Diffusion-Based Planning

Coordinating multiple robots in shared environments requires generating feasible trajectories for each agent while accounting for interactions among agents. Centralized planning approaches become difficult to scale as the number of robots increases, while decentralized approaches that allow each agent to plan independently do not inherently account for inter-agent interactions. This paper presents a framework for coordinated multi-robot motion planning that combines decentralized generative trajectory planning with multi-agent reinforcement learning (MARL)-based coordination. Each robot independently generates candidate trajectories using a diffusion model trained on single-agent motion data, leveraging the generative model's ability to produce feasible and diverse trajectories. To reduce conflicts between agents, a centralized value function trained via MARL guides the reverse diffusion process through gradient-based steering, enabling interaction-aware trajectory generation without centralized joint planning or retraining of the generative model. This guidance follows an exponential tilting formulation, in which the value function biases the denoising distribution toward trajectories with higher expected multi-agent return. The framework is evaluated in a simulated maze environment with four mobile robots. Experimental results show that the proposed value-guided diffusion planning reduces the inter-agent interference rate from 55.4% to 41.8%, demonstrating that coordination can be effectively achieved while preserving the scalability of decentralized trajectory generation. These results suggest that MARL-based value guidance can effectively introduce coordination into decentralized generative planners without requiring a fully joint multi-robot model.

Diffusion models provide strong priors for generating structured data, but many tasks require outputs beyond the scale on which these models are typically trained. Compositional generation addresses this by composing overlapping local plans from a pretrained short-horizon prior into a long-horizon output. However, standard composition primarily enforces agreement between neighboring local plans, yielding local consistency without directly specifying the global structure of the full composition. As a result, locally compatible plans may still form an implausible route, task sequence, or temporal evolution. Existing methods improve global coherence by repeatedly propagating local consistency signals or by adding inference-time optimization, but these procedures become expensive as the number or dimensionality of local plans increases. We propose Coarse-to-Fine Compositional Diffusion (CoFi), an inference-time sampler that separates global structure formation from local detail refinement. CoFi first aligns local denoised estimates around a shared coarse structure, producing a global scaffold that captures the long-range task-level arrangement. It then diffuses this scaffold to an intermediate noise level and denoises it with the same pretrained local prior, restoring local fine structure while preserving the scaffold-induced global coherence. Across long-horizon robotic planning, panoramic image generation, and long video generation, CoFi not only improves both global coherence and local sample quality over prior compositional baselines, but also requires 2-8x fewer denoiser evaluations.

The diffusion based robot navigation world models are typically trained using parallel supervision, while autoregressive inference is employed during path planning. This results in a distribution shift between training and inference, which destabilizes the performance over long-horizon prediction. We propose AR Forcing, an autoregressive training strategy, which integrates the standard diffusion loss into the autoregressive training loop. At each step, the model uses its own predictions to update the context and optimize the single step noise prediction objective, thereby explicitly exposing the model to the inference state distribution during training. Our method does not require additional discriminators or distribution-matching losses, retains the original diffusion framework and sampler, and is easy to integrate. Experiments on multi-domain navigation datasets (RECON, SCAND, HuRoN, TartanDrive) show that compared with strong baselines, AR Forcing improved the consistency of generated images during long-horizon navigation and the accuracy of predicted trajectories, enhancing robustness of the model in complex known and unknown environments. We will release the code soon.

Diffusion-based planning has achieved strong results in single-agent offline reinforcement learning, yet scaling to many-agent systems remains intractable due to the curse of dimensionality in the joint trajectory space. We introduce MF-Diffuser, a framework that lifts trajectory planning to the Wasserstein space of trajectory distributions, where the propagation of chaos ensures a small representative subset of agents captures the full population dynamics. Our approach features a value-weighted chaotic entropy objective that reconciles generative fidelity with return maximization, and a hierarchical coarse-to-fine strategy that progressively grows the agent population during denoising. We establish end-to-end suboptimality bounds with four interpretable terms, revealing that mean-field approximation error scales as $O(H^2/\sqrt{N})$ while offline distribution shift provably does not grow with population size $N$, and prove the generated policy is an approximate mean-field Nash equilibrium with explicit convergence guarantees. Experiments on three mean-field RL benchmarks -- spanning stage games, sequential dynamics, and adversarial team competition -- show MF-Diffuser achieves the best return in the majority of settings, with the largest gains on suboptimal offline data and at extreme scales ($N \geq 10^3$).

Diffusion models are effective for waypoint prediction in visual navigation, but standard sampling and test time guidance can produce unreliable or inefficient trajectories when updates drift off the training manifold. We propose Fisher Preserving Guidance with Outer Product Span Projection, a training-free inference method that avoids large Fisher drift associated with off-distribution actions while optimizing a task objective. Our method computes the Fisher-preserving update via a low-rank Jacobian factorization, requiring only a single backward pass per step and enabling real-time use. We further introduce Truncated Fisher Denoising Sensitivity as an uncertainty signal and use it for robust multi-sample action blending. Experiments on toy and realistic navigation benchmarks, including Maze2D with TSDF-based guidance, PushT with official Diffusion Policy weights, and visual navigation in simulation and on real robots, demonstrate consistent improvements in performance over strong diffusion-policy baselines without additional training.

Decentralized multi-robot motion planning requires each robot to generate collision-free trajectories from local observations, without global sensing or reliable communication. However, most existing planners, whether classical or learning-based, generate trajectories from a static snapshot of the local observation, which limits their ability to anticipate the future behavior of neighboring robots. This limitation is critical as the number of robots increases and the environment becomes more cluttered. To overcome this challenge, this paper introduces Simulation-Informed Diffusion (SID), a decentralized framework built on constraint-aware diffusion models (CADM). SID first uses CADM to simulate the future trajectories of neighboring robots from their currently observed states, and then uses the same CADM to plan each robot's own trajectory under safety constraints informed by these simulations. Crucially, the accurate simulation of neighbors enables a minimal communication scheme that triggers coordination only when necessary in highly congested scenarios. Experiments across diverse environments show that SID consistently outperforms baseline methods in terms of planning effectiveness and constraint satisfaction, and scales to scenarios with 108 robots and 160 obstacles.

Off-dynamics offline reinforcement learning seeks to learn a target-domain policy from a large source dataset and a limited target dataset under mismatched transition dynamics. Existing approaches such as reward augmentation and data filtering are constrained to the source dataset and cannot synthesize new target behavior to improve coverage beyond the collected source trajectories. While recent model-based methods attempt to address this by learning target-aware dynamics, the generated experience is constructed only at the transition level, which leads to accumulated errors over long horizons. These limitations necessitate a shift toward trajectory-level generation for off-dynamics offline RL. We propose CEDGE, a Cross-domain Energy-guided Diffusion GEneration framework. CEDGE trains a trajectory diffusion model on source-domain trajectories and adapts the generated samples to the target domain through energy guidance. This guidance is derived by minimizing the distribution mismatch between the source and desired target-domain trajectories and is decomposed into return, domain, and behavior energy components. The resulting energy-guided trajectories are useful both for direct planning and as synthetic data for policy learning. Since target adaptation is achieved via energy guidance rather than retraining the diffusion model, CEDGE can be efficiently adapted to new target dynamics compared to previous methods. Experiments on the ODRL benchmark demonstrate that trajectory-level energy-guided generation improves diffusion planning under dynamics shifts and produces synthetic data that improves downstream target policy learning.

The motion planning problem for robotic manipulation can be addressed through classical or deep learning approaches. Existing methods face significant challenges in generalizing to diverse settings. In this study, we present a method with high generalization capability that generates collision-free trajectories using diffusion models where the denoising process is guided by the gradient of the total collision cost. We are also presenting a dynamic approach for choosing start step of the gradient guidance. Experimental results demonstrate that guiding the diffusion model dynamically with the sum of collision costs offers more robust performance by overcoming the generalization issues faced by competing methods. The proposed model demonstrates its effectiveness by achieving the highest performance on diverse test settings in M$π$nets\ dataset among the compared methods.

We consider the problem of combining potential field and ergodic search on multi-robot systems. Traditional ergodic search algorithms use metrics for ergodicity that account for the desired distribution at different scales. Recently, a heat equation-driven ergodic approach was proposed, which adds flexibility to the smoothing of the ergodic metric. However, such an approach, as it is an isotropic diffusion, propagates the error uniformly in all directions, regardless of changes in the desired distribution. We introduce a general class of anisotropic diffusion formulation of the ergodicity problem, which generates a potential field for the ergodic search. We demonstrate that this approach generalizes previous results, which consider radial basis functions and the solution of the heat equation to represent the difference between the goal density distribution and the covered trajectories. In our solution, the agent movement is directed using the gradient of the solution of the Perona-Malik diffusion, and our formulation includes the heat equation as a special case. We demonstrate the methodology with a series of simulations in different scenarios.

Current end-to-end autonomous driving systems are fundamentally limited by a mismatch between temporal causal reasoning and global trajectory consistency. Autoregressive (AR) models capture interaction-aware temporal dependencies via causal factorization, but their step-wise decoding leads to error accumulation and suboptimal global structure. In contrast, diffusion models optimize trajectories globally but lack explicit causal constraints, making them unreliable in interactive and safety-critical scenarios. This dichotomy reveals a deeper issue: existing methods treat causal modeling and global optimization as separate paradigms, without a principled way to unify them within a single trajectory distribution. To address this, we propose ChainFlow-VLA, which unifies causal generation and global refinement within a unified probabilistic framework. We formulate planning as a mixture over AR-induced modes and learn Vision-Language Model (VLM)-conditioned residual distributions over these modes. An autoregressive generator (Chain) produces a discrete set of causal trajectory modes, followed by a diffusion-based refiner (Flow) that leverages VLM hidden states as semantic priors to perform mode-conditioned correction in residual space while preserving causal structure. This straightforward conditioning seamlessly injects high-level scene understanding into fine-grained trajectory adjustments. Experiments demonstrate that ChainFlow-VLA achieves robust planning in ambiguous and long-tail scenarios, achieving a state-of-the-art score of 94.85 on the NAVSIM v1 leaderboard, matching human-level performance (94.8). Code will be available at https://github.com/AFARI-Research/ChainFlow-VLA.

Ride-hailing platforms like DiDi Chuxing operate in highly dynamic environments where balancing driver supply and passenger demand is critical. Although driver-side subsidies serve as a primary lever to align these forces and improve key KPIs like completed rides (\texttt{Rides}) and gross merchandise value (\texttt{GMV}), optimizing them in production requires simultaneously meeting three constraints: (i) responsiveness to stochastic shocks, (ii) strict subsidy-rate caps, and (iii) low-latency execution at city scale. These requirements rule out expensive per-order optimization, calling for a forward-looking, constraint-aware city-level controller for online sequential decision making. To meet these requirements, we introduce D$^3$-Subsidy (Dynamic Driver-side Diffusion-based Subsidy), a hierarchical diffusion-based framework for deployable city-wide subsidy control. To bridge the train-inference gap, D$^3$-Subsidy employs a prefix-conditioned diffusion model that samples plausible future trajectories from immutable historical observations, ensuring the training protocol aligns with the fixed-history nature of online deployment. These generated plans are then decoded by a context-conditioned inverse module into low-dimensional city-level control signals. For scalable execution, we bridge the gap between city-level planning and fine-grained dispatch via a Lagrangian-dual-derived mapping, which embeds subsidy-rate caps directly into order-driver incentives without iterative optimization. Additionally, a multi-city pretraining strategy with parameter-efficient fine-tuning enables robust transfer across heterogeneous cities. Extensive offline evaluations demonstrate that D$^3$-Subsidy improves \texttt{Rides} and \texttt{GMV} while enhancing cap compliance, and a real-world A/B test confirms significant uplift while keeping budget-related violation metrics within operational thresholds.

Compositional diffusion models offer a promising route to long-horizon planning by denoising multiple overlapping sub-trajectories while ensuring that together they constitute a global solution. However, enforcing local behavior over long chains is often insufficient for a coherent global structure to emerge. Recent works tackle this limitation through intrinsic search, which explores multiple paths during the denoising process. While intrinsic search improves global coherence, it comes at the cost of repeated evaluations of an already compute-heavy model. In this work, we argue that extrinsic search, performed outside the denoising process, offers a more effective mode of exploration for long-horizon planning while naturally enabling the use of classical algorithms to solve unseen combinatorial tasks at test time. Our eXtrinsic search-guided Diffuser (XDiffuser) first computes a plan over a state-space graph -- serving as a lightweight local connectivity oracle for the diffusion model. The plan is then used to guide denoising for a single trajectory, effectively offloading the burden of exploration. XDiffuser outperforms diffusion-based baselines on long-horizon tasks, with particularly large gains in the low-quality data regime and on unseen tasks beyond goal-reaching, including multi-agent coordination and TSP-style reasoning. Project website: https://yanivhass.github.io/XDiffuser-site/

End-to-End (E2E) autonomous driving models have shown growing capability in recent years, with performance improving on increasingly challenging benchmarks. However, modern generative E2E planners still suffer from a substantial number of catastrophic failures in safety-critical scenarios. We find that many such failures arise from violations of physical constraints and safety requirements, leading to unsafe behavior. Motivated by this finding, in this paper, we focus on improving safety outcomes in generative end-to-end driving with a targeted reduction of catastrophic planning failures, instead of enhancing average planning quality. Towards this end, we propose DriveSafer, a failure-aware safety framework for end-to-end planners. DriveSafer explicitly steers generative planners towards safe behaviors leveraging both training-time safety constraints and inference-time safety guidance. Compared to the state-of-the-art DiffusionDrive model, on the NAVSIM benchmark, DriveSafer reduces the number of catastrophic failures (PDMS=0) by 48%, with over 65% reduction in drivable-area compliance failures.

Recent work has framed decision-making as a sequence modeling problem using generative models such as diffusion models. Although promising, these approaches often overlook latent factors that exhibit evolving dynamics, elements that are fundamental to environment transitions, reward structures, and high-level agent behavior. Explicitly modeling these hidden processes is essential for both precise dynamics modeling and effective decision-making. In this paper, we propose a unified framework that explicitly incorporates latent dynamic inference into generative decision-making from minimal yet sufficient observations. We theoretically show that under mild conditions, the latent process can be identified from small temporal blocks of observations. Building on this insight, we introduce Ada-Diffuser, a causal diffusion model that learns the temporal structure of observed interactions and the underlying latent dynamics simultaneously, and furthermore, leverages them for planning and control. With a modular design, Ada-Diffuser supports both planning and policy learning tasks, enabling adaptation to latent variations in dynamics, rewards, and latent actions. Experiments on simulated control and robotic benchmarks demonstrate its effectiveness in accurate latent inference and adaptive policy learning.

Multi-Agent Path Finding (MAPF) is a coordination problem that requires computing globally consistent, collision-free trajectories from individual start positions to assigned goal positions under combinatorial planning complexity. In dense environments, suboptimal initial plans induce compound conflicts that hinder feasible repair. For repair-based solvers like LNS2, initial plan quality critically affects downstream repair, yet this factor remains underexplored. We propose DiffLNS, a hybrid framework that integrates a discrete denoising diffusion probabilistic model (D3PM) with LNS2. The D3PM serves as an initializer with sparse social attention that learns a spatiotemporal prior over coordinated multi-agent action trajectories from expert demonstrations and samples multiple joint plans. Operating directly on the categorical action space, our discrete diffusion preserves the MAPF action structure and samples from a multimodal joint-plan distribution to produce diverse drafts well suited for neighborhood repair. These drafts act as warm starts for downstream repair, which completes unfinished trajectories and resolves remaining conflicts under hard MAPF constraints. Experimental results show that despite being trained only on instances with at most 96 agents, the initializer generalizes to scenarios with up to 312 agents at inference time. Across 20 complex and congested settings, DiffLNS achieves an average success rate of 95.8%, outperforming the strongest tested baseline by 9.6 percentage points and matching or exceeding all baselines in all 20 settings. To the best of our knowledge, this is the first work to leverage discrete diffusion for warm-starting an LNS-based MAPF solver.

A plausible scene evolution depends on the maneuver being considered, while a good maneuver depends on how the scene may evolve. Existing World Action Models (WAMs) largely miss this reciprocity, treating world prediction and action generation as either isolated parallel branches or rigid predict-then-plan pipelines. We formalize this perspective as World-Action Interactive Models (WAIMs), and instantiate it in autonomous driving with \textbf{DAWN} (\textbf{D}enoising \textbf{A}ctions and \textbf{W}orld i\textbf{N}teractive model), a simple yet strong latent generative baseline. DAWN operates in a compact semantic latent space and couples a \emph{World Predictor} with a \emph{World-Conditioned Action Denoiser}: the predicted world hypothesis conditions action denoising, while the denoised action hypothesis is fed back to update the world prediction, so that both are recursively refined during inference. Rather than eliminating test-time world evolution altogether or rolling out the full future in pixel space, DAWN performs a short explicit latent rollout that is sufficient to support long-horizon trajectory generation in complex interactive scenes. Experiments show that DAWN achieves strong planning performance and favorable safety-related results across multiple autonomous driving benchmarks. More broadly, our results suggest that interactive world-action generation is a principled path toward truly actionable world models.

Vision-Language-Action (VLA) models have emerged as a promising paradigm for end-to-end autonomous driving. However, existing reasoning mechanisms still struggle to provide planning-oriented intermediate representations: textual Chain-of-Thought (CoT) fails to preserve continuous spatiotemporal structure, while latent world reasoning remains difficult to use as a direct condition for action generation. In this paper, we propose CoWorld-VLA, a multi-expert world reasoning framework for autonomous driving, where world representations serve as explicit conditions to guide action planning. CoWorld-VLA extracts complementary world information through multi-source supervision and encodes it into expert tokens within the VLA, thereby providing planner-accessible conditioning signals. Specifically, we construct four types of tokens: semantic interaction, geometric structure, dynamic evolution, and ego trajectory tokens, which respectively model interaction intent, spatial structure, future temporal dynamics, and behavioral goals. During action generation, CoWorld-VLA employs a diffusion-based hierarchical multi-expert fusion planner, which is coupled with scene context throughout the joint denoising process to generate continuous ego trajectories. Experiments show that CoWorld-VLA achieves competitive results in both future scene generation and planning on the NAVSIM v1 benchmark, demonstrating strong performance in collision avoidance and trajectory accuracy. Ablation studies further validate the complementarity of expert tokens and their effectiveness as planning conditions for action generation. Code will be available at https://github.com/AFARI-Research/CoWorld-VLA.

Diffusion-based trajectory planners can synthesize rich, multimodal robot motions, but their iterative denoising makes online planning and control prohibitively slow. Existing accelerations either modify the sampler or compress the network--sacrificing plan quality or requiring retraining without accounting for downstream control risk. We address the problem of making diffusion-based trajectory planners fast enough for real-time robot use without retraining the model or sacrificing trajectory quality, and in a way that works across diverse state-space diffusion architectures. Our key insight is that diffusion trajectory planners expose two signals we can exploit: a cheap probe of how their internal trajectory representation changes across steps, and analytic coefficients that describe how denoiser errors affect the sampler's state update. By calibrating the first signal against the second on offline runs, we obtain a per-step score that upper-bounds how far the final trajectory can deviate when we reuse a cached denoiser output, and we treat this bound as an uncertainty budget that we can spend over the denoising process. Building on this insight, we present Muninn, a training-free caching wrapper that tracks this uncertainty budget during sampling and, at each diffusion step, chooses between reusing a cached denoiser output when the predicted deviation is small and recomputing the denoiser when it is not. Across standard benchmarks Muninn delivers up to 4.6x wall-clock speedups across several trajectory diffusion models by reducing denoiser evaluations, while preserving task performance and safety metrics. Muninn further certifies that cached rollouts remain within a specified distance of their full-compute counterparts, and we validate these gains in real-time closed-loop navigation and manipulation hardware deployments. Project page: https://github.com/gokulp01/Muninn.

Reasoning-based end-to-end (E2E) autonomous driving has recently emerged as a promising approach to improving the interpretability of driving decisions as it can generate human-readable reasoning together with predicted trajectories. Such approaches commonly generate multiple trajectories to capture diverse future behaviors, and they fall into two categories: (1) multi-reasoning, where one reasoning sequence is generated per trajectory, and (2) single-reasoning, where a single reasoning is shared across all trajectories. The former offers richer diversity at the cost of redundant computation, while the latter is more efficient but is often assumed to sacrifice diversity. Alpamayo 1, a representative system, adopts the multi-reasoning approach and achieves competitive trajectory prediction performance. However, the efficiency of this design remains largely unexplored, making it a well-motivated subject for investigation. In this paper, we systematically analyze and improve Alpamayo 1 in two ways. First, we reduce inference latency while preserving trajectory diversity by redesigning Alpamayo 1 into a single-reasoning system. Through extensive experiments, we find that replacing multi-reasoning with single-reasoning does not meaningfully degrade trajectory diversity. Second, we accelerate diffusion-based action generation by eliminating inter-block overhead arising from unnecessary copy operations and inefficient kernel execution. Through closed-loop and open-loop experiments, we validate both optimizations, demonstrating a 69.23% reduction in inference latency while maintaining trajectory diversity and prediction quality. These results highlight the importance of jointly analyzing system architecture and runtime execution to improve the efficiency of reasoning-based E2E AD systems.

Recent advances in generative models have shown promise in generating behavior plans for long-horizon, sparse reward tasks. While these approaches have achieved promising results, they often lack a principled framework for hierarchical decomposition and struggle with the computational demands of real-time execution, due to their iterative denoising process. In this work, we introduce Hierarchical Diffusion-Flow (HDFlow), a novel hierarchical planning framework that optimally leverages the strengths of diffusion and rectified flow models to overcome the limitations of single-paradigm generative planners. HDFlow employs a high-level diffusion planner to generate sequences of strategic subgoals in a learned latent space, capitalizing on diffusion's powerful exploratory capabilities. These subgoals then guide a low-level rectified flow planner that generates smooth and dense trajectories, exploiting the speed and efficiency of ordinary differential equation (ODE)-based trajectory generation. We evaluate HDFlow on four challenging furniture assembly tasks in both simulation and real-world, where it significantly outperforms state-of-the-art methods. Furthermore, we also showcase our method's generalizability on two long-horizon benchmarks comprising diverse locomotion and manipulation tasks. Project website: https://hdflow-page.github.io/

Compositional diffusion planning generates long-horizon trajectories by stitching together overlapping short-horizon segments through score composition. However, when local plan distributions are multimodal, existing compositional methods suffer from mode-averaging, where averaging incompatible local modes leads to plans that are neither locally feasible nor globally coherent. We propose Refining Compositional Diffusion (RCD), a training-free guidance method that steers compositional sampling toward high-density, globally coherent plans. RCD leverages the self-reconstruction error of a pretrained diffusion model as a proxy for the log-density of composed plans, combined with an overlap consistency term that enforces consistency at segment boundaries. We show that the combined guidance concentrates sampling on high-density plans that mitigate mode-averaging. Experiments on challenging long-horizon tasks from OGBench, including locomotion, object manipulation, and pixel-based observations, demonstrate that RCD consistently outperforms existing methods.

Offline safe reinforcement learning often requires policies to adapt at deployment time to safety budgets that vary across episodes or change within a single episode. While diffusion-based planners enable flexible trajectory generation, existing guidance schemes often treat reward improvement and constraint satisfaction as competing gradient objectives, which can lead to unreliable safety compliance under cost limits. We reinterpret adaptive safe trajectory generation as sampling from a constrained trajectory distribution, where the budget restricts the trajectory region, and reward shapes preferences within that region. This perspective motivates Safe Decoupled Guidance Diffusion (SDGD), which conditions classifier-free guidance on the cost limit to bias sampling toward trajectories satisfying the specified limit, while using reward-gradient guidance to refine trajectories for higher return. Because direct reward guidance can increase return while also steering samples toward trajectories with higher cumulative cost, we introduce Feasible Trajectory Relabeling (FTR) to reshape reward targets and discourage such directions. We further provide a first-order sampling-time analysis showing that FTR suppresses reward-induced cost drift under a prefix-restorative alignment condition. Extensive evaluations on the DSRL benchmark show that SDGD achieves the strongest safety compliance among baselines, satisfying the constraint on 94.7% of tasks (36/38), while obtaining the highest reward among safe methods on 21 tasks.

We present Action Agent, a two-stage framework that unifies agentic navigation video generation with flow-constrained diffusion control for multi-embodiment robot navigation. In Stage I, a large language model (LLM) acts as an orchestration module that selects video diffusion models, refines prompts through iterative validation, and accumulates cross-task memory to synthesize physically plausible first-person navigation videos from language and image inputs. This increases video generation success from 35% (single-shot) to 86% across 50 navigation tasks. In Stage II, we introduce FlowDiT, a Flow-Constrained Diffusion Transformer that converts optimized goal videos and language instructions into continuous velocity commands using action-space denoising diffusion. FlowDiT integrates DINOv2 visual features, learned optical flow for ego-motion representation, and CLIP language embeddings for semantic stopping. We pretrain on the RECON outdoor navigation dataset and fine-tune on 203 Unitree G1 humanoid episodes collected in Isaac Sim to calibrate velocity dynamics. A single 43M-parameter checkpoint achieves 73.2% navigation success in simulation and 64.7% task completion on a real Unitree G1 in unseen indoor environments under open-loop execution, while operating at 40--47 Hz. We evaluate Action Agent across three embodiments: a Unitree G1 humanoid (real hardware), a drone, and a wheeled mobile robot (Isaac Sim), demonstrating that decoupling trajectory imagination from execution yields a scalable and embodiment-aware paradigm for language-guided navigation.

Visual planning represents a crucial facet of human intelligence, especially in tasks that require complex spatial reasoning and navigation. Yet, in machine learning, this inherently visual problem is often tackled through a verbal-centric lens. While recent research demonstrates the promise of fully visual approaches, they suffer from significant computational inefficiency due to the step-by-step planning-by-generation paradigm. In this work, we present EAR, an editing-as-reasoning paradigm that reformulates visual planning as a single-step image transformation. To isolate intrinsic reasoning from visual recognition, we employ abstract puzzles as probing tasks and introduce AMAZE, a procedurally generated dataset that features the classical Maze and Queen problems, covering distinct, complementary forms of visual planning. The abstract nature of AMAZE also facilitates automatic evaluation of autoregressive and diffusion-based models in terms of both pixel-wise fidelity and logical validity. We assess leading proprietary and open-source editing models. The results show that they all struggle in the zero-shot setting, finetuning on basic scales enables remarkable generalization to larger in-domain scales and out-of-domain scales and geometries. However, our best model that runs on high-end hardware fails to match the zero-shot efficiency of human solvers, highlighting a persistent gap in neural visual reasoning.

Multi-modal trajectory generation is essential for safe autonomous driving, yet existing diffusion-based planners suffer from high inference latency due to iterative neural function evaluations. This paper presents MISTY (Mixer-based Inference for Single-step Trajectory-drifting Yield), a high-throughput generative motion planner that achieves state-of-the-art closed-loop performance with pure single-step inference. MISTY integrates a vectorized Sub-Graph encoder to capture environment context, a Variational Autoencoder to structure expert trajectories into a compact 32-dimensional latent manifold, and an ultra-lightweight MLP-Mixer decoder to eliminate quadratic attention complexity. Importantly, we introduce a latent-space drifting loss that shifts the complex distribution evolution entirely to the training phase. By formulating explicit attractive and repulsive forces, this mechanism empowers the model to synthesize novel, proactive maneuvers, such as active overtaking, that are virtually absent from the raw expert demonstrations. Extensive evaluations on the nuPlan benchmark demonstrate that MISTY achieves state-of-the-art results on the challenging Test14-hard split, with comprehensive scores of 80.32 and 82.21 in non-reactive and reactive settings, respectively. Operating at over 99 FPS with an end-to-end latency of 10.1 ms, MISTY offers an order-of-magnitude speedup over iterative diffusion planners while while achieving significantly robust generation.

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.

Autonomous driving in complex traffic requires planners that generalize beyond hand-crafted rules, motivating data-driven approaches that learn behavior from expert demonstrations. Diffusion-based trajectory planners have recently shown strong closed-loop performance by iteratively denoising a full-horizon plan, but they remain difficult to certify and can fail catastrophically in rare or out-of-distribution scenarios. To address this challenge, we present PC-Diffuser, a safety augmentation framework that embeds a certifiable, path-consistent barrier-function structure directly into the denoising loop of diffusion planning. The key idea is to make safety an intrinsic part of trajectory generation rather than a post-hoc fix: we enforce forward invariance along the rollout while preserving the diffusion model's intended path geometry. Specifically, PC-Diffuser (i) evaluates collision risk using a capsule-distance barrier function that better reflects vehicle geometry and reduces unnecessary conservativeness, (ii) converts denoised waypoints into dynamically feasible motion under a kinematic bicycle model, and (iii) applies a path-consistent safety filter that eliminates residual constraint violations without geometric distortion, so the corrected plan remains close to the learned distribution. By injecting these safety-consistent corrections at every denoising step and feeding the refined trajectory back into the diffusion process, PC-Diffuser enables iterative, context-aware safeguarding instead of post-hoc repair...

Visual traversability estimation is central to autonomous navigation, yet most approaches either rely on prompt-driven Vision-Language Model (VLM) or decouple traversability from trajectory planning, requiring separate planners with heavy mapping, manual tuning, and extended deployment time. We propose EmbodiedDiffusion, a diffusion-based framework that simultaneously predicts traversability maps and generates feasible trajectories from RGB images using planner-free synthetic supervision and embodiment conditioning for cross-platform transfer. The framework distills category-level traversability semantics from a VLM teacher into a lightweight student model during training, enabling prompt-free, real-time inference at deployment. A modular FiLM-based conditioning mechanism isolates embodiment-specific reasoning into a compact trainable subset of the network, allowing rapid adaptation to new robot platforms without retraining the visual backbone or the trajectory diffusion model. Across indoor environments with quadruped and aerial robots, EmbodiedDiffusion achieves 80-100% navigation success in the full-data regime with real-time inference (90 ms) and adapts to new platforms using only 10 min of visual data collection, demonstrating scalable, unified traversability reasoning and trajectory generation for heterogeneous robots.

Most end-to-end autonomous driving methods rely on imitation learning from single expert demonstrations, often leading to conservative and homogeneous behaviors that limit generalization in complex real-world scenarios. In this work, we propose DIVER, an end-to-end driving framework that integrates reinforcement learning with diffusion-based generation to produce diverse and feasible trajectories. At the core of DIVER lies a reinforced diffusion-based generation mechanism. First, the model conditions on map elements and surrounding agents to generate multiple reference trajectories from a single ground-truth trajectory, alleviating the limitations of imitation learning that arise from relying solely on single expert demonstrations. Second, reinforcement learning is employed to guide the diffusion process, where reward-based supervision enforces safety and diversity constraints on the generated trajectories, thereby enhancing their practicality and generalization capability. Furthermore, to address the limitations of L2-based open-loop metrics in capturing trajectory diversity, we propose a novel Diversity metric to evaluate the diversity of multi-mode predictions.Extensive experiments on the closed-loop NAVSIM and Bench2Drive benchmarks, as well as the open-loop nuScenes dataset, demonstrate that DIVER significantly improves trajectory diversity, effectively addressing the mode collapse problem inherent in imitation learning.

This work presents an optimization method for generating kinodynamically feasible and collision-free multi-robot trajectories that exploits an incremental denoising scheme in diffusion models. Our key insight is that high-quality trajectories can be discovered merely by denoising noisy trajectories sampled from a distribution. This approach has no learning component, relying instead on only two ingredients: a dynamical model of the robots to obtain feasible trajectories via rollout, and a fitness function to guide denoising with Monte Carlo gradient approximation. The proposed framework iteratively optimizes a deformation for the previous trajectory with the current denoising process, allows anytime refinement as time permits, supports different dynamics, and benefits from GPU acceleration. Our evaluations for differential-drive and holonomic teams with up to 16 robots in 2D and 3D worlds show its ability to discover high-quality solutions faster than other black-box optimization methods such as MPPI. In a 2D holonomic case with 16 robots, it is almost twice as fast. As evidence for feasibility, we demonstrate zero-shot deployment of the planned trajectories on eight multirotors. Code and video: https://github.com/proroklab/d4orm