lower perplexity than the 1,024-step teacher while being 128x faster, with gains consistent across source distributions and three evaluators of increasing scale. TS-DFM achieves the best perplexity of any discrete-generation baseline we compare against, including methods trained on 6x more data or using 5x larger models.

Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple, this combination has a number of empirical shortcomings, suggesting that learned models may not be well-suited to standard trajectory optimization. In this paper, we consider what it would look like to fold as much of the trajectory optimization pipeline as possible into the modeling problem, such that sampling from the model and planning with it become nearly identical. The core of our technical approach lies in a diffusion probabilistic model that plans by iteratively denoising trajectories. We show how classifier-guided sampling and image inpainting can be reinterpreted as coherent planning strategies, explore the unusual and useful properties of diffusion-based planning methods, and demonstrate the effectiveness of our framework in control settings that emphasize long-horizon decision-making and test-time flexibility.

Most agent frameworks are built around the language model: a conversation loop comes first, then tools, then rules, and finally a logging layer bolted on for observability, with state persisted as retrievable "memory." We describe ActiveGraph, a runtime that inverts this arrangement. The append-only event log is the source of truth; the working graph is a deterministic projection of that log; and behaviors--ordinary functions, classes, LLM-backed routines, or logic attached to typed edges--react to changes in the graph and emit new events. No component instructs another; coordination happens entirely through the shared graph. This single design decision yields three properties that retrieval-and-summarization memory systems do not provide: deterministic replay of any run from its log, cheap forking that branches a run at any event without re-executing the shared prefix, and end-to-end lineage from a high-level goal down to the individual model call that produced each artifact. We present the architecture, a determinism contract that makes replay sound, and a worked diligence example whose full causal structure is reconstructable from the log alone. We discuss--without claiming to demonstrate--why this substrate is unusually well suited to self-improving agents, and how it extends the BabyAGI lineage and prior graph-memory research.

Diffusion model has demonstrated remarkable capability in video generation, which further sparks interest in introducing trajectory control into the generation process. While existing works mainly focus on training-based methods (e.g., conditional adapter), we argue that diffusion model itself allows decent control over the generated content without requiring any training. In this study, we introduce a tuning-free framework to achieve trajectory-controllable video generation, by imposing guidance on both noise construction and attention computation. Specifically, 1) we first show several instructive phenomenons and analyze how initial noises influence the motion trajectory of generated content. 2) Subsequently, we propose FreeTraj, a tuning-free approach that enables trajectory control by modifying noise sampling and attention mechanisms. 3) Furthermore, we extend FreeTraj to facilitate longer and larger video generation with controllable trajectories. Equipped with these designs, users have the flexibility to provide trajectories manually or opt for trajectories automatically generated by the LLM trajectory planner. Extensive experiments validate the efficacy of our approach in enhancing the trajectory controllability of video diffusion models.

Recent work has demonstrated the effectiveness of formulating decision making as a supervised learning problem on offline-collected trajectories. However, the benefits of performing sequence modeling on trajectory data is not yet clear. In this work we investigate if sequence modeling has the capability to condense trajectories into useful representations that can contribute to policy learning. To achieve this, we adopt a two-stage framework that first summarizes trajectories with sequence modeling techniques, and then employs these representations to learn a policy along with a desired goal. This design allows many existing supervised offline RL methods to be considered as specific instances of our framework. Within this framework, we introduce Goal-Conditioned Predicitve Coding (GCPC), an approach that brings powerful trajectory representations and leads to performant policies. We conduct extensive empirical evaluations on AntMaze, FrankaKitchen and Locomotion environments, and observe that sequence modeling has a significant impact on some decision making tasks. In addition, we demonstrate that GCPC learns a goal-conditioned latent representation about the future, which serves as an "implicit planner", and enables competitive performance on all three benchmarks.

We identify a fundamental Narrow Policy limitation undermining the performance of autonomous VLA models, where driving Imitation Learning (IL) tends to collapse exploration and limit the potential of subsequent Reinforcement Learning (RL) stages, which often saturate prematurely due to insufficient feedback diversity. Thereby, we propose Curious-VLA, a framework that alleviates the exploit-explore dilemma through a two-stage design. During IL, we introduce a Feasible Trajectory Expansion (FTE) strategy to generate multiple physically valid trajectories and a step-wise normalized trajectory representation to adapt this diverse data. In the RL stage, we present Adaptive Diversity-Aware Sampling (ADAS) that prioritizes high-diversity samples and introduce Spanning Driving Reward (SDR) with a focal style weighting to amplify reward's value span for improving sensitivity to driving quality. On the Navsim benchmark, Curious-VLA achieves SoTA results (PDMS 90.3, EPDMS 85.4) and a Best-of-N PDMS of 94.8, demonstrating its effectiveness in unlocking the exploratory potential of VLA models. Code: https://github.com/Mashiroln/curious_vla.git.

The Instruction-Driven Game Engine (IDGE) project aims to democratize game development by enabling a large language model (LLM) to follow free-form game descriptions and generate game-play processes. The IDGE allows users to create games simply by natural language instructions, which significantly lowers the barrier for game development. We approach the learning process for IDGEs as a Next State Prediction task, wherein the model autoregressively predicts the game states given player actions. The computation of game states must be precise; otherwise, slight errors could corrupt the game-play experience. This is challenging because of the gap between stability and diversity. To address this, we train the IDGE in a curriculum manner that progressively increases its exposure to complex scenarios. Our initial progress lies in developing an IDGE for Poker, which not only supports a wide range of poker variants but also allows for highly individualized new poker games through natural language inputs. This work lays the groundwork for future advancements in transforming how games are created and played.

Enabling effective collaboration among LLMs is a crucial step toward developing autonomous systems capable of solving complex problems. While LLMs are typically used as single-model generators, where humans critique and refine their outputs, the potential for jointly-trained collaborative models remains largely unexplored. Despite promising results in multi-agent communication and debate settings, little progress has been made in training models to work together on tasks. In this paper, we present a first step toward "Multi-agent LLM training" (MALT) on reasoning problems. Our approach employs a sequential multi-agent setup with heterogeneous LLMs assigned specialized roles: a generator, verifier, and refinement model iteratively solving problems. We propose a trajectory-expansion-based synthetic data generation process and a credit assignment strategy driven by joint outcome based rewards. This enables our post-training setup to utilize both positive and negative trajectories to autonomously improve each model's specialized capabilities as part of a joint sequential system. We evaluate our approach across MATH, GSM8k, and CQA, where MALT on Llama 3.1 8B models achieves relative improvements of 14.14%, 7.12%, and 9.40% respectively over the same baseline model. This demonstrates an early advance in multi-agent cooperative capabilities for performance on mathematical and common sense reasoning questions. More generally, our work provides a concrete direction for research around multi-agent LLM training approaches.

Steering intermediate representations has emerged as a powerful strategy for controlling generative models, particularly in post-deployment alignment and safety settings. However, despite its empirical success, it currently lacks a comprehensive theoretical framework. In this paper, we bridge this gap by formalizing the theory of concept steering. First, we establish a link between steering and affine concept erasure, proving that the standard approach for removing unwanted behaviors is a special case of LEACE (a closed-form method for affine erasure). Next, we formulate a principled theoretical framework for concept switching, LEACE-Switch, and characterize the assumptions under which it provides an optimal affine solution. Building on this analysis, we then introduce MidSteer (Minimal Disturbance concept Steering), a more general affine framework for concept manipulation that relaxes these assumptions and enables directed, minimal-disturbance transformations. We demonstrate that MidSteer performs favorably across a range of tasks, modalities, and architectures, including vision diffusion models and large language models.

Large language model (LLM)-driven agents are emerging as a powerful new paradigm for solving complex problems. Despite the empirical success of these practices, a theoretical framework to understand and unify their macroscopic dynamics remains lacking. This Letter proposes a method based on the least action principle to estimate the underlying generative directionality of LLMs embedded within agents. By experimentally measuring the transition probabilities between LLM-generated states, we statistically discover a detailed balance in LLM-generated transitions, indicating that LLM generation may not be achieved by generally learning rule sets and strategies, but rather by implicitly learning a class of underlying potential functions that may transcend different LLM architectures and prompt templates. To our knowledge, this is the first discovery of a macroscopic physical law in LLM generative dynamics that does not depend on specific model details. This work is an attempt to establish a macroscopic dynamics theory of complex AI systems, aiming to elevate the study of AI agents from a collection of engineering practices to a science built on effective measurements that are predictable and quantifiable.

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models. We characterize an implicit denoising trajectory and discuss its vital role in forming the coupled sampling trajectory with a strong shape regularity, regardless of the generated content. We also describe a dynamic programming-based scheme to make the time schedule in sampling better fit the underlying trajectory structure. This simple strategy requires minimal modification to any given ODE-based numerical solvers and incurs negligible computational cost, while delivering superior performance in image generation, especially in 5sim 10 function evaluations.

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.

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sampled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on completeness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show experimentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the adjoint method, many downstream tasks such as active learning, exploration in reinforcement learning, robust control, or filtering require accurate estimates of predictive uncertainties. In this work, we propose a novel approach towards estimating epistemically uncertain neural ODEs, avoiding the numerical integration bottleneck. Instead of modeling uncertainty in the ODE parameters, we directly model uncertainties in the state space. Our algorithm - distributional gradient matching (DGM) - jointly trains a smoother and a dynamics model and matches their gradients via minimizing a Wasserstein loss. Our experiments show that, compared to traditional approximate inference methods based on numerical integration, our approach is faster to train, faster at predicting previously unseen trajectories, and in the context of neural ODEs, significantly more accurate.

Training API-calling large language model (LLM) agents demands massive amounts of high-quality trajectories. However, collecting such data at scale typically requires fully implemented environments with executable APIs and realistic, pre-populated backend databases, creating a major bottleneck for scalability. To overcome this, we propose an environment-free synthetic data generation approach that leverages LLMs as on-the-fly digital world models. Given only API specifications, our method generates trajectories mimicking interactions between an agent and a stateful environment. Specifically, an LLM first generates diverse tasks solvable with the provided APIs. A teacher agent then iteratively solves each task while an LLM simulator generates coherent synthetic API responses conditioned on the task context and simulation history. Finally, an LLM judge filters the trajectories to ensure the quality of the resulting dataset. We evaluate our approach on the challenging AppWorld and OfficeBench benchmarks, which include both information-retrieval and state-changing tasks. Fine-tuning models on our synthetic data yields significant performance gains, demonstrating that effective supervision for API-calling agents can be generated without any executable environment. Our results establish LLM-based API simulation as a practical, scalable solution for training agents across diverse API ecosystems.

Large Reasoning Models (LRMs) introduce new opportunities for safety monitoring through their Chain of Thought (CoT) reasoning. However, CoT is not always faithful to the model's final output, undermining its reliability as a monitoring tool. To address this, we investigate the hidden representations of LRMs to determine whether future behavior can be predicted from prompt and CoT representations. By evaluating a probe at each generated token, we construct a probe trajectory, the continuous evolution of a concept's probability across the reasoning process. We find that future model behavior is more distinguishable when examined over the full trajectory than from a single static prediction. To characterize these temporal dynamics, we extract signal-processing features that capture volatility, trend, and steady-state behavior, significantly improving the separation of future model states. We also present two methodological insights. First, template-based training data achieves near-parity with dynamically generated model responses, eliminating the need for a costly initial inference and labeling. Second, the choice of pooling operation is critical: average-pooling and last-token methods collapse to near-random performance, while max-pooling achieves up to 95% AUROC and yields stable probe trajectories. Using four datasets and four reasoning models across the domains of safety and mathematics, we demonstrate that trajectory features encode task-specific dynamics that improve outcome separability. These findings establish probe trajectories as a complementary framework for monitoring LRM behavior. Warning: This article contains potentially harmful content.

Recent work suggests that large language models may implicitly learn world models. How should we assess this possibility? We formalize this question for the case where the underlying reality is governed by a deterministic finite automaton. This includes problems as diverse as simple logical reasoning, geographic navigation, game-playing, and chemistry. We propose new evaluation metrics for world model recovery inspired by the classic Myhill-Nerode theorem from language theory. We illustrate their utility in three domains: game playing, logic puzzles, and navigation. In all domains, the generative models we consider do well on existing diagnostics for assessing world models, but our evaluation metrics reveal their world models to be far less coherent than they appear. Such incoherence creates fragility: using a generative model to solve related but subtly different tasks can lead to failures. Building generative models that meaningfully capture the underlying logic of the domains they model would be immensely valuable; our results suggest new ways to assess how close a given model is to that goal.

From a viewpoint of stochastic thermodynamics, we derive equations that describe the collective dynamics near the order-disorder transition in the globally coupled XY model and near the synchronization-desynchronization transition in the Kuramoto model. A new way of thinking is to interpret the deterministic time evolution of a macroscopic variable as an external operation to a thermodynamic system. We then find that the irreversible work determines the equation for the collective dynamics. When analyzing the Kuramoto model, we employ a generalized concept of irreversible work which originates from a non-equilibrium identity associated with steady state thermodynamics.

Modularization is a cornerstone of computer science, abstracting complex functions into atomic building blocks. In this paper, we introduce a new level of modularization by abstracting generative models into atomic generative modules. Analogous to fractals in mathematics, our method constructs a new type of generative model by recursively invoking atomic generative modules, resulting in self-similar fractal architectures that we call fractal generative models. As a running example, we instantiate our fractal framework using autoregressive models as the atomic generative modules and examine it on the challenging task of pixel-by-pixel image generation, demonstrating strong performance in both likelihood estimation and generation quality. We hope this work could open a new paradigm in generative modeling and provide a fertile ground for future research. Code is available at https://github.com/LTH14/fractalgen.

Large language models (LLMs) have shown strong empirical gains as self-evolving agents for CUDA kernel generation, driven by feedback-conditioned planning across generations. However, how planning decisions attribute and combine heterogeneous feedback signals remains opaque. Standard end-to-end ablations fail to resolve this question, as iterative planning amplifies early perturbations and conflates feedback effects with trajectory-dependent drift. We introduce CUDAnalyst, a unified analysis layer for controlled, generation-level attribution of planning decisions to feedback components via trajectory freezing and selective feedback injection. CUDAnalyst enables stable generation-level evaluation and principled coalitional-style attribution of feedback effects and interactions. Our results show that explicit planning is beneficial only when feedback is aligned, that effective planning emerges from structured multi-feedback interactions, and that high-level plans from stronger reasoning models can partially transfer to weaker ones. These trends hold across reference backbones, representative workloads, and reference induction regimes, indicating that the identified feedback-to-plan structure is robust within the controlled axes studied.

Enabling Large Language Models (LLMs) to effectively utilize tools in multi-turn interactions is essential for building capable autonomous agents. However, acquiring diverse and realistic multi-turn tool-use data remains a significant challenge. In this work, we propose a novel text-based paradigm. We observe that textual corpora naturally contain rich, multi-step problem-solving experiences, which can serve as an untapped, scalable, and authentic data source for multi-turn tool-use tasks. Based on this insight, we introduce GEM, a data synthesis pipeline that enables the generation and extraction of multi-turn tool-use trajectories from text corpora through a four-stage process: relevance filtering, workflow & tool extraction, trajectory grounding, and complexity refinement. To reduce the computational cost, we further train a specialized Trajectory Synthesizer via supervised fine-tuning. This model distills the complex generation pipeline into an efficient, end-to-end trajectory generator. Experiments demonstrate that our GEM-32B achieve a 16.5% improvement on the BFCL V3 Multi-turn benchmark. Our models partially surpass the performance of models trained on τ - bench (Airline and Retail) in-domain data, highlighting the superior generalization capability derived from our text-based synthesis paradigm. Notably, our Trajectory Synthesizer matches the quality of the full pipeline while significantly reducing inference latency and costs.

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

Large Language Model (LLM)-based agents have fundamentally reshaped artificial intelligence by integrating external tools and planning capabilities. While memory mechanisms have emerged as the architectural cornerstone of these systems, current research remains fragmented, oscillating between operating system engineering and cognitive science. This theoretical divide prevents a unified view of technological synthesis and a coherent evolutionary perspective. To bridge this gap, this survey proposes a novel evolutionary framework for LLM agent memory mechanisms, formalizing the development process into three stages: Storage (trajectory preservation), Reflection (trajectory refinement), and Experience (trajectory abstraction). We first formally define these three stages before analyzing the three core drivers of this evolution: the necessity for long-range consistency, the challenges in dynamic environments, and the ultimate goal of continual learning. Furthermore, we specifically explore two transformative mechanisms in the frontier Experience stage: proactive exploration and cross-trajectory abstraction. By synthesizing these disparate views, this work offers robust design principles and a clear roadmap for the development of next-generation LLM agents.

In this paper, we investigate the obstacle avoidance and navigation problem in the robotic control area. For solving such a problem, we propose revised Deep Deterministic Policy Gradient (DDPG) and Proximal Policy Optimization algorithms with an improved reward shaping technique. We compare the performances between the original DDPG and PPO with the revised version of both on simulations with a real mobile robot and demonstrate that the proposed algorithms achieve better results.

Autonomous 6G network management requires agents that can execute tools, observe the resulting state changes, and adapt their decisions accordingly. Existing benchmarks based on static questions or scripted episode replay, however, do not support such closed-loop interaction, limiting agents to passive evaluation without the ability to learn from environmental feedback. This paper presents 6GAgentGym to provide closed-loop capability. The framework provides an interactive environment with 42 typed tools whose effect classification distinguishes read-only observation from state-mutating configuration, backed by a learned Experiment Model calibrated on NS-3 simulation data. 6G-Forge bootstraps closed-loop training trajectories from NS-3 seeds via iterative Self-Instruct generation with execution verification against the Experiment Model. Supervised fine-tuning on the resulting corpus followed by reinforcement learning with online closed-loop interaction enables an 8B open-source model to achieve comparable overall success rate to GPT-5 on the accompanying 6GAgentBench, with stronger performance on long-horizon tasks. Together, these components provide a viable path toward autonomous, closed-loop network management.

Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on large-scale datasets, numerical simulation requires multiple evaluations of a neural network, leading to a slow sampling speed. We attribute the reason to the high curvature of the learned generative trajectories, as it is directly related to the truncation error of a numerical solver. Based on the relationship between the forward process and the curvature, here we present an efficient method of training the forward process to minimize the curvature of generative trajectories without any ODE/SDE simulation. Experiments show that our method achieves a lower curvature than previous models and, therefore, decreased sampling costs while maintaining competitive performance. Code is available at https://github.com/sangyun884/fast-ode.

Recent advancements in generative modeling have made it possible to generate high-quality content from context information, but a key question remains: how to teach models to know when to generate content? To answer this question, this study proposes a novel event generative model that draws its statistical intuition from marked temporal point processes, and offers a clean, flexible, and computationally efficient solution for a wide range of applications involving multi-dimensional marks. We aim to capture the distribution of the point process without explicitly specifying the conditional intensity or probability density. Instead, we use a conditional generator that takes the history of events as input and generates the high-quality subsequent event that is likely to occur given the prior observations. The proposed framework offers a host of benefits, including exceptional efficiency in learning the model and generating samples, as well as considerable representational power to capture intricate dynamics in multi- or even high-dimensional event space. Our numerical results demonstrate superior performance compared to other state-of-the-art baselines.

This paper proposes a novel sampling-based motion planner, which integrates in RRT* (Rapidly exploring Random Tree star) a database of pre-computed motion primitives to alleviate its computational load and allow for motion planning in a dynamic or partially known environment. The database is built by considering a set of initial and final state pairs in some grid space, and determining for each pair an optimal trajectory that is compatible with the system dynamics and constraints, while minimizing a cost. Nodes are progressively added to the tree of feasible trajectories in the RRT* algorithm by extracting at random a sample in the gridded state space and selecting the best obstacle-free motion primitive in the database that joins it to an existing node. The tree is rewired if some nodes can be reached from the new sampled state through an obstacle-free motion primitive with lower cost. The computationally more intensive part of motion planning is thus moved to the preliminary offline phase of the database construction {at the price of some performance degradation due to gridding. Grid resolution can be tuned so as to compromise between (sub)optimality and size of the database. The planner is shown to be }asymptotically optimal as the grid resolution goes to zero and the number of sampled states grows to infinity.

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.

Existing industrial-scale navigation applications contend with massive road networks, typically employing two main categories of approaches for route planning. The first relies on precomputed road costs for optimal routing and heuristic algorithms for generating alternatives, while the second, generative methods, has recently gained significant attention. However, the former struggles with personalization and route diversity, while the latter fails to meet the efficiency requirements of large-scale real-time scenarios. To address these limitations, we propose GenMRP, a generative framework for multi-route planning. To ensure generation efficiency, GenMRP first introduces a skeleton-to-capillary approach that dynamically constructs a relevant sub-network significantly smaller than the full road network. Within this sub-network, routes are generated iteratively. The first iteration identifies the optimal route, while the subsequent ones generate alternatives that balance quality and diversity using the newly proposed correctional boosting approach. Each iteration incorporates road features, user historical sequences, and previously generated routes into a Link Cost Model to update road costs, followed by route generation using the Dijkstra algorithm. Extensive experiments show that GenMRP achieves state-of-the-art performance with high efficiency in both offline and online environments. To facilitate further research, we have publicly released the training and evaluation dataset. GenMRP has been fully deployed in a real-world navigation app, demonstrating its effectiveness and benefits.

Signal Temporal Logic (STL) is a powerful specification language for describing complex temporal behaviors of continuous signals, making it well-suited for high-level robotic task descriptions. However, generating executable plans for STL tasks is challenging, as it requires consideration of the coupling between the task specification and the system dynamics. Existing approaches either follow a model-based setting that explicitly requires knowledge of the system dynamics or adopt a task-oriented data-driven approach to learn plans for specific tasks. In this work, we address the problem of generating executable STL plans for systems with unknown dynamics. We propose a hierarchical planning framework that enables zero-shot generalization to new STL tasks by leveraging only task-agnostic trajectory data during offline training. The framework consists of three key components: (i) decomposing the STL specification into several progresses and time constraints, (ii) searching for timed waypoints that satisfy all progresses under time constraints, and (iii) generating trajectory segments using a pre-trained diffusion model and stitching them into complete trajectories. We formally prove that our method guarantees STL satisfaction, and simulation results demonstrate its effectiveness in generating dynamically feasible trajectories across diverse long-horizon STL tasks.

Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled generation in general. In this work we introduce D-Flow, a simple framework for controlling the generation process by differentiating through the flow, optimizing for the source (noise) point. We motivate this framework by our key observation stating that for Diffusion/FM models trained with Gaussian probability paths, differentiating through the generation process projects gradient on the data manifold, implicitly injecting the prior into the optimization process. We validate our framework on linear and non-linear controlled generation problems including: image and audio inverse problems and conditional molecule generation reaching state of the art performance across all.

Reinforcement Learning (RL) has recently emerged as a powerful technique for improving image and video generation in Diffusion and Flow Matching models, specifically for enhancing output quality and alignment with prompts. A critical step for applying online RL methods on Flow Matching is the introduction of stochasticity into the deterministic framework, commonly realized by Stochastic Differential Equation (SDE). Our investigation reveals a significant drawback to this approach: SDE-based sampling introduces pronounced noise artifacts in the generated images, which we found to be detrimental to the reward learning process. A rigorous theoretical analysis traces the origin of this noise to an excess of stochasticity injected during inference. To address this, we draw inspiration from Denoising Diffusion Implicit Models (DDIM) to reformulate the sampling process. Our proposed method, Coefficients-Preserving Sampling (CPS), eliminates these noise artifacts. This leads to more accurate reward modeling, ultimately enabling faster and more stable convergence for reinforcement learning-based optimizers like Flow-GRPO and Dance-GRPO. Code will be released at https://github.com/IamCreateAI/FlowCPS

Recent successful generative models are trained by fitting a neural network to an a-priori defined tractable probability density path taking noise to training examples. In this paper we investigate the space of Gaussian probability paths, which includes diffusion paths as an instance, and look for an optimal member in some useful sense. In particular, minimizing the Kinetic Energy (KE) of a path is known to make particles' trajectories simple, hence easier to sample, and empirically improve performance in terms of likelihood of unseen data and sample generation quality. We investigate Kinetic Optimal (KO) Gaussian paths and offer the following observations: (i) We show the KE takes a simplified form on the space of Gaussian paths, where the data is incorporated only through a single, one dimensional scalar function, called the data separation function. (ii) We characterize the KO solutions with a one dimensional ODE. (iii) We approximate data-dependent KO paths by approximating the data separation function and minimizing the KE. (iv) We prove that the data separation function converges to 1 in the general case of arbitrary normalized dataset consisting of n samples in d dimension as n/drightarrow 0. A consequence of this result is that the Conditional Optimal Transport (Cond-OT) path becomes kinetic optimal as n/drightarrow 0. We further support this theory with empirical experiments on ImageNet.

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.

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.

In many domains generating variable length sequences through insertions provides greater flexibility over autoregressive models. However, the action space of insertion models is much larger than that of autoregressive models (ARMs) making the learning challenging. To address this, we incorporate trainable order dynamics into the target rates for discrete flow matching, and show that with suitable choices of parameterizations, joint training of the target order dynamics and the generator is tractable without the need for numerical simulation. As the generative insertion model, we use a variable length masked diffusion model, which generates by inserting and filling mask tokens. On graph traversal tasks for which a locally optimal insertion order is known, we explore the choices of parameterization empirically and demonstrate the trade-offs between flexibility, training stability and generation quality. On de novo small molecule generation, we find that the learned order dynamics leads to an increase in the number of valid molecules generated and improved quality, when compared to uniform order dynamics.

Despite rapid advances in text-to-image generation, faithfully realizing user intent remains challenging, often requiring manual multi-turn trial and error. To automate this process, existing systems rely on either simple prompt rewriting or closed-loop agents driven by hand-crafted rules, rather than learning to adapt actions to the evolving generation process. In this paper, we reformulate image generation as a state-conditioned action-making problem and propose Generation Navigator, a multi-turn T2I agent that learns to dynamically steer the generation trajectory and output the next action. However, training this agent via reinforcement learning introduces a critical credit assignment challenge: naively rewarding a trajectory based solely on a single state assigns equal credit to all actions in the rollout, ignores the quality dynamics across turns, and fails to distinguish actions that improve the trajectory from those that degrade it or waste turns without progress. We resolve this with PRE-GRPO (Peak-Retention-Efficiency Group Relative Policy Optimization), a trajectory-level reinforcement learning objective that explicitly rewards discovering a high-quality image (Peak), avoiding subsequent quality degradation across turns (Retention), and minimizing unnecessary turns (Efficiency). Experiments show substantial improvements across benchmarks, reaching a WISE score of 0.90 and 79.06% reasoning accuracy on T2I-ReasonBench.

Large Language Model (LLM)-based agents have recently shown impressive capabilities in complex reasoning and tool use via multi-step interactions with their environments. While these agents have the potential to tackle complicated tasks, their problem-solving process, i.e., agents' interaction trajectory leading to task completion, remains underexploited. These trajectories contain rich feedback that can navigate agents toward the right directions for solving problems correctly. Although prevailing approaches, such as Monte Carlo Tree Search (MCTS), can effectively balance exploration and exploitation, they ignore the interdependence among various trajectories and lack the diversity of search spaces, which leads to redundant reasoning and suboptimal outcomes. To address these challenges, we propose SE-Agent, a Self-Evolution framework that enables Agents to optimize their reasoning processes iteratively. Our approach revisits and enhances former pilot trajectories through three key operations: revision, recombination, and refinement. This evolutionary mechanism enables two critical advantages: (1) it expands the search space beyond local optima by intelligently exploring diverse solution paths guided by previous trajectories, and (2) it leverages cross-trajectory inspiration to efficiently enhance performance while mitigating the impact of suboptimal reasoning paths. Through these mechanisms, SE-Agent achieves continuous self-evolution that incrementally improves reasoning quality. We evaluate SE-Agent on SWE-bench Verified to resolve real-world GitHub issues. Experimental results across five strong LLMs show that integrating SE-Agent delivers up to 55% relative improvement, achieving state-of-the-art performance among all open-source agents on SWE-bench Verified. Our code and demonstration materials are publicly available at https://github.com/JARVIS-Xs/SE-Agent.

Rapidly-exploring Random Trees (RRT) and its variations have emerged as a robust and efficient tool for finding collision-free paths in robotic systems. However, adding dynamic constraints makes the motion planning problem significantly harder, as it requires solving two-value boundary problems (computationally expensive) or propagating random control inputs (uninformative). Alternatively, Iterative Discontinuity Bounded A* (iDb-A*), introduced in our previous study, combines search and optimization iteratively. The search step connects short trajectories (motion primitives) while allowing a bounded discontinuity between the motion primitives, which is later repaired in the trajectory optimization step. Building upon these foundations, in this paper, we present iDb-RRT, a sampling-based kinodynamic motion planning algorithm that combines motion primitives and trajectory optimization within the RRT framework. iDb-RRT is probabilistically complete and can be implemented in forward or bidirectional mode. We have tested our algorithm across a benchmark suite comprising 30 problems, spanning 8 different systems, and shown that iDb-RRT can find solutions up to 10x faster than previous methods, especially in complex scenarios that require long trajectories or involve navigating through narrow passages.

Density of the reachable states can help understand the risk of safety-critical systems, especially in situations when worst-case reachability is too conservative. Recent work provides a data-driven approach to compute the density distribution of autonomous systems' forward reachable states online. In this paper, we study the use of such approach in combination with model predictive control for verifiable safe path planning under uncertainties. We first use the learned density distribution to compute the risk of collision online. If such risk exceeds the acceptable threshold, our method will plan for a new path around the previous trajectory, with the risk of collision below the threshold. Our method is well-suited to handle systems with uncertainties and complicated dynamics as our data-driven approach does not need an analytical form of the systems' dynamics and can estimate forward state density with an arbitrary initial distribution of uncertainties. We design two challenging scenarios (autonomous driving and hovercraft control) for safe motion planning in environments with obstacles under system uncertainties. We first show that our density estimation approach can reach a similar accuracy as the Monte-Carlo-based method while using only 0.01X training samples. By leveraging the estimated risk, our algorithm achieves the highest success rate in goal reaching when enforcing the safety rate above 0.99.

Generating high-quality time series data has emerged as a critical research topic due to its broad utility in supporting downstream time series mining tasks. A major challenge lies in modeling the intrinsic stochasticity of temporal dynamics, as real-world sequences often exhibit random fluctuations and localized variations. While diffusion models have achieved remarkable success, their generation process is computationally inefficient, often requiring hundreds to thousands of expensive function evaluations per sample. Flow matching has emerged as a more efficient paradigm, yet its conventional ordinary differential equation (ODE)-based formulation fails to explicitly capture stochasticity, thereby limiting the fidelity of generated sequences. By contrast, stochastic differential equation (SDE) are naturally suited for modeling randomness and uncertainty. Motivated by these insights, we propose TimeFlow, a novel SDE-based flow matching framework that integrates a encoder-only architecture. Specifically, we design a component-wise decomposed velocity field to capture the multi-faceted structure of time series and augment the vanilla flow-matching optimization with an additional stochastic term to enhance representational expressiveness. TimeFlow is flexible and general, supporting both unconditional and conditional generation tasks within a unified framework. Extensive experiments across diverse datasets demonstrate that our model consistently outperforms strong baselines in generation quality, diversity, and efficiency.

Agentic systems involved in high-stake decision-making under adversarial pressure need formal guarantees not offered by existing approaches. Motivated by the operational needs of security operations centers (SOCs) that must configure endpoint detection and response (EDR) policies under adversarial pressure, we present a tool-mediated architecture: LLM agents use deterministic tools (Stackelberg best-response, Bayesian observer updates, attack-graph primitives) and select from finite action catalogs enforced at the tool-output interface. A composite Lyapunov function machine-checked in Lean 4 with zero sorry certifies controllability, observability from asymmetric sensor data, and Input-to-State Stability (ISS) robustness under intelligent adversarial disturbance, with two corollaries extending the certificate to any controller or adversary from the catalogs. On 282 real enterprise attack graphs, the claims hold with margin. On paired offensive/defensive telemetry, a tool-mediated Claude Sonnet 4 controller reduces the attacker's expected payoff (game value) by 59% relative to a deterministic greedy baseline, with zero variance across 40 runs at four temperatures. A Claude Haiku 4.5 controller converges to suboptimal game values but stays catalog-bounded over an additional 40 runs, demonstrating that architectural stability is not dependent on the controller capability. The LLM agent's non-determinism furthers creative exploration of strategies, while the tool-mediated architecture ensures system stability.