Daily Papers

Looped Transformers increase test-time computation by repeatedly applying a shared recurrent block. Learned halting objectives in looped Transformers typically use a single exit distribution both as the inference-time stopping rule and as the training-time weighting of per-depth losses. This entangles exit selection with trajectory formation: the gate not only chooses which recurrent state to use, but also determines how strongly each intermediate state is supervised. Consequently, poor adaptive-compute performance can arise from the readout, the induced trajectory, or their interaction. We study adaptive depth in looped Transformers through this trajectory--readout lens, across controlled synthetic tasks (modular arithmetic and binary parity) and large-scale Ouro-1.4B and 2.6B checkpoints. We find that fixed-prior depth supervision, which shapes the trajectory without an input-dependent halting policy, produces difficulty-aware trajectories whose intermediate states expose useful stopping signals, and that simple post-hoc confidence readouts often match or outperform learned linear and MLP gates. Fitting gates on frozen trajectories localizes the failure: it appears to stem mainly from the trajectory induced by joint gate training rather than from limited gate expressivity. The same pattern is present in Ouro evaluations, where pretrained ponder gates are competitive but not uniformly Pareto-optimal, and measured latency confirms that the resulting reductions in average exit depth translate into practical inference-time savings. Our systematic diagnostic evaluation reframes adaptive depth in looped Transformers as a joint problem of trajectory formation and exit readout, rather than gate learning alone, highlighting a distinction that prior learned-halting work has often left implicit.

Agent skills can remarkably improve task success rates by using human-written procedural documents, but their quality is difficult to assess without environment-grounded verification. Existing skill generation methods heavily rely on preference logs rather than direct environment interaction, often yielding negligible or even degraded gains. We identify that it is a fundamental timing bottleneck: robust skills should be posterior-based, distilled from empirical environment interaction rather than prior plans. In this study, we introduce the Posterior Distillation Index (PDI), a trajectory-level metric that quantifies how well a distilled skill is grounded in the task-environment evidence. To operationalize PDI, we present SPARK (Structured Pipelines for Autonomous Runnable tasKs and sKill generation) for preserving task execution evidence towards full trajectory-level analysis. SPARK generates environment-verified trajectories used to compute PDI, and it applies PDI as an online diagnostic and intervention signal to ensure posterior skill formation. Across 86 runnable tasks, SPARK-generated skills consistently surpass no-skill baselines and outperform human-written skills on student models (inference cost up to 1,000x cheaper than teacher models). These findings show that PDI-guided distillation produces efficient and transferable skills grounded in the task-environment interaction. We release our code at https://github.com/EtaYang10th/spark-skills .

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path, and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Furthermore, we discretize the set of velocity profiles along a given path into a selection of acceleration way-points along the path. Gradient-descent is then employed to minimize cost over feasible choices of the second derivative of curvature, and acceleration way-points, resulting in a method that repeatedly solves the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods.

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 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.

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.

We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To solve it, we propose a biconvex method that quickly produces an initial trajectory and iteratively refines it by solving two convex subproblems in alternation. This method is guaranteed to converge, returns a feasible trajectory even if stopped early, and does not require the selection of any line-search or trust-region parameter. Exhaustive experiments show that our method finds high-quality trajectories in a fraction of the time of state-of-the-art solvers for nonconvex optimization. In addition, it achieves runtimes comparable to industry-standard waypoint-based motion planners, while consistently designing lower-duration trajectories than existing optimization-based planners.

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/.

Coordinated path following in multi-agent systems is a key challenge in robotics, with applications in automated logistics, surveillance, and collaborative exploration. Traditional formation control techniques often rely on time-parameterized trajectories and path integrals, which can result in synchronization issues and rigid behavior. In this work, we address the problem of sequential path following, where agents maintain fixed spatial separation along a common trajectory, guided by a leader under centralized control. We introduce Robot Conga, a leader-follower control strategy that updates each agent's desired state based on the leader's spatial displacement rather than time, assuming access to a global position reference, an assumption valid in indoor environments equipped with motion capture, vision-based tracking, or UWB localization systems. The algorithm was validated in simulation using both TurtleBot3 and quadruped (Laikago) robots. Results demonstrate accurate trajectory tracking, stable inter-agent spacing, and fast convergence, with all agents aligning within 250 time steps (approx. 0.25 seconds) in the quadruped case, and almost instantaneously in the TurtleBot3 implementation.

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.

Recent advances in motion planning for autonomous driving have led to models capable of generating high-quality trajectories. However, most existing planners tend to fix their policy after supervised training, leading to consistent but rigid driving behaviors. This limits their ability to reflect human preferences or adapt to dynamic, instruction-driven demands. In this work, we propose a diffusion-based multi-head trajectory planner(M-diffusion planner). During the early training stage, all output heads share weights to learn to generate high-quality trajectories. Leveraging the probabilistic nature of diffusion models, we then apply Group Relative Policy Optimization (GRPO) to fine-tune the pre-trained model for diverse policy-specific behaviors. At inference time, we incorporate a large language model (LLM) to guide strategy selection, enabling dynamic, instruction-aware planning without switching models. Closed-loop simulation demonstrates that our post-trained planner retains strong planning capability while achieving state-of-the-art (SOTA) performance on the nuPlan val14 benchmark. Open-loop results further show that the generated trajectories exhibit clear diversity, effectively satisfying multi-modal driving behavior requirements. The code and related experiments will be released upon acceptance of the paper.

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.

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.

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

Multi-turn user-facing agents must infer user intent from incomplete requests, collect missing information through dialogue and tools, and execute valid actions. A training trajectory records this process as an interleaved sequence of user messages, agent responses, tool calls, etc. Synthesizing sufficiently complex trajectory has become a central route to train agents: existing pipelines often increase difficulty by composing multiple user requests into longer tasks, producing write-intensive trajectories that train sequential execution. We argue that a single write decision can itself be difficult when the agent must gather and compare substantial read-tool evidence before its arguments become identifiable, a challenge that write-intensive data alone cannot address. Guided by this insight, we propose WRIT (Write-Read Intensive Trajectory Synthesis), a pipeline for synthesizing multi-turn agent training trajectories along two complexity axes: the number of write decisions in a task and the evidence burden of each individual decision. WRIT first generates write-intensive and read-heavy tasks. It then diversifies user behavior instructions to reflect realistic conversational variation, and finally simulates agent-user interactions in an executable environment to produce complete training trajectories. The resulting data trains agents not only for longer task execution, but also for robust, evidence-grounded decision making under high information load. With only 2K synthesized trajectories, a 4B model trained on WRIT outperforms GPT-5.1 no-think on τ^2-bench and substantially reduces inference-time token usage, showing that compact SFT data can convert part of expensive test-time reasoning into efficient agent behavior.

Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous differential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization problem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of Bézier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap rounding of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time.

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 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.

Trajectory generation has garnered significant attention from researchers in the field of spatio-temporal analysis, as it can generate substantial synthesized human mobility trajectories that enhance user privacy and alleviate data scarcity. However, existing trajectory generation methods often focus on improving trajectory generation quality from a singular perspective, lacking a comprehensive semantic understanding across various scales. Consequently, we are inspired to develop a HOlistic SEmantic Representation (HOSER) framework for navigational trajectory generation. Given an origin-and-destination (OD) pair and the starting time point of a latent trajectory, we first propose a Road Network Encoder to expand the receptive field of road- and zone-level semantics. Second, we design a Multi-Granularity Trajectory Encoder to integrate the spatio-temporal semantics of the generated trajectory at both the point and trajectory levels. Finally, we employ a Destination-Oriented Navigator to seamlessly integrate destination-oriented guidance. Extensive experiments on three real-world datasets demonstrate that HOSER outperforms state-of-the-art baselines by a significant margin. Moreover, the model's performance in few-shot learning and zero-shot learning scenarios further verifies the effectiveness of our holistic semantic representation.

We propose GoalFlow, an end-to-end autonomous driving method for generating high-quality multimodal trajectories. In autonomous driving scenarios, there is rarely a single suitable trajectory. Recent methods have increasingly focused on modeling multimodal trajectory distributions. However, they suffer from trajectory selection complexity and reduced trajectory quality due to high trajectory divergence and inconsistencies between guidance and scene information. To address these issues, we introduce GoalFlow, a novel method that effectively constrains the generative process to produce high-quality, multimodal trajectories. To resolve the trajectory divergence problem inherent in diffusion-based methods, GoalFlow constrains the generated trajectories by introducing a goal point. GoalFlow establishes a novel scoring mechanism that selects the most appropriate goal point from the candidate points based on scene information. Furthermore, GoalFlow employs an efficient generative method, Flow Matching, to generate multimodal trajectories, and incorporates a refined scoring mechanism to select the optimal trajectory from the candidates. Our experimental results, validated on the NavsimDauner2024_navsim, demonstrate that GoalFlow achieves state-of-the-art performance, delivering robust multimodal trajectories for autonomous driving. GoalFlow achieved PDMS of 90.3, significantly surpassing other methods. Compared with other diffusion-policy-based methods, our approach requires only a single denoising step to obtain excellent performance. The code is available at https://github.com/YvanYin/GoalFlow.

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/

Imitation learning method has shown immense promise for robotic manipulation, yet its practical deployment is fundamentally constrained by the data scarcity. Despite prior work on collecting large-scale datasets, there still remains a significant gap to robust spatial generalization. We identify a key limitation: individual trajectories, regardless of their length, are typically collected from a single, static spatial configuration of the environment. This includes fixed object and target spatial positions as well as unchanging camera viewpoints, which significantly restricts the diversity of spatial information available for learning. To address this critical bottleneck in data efficiency, we propose MOtion-Based Variability Enhancement (MOVE), a simple yet effective data collection paradigm that enables the acquisition of richer spatial information from dynamic demonstrations. Our core contribution is an augmentation strategy that injects motion into any movable objects within the environment for each demonstration. This process implicitly generates a dense and diverse set of spatial configurations within a single trajectory. We conduct extensive experiments in both simulation and real-world environments to validate our approach. For example, in simulation tasks requiring strong spatial generalization, MOVE achieves an average success rate of 39.1\%, a 76.1\% relative improvement over the static data collection paradigm (22.2\%), and yields up to 2--5times gains in data efficiency on certain tasks. Our code is available at https://github.com/lucywang720/MOVE.

Coordinated flight of multiple drones allows to achieve tasks faster such as search and rescue and infrastructure inspection. Thus, pushing the state-of-the-art of aerial swarms in navigation speed and robustness is of tremendous benefit. In particular, being able to account for unexplored/unknown environments when planning trajectories allows for safer flight. In this work, we propose the first high-speed, decentralized, and synchronous motion planning framework (HDSM) for an aerial swarm that explicitly takes into account the unknown/undiscovered parts of the environment. The proposed approach generates an optimized trajectory for each planning agent that avoids obstacles and other planning agents while moving and exploring the environment. The only global information that each agent has is the target location. The generated trajectory is high-speed, safe from unexplored spaces, and brings the agent closer to its goal. The proposed method outperforms four recent state-of-the-art methods in success rate (100% success in reaching the target location), flight speed (67% faster), and flight time (42% lower). Finally, the method is validated on a set of Crazyflie nano-drones as a proof of concept.

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.

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

The objective function used in trajectory optimization is often non-convex and can have an infinite set of local optima. In such cases, there are diverse solutions to perform a given task. Although there are a few methods to find multiple solutions for motion planning, they are limited to generating a finite set of solutions. To address this issue, we presents an optimization method that learns an infinite set of solutions in trajectory optimization. In our framework, diverse solutions are obtained by learning latent representations of solutions. Our approach can be interpreted as training a deep generative model of collision-free trajectories for motion planning. The experimental results indicate that the trained model represents an infinite set of homotopic solutions for motion planning problems.

Drones equipped with cameras are emerging as a powerful tool for large-scale aerial 3D scanning, but existing automatic flight planners do not exploit all available information about the scene, and can therefore produce inaccurate and incomplete 3D models. We present an automatic method to generate drone trajectories, such that the imagery acquired during the flight will later produce a high-fidelity 3D model. Our method uses a coarse estimate of the scene geometry to plan camera trajectories that: (1) cover the scene as thoroughly as possible; (2) encourage observations of scene geometry from a diverse set of viewing angles; (3) avoid obstacles; and (4) respect a user-specified flight time budget. Our method relies on a mathematical model of scene coverage that exhibits an intuitive diminishing returns property known as submodularity. We leverage this property extensively to design a trajectory planning algorithm that reasons globally about the non-additive coverage reward obtained across a trajectory, jointly with the cost of traveling between views. We evaluate our method by using it to scan three large outdoor scenes, and we perform a quantitative evaluation using a photorealistic video game simulator.

Urban mobility is naturally expressed both as trajectories in space and as natural-language descriptions of travel intent, constraints, and preferences. However, prior work rarely evaluates these two modalities together on the same real-world trajectories: trajectory modeling often stays geometry-centric, while language-centric mobility benchmarks frequently target route planning and tool use rather than fine-grained, verifiable alignment between text and the underlying route. We introduce TrajPrism, a multi-task benchmark for language-trajectory alignment that unifies (i) instruction-conditioned trajectory generation, (ii) language-driven semantic trajectory retrieval, and (iii) trajectory captioning, together with an evaluation protocol that measures trajectory fidelity, retrieval quality, and language groundedness. We construct TrajPrism by pairing real urban trajectories with judge-filtered language annotations generated under a four-dimensional travel-intent taxonomy. The benchmark contains 300K selected trajectories across Porto, San Francisco, and Beijing, yielding 2.1M task instances from three instruction variants, three retrieval queries, and one caption per trajectory. We further develop proof-of-concept models for each task: TrajAnchor for instruction-conditioned trajectory generation, TrajFuse for semantic trajectory retrieval, and TrajRap for trajectory captioning. These models instantiate the proposed tasks and show that geometry-only trajectory baselines leave a large gap on our protocol, especially where language is part of the input-output interface. We release TrajPrism with code and a reproducible annotation pipeline that is designed to be portable across cities, given compatible trajectory inputs and map resources.

End-to-end planning has emerged as a dominant paradigm for autonomous driving, where recent models often adopt a scoring-selection framework to choose trajectories from a large set of candidates, with diffusion-based decoding showing strong promise. However, directly selecting from the entire candidate space remains difficult to optimize, and Gaussian perturbations used in diffusion often introduce unrealistic trajectories that complicate the denoising process. In addition, for training these models, reinforcement learning (RL) has shown promise, but existing end-to-end RL approaches typically rely on a single coupled reward without structured signals, limiting optimization effectiveness. To address these challenges, we propose HAD, an end-to-end planning framework with a Hierarchical Diffusion Policy that decomposes planning into a coarse-to-fine process. To improve trajectory generation, we introduce Structure-Preserved Trajectory Expansion, which produces realistic candidates while maintaining kinematic structure. For policy learning, we develop Metric-Decoupled Policy Optimization (MDPO) to enable structured RL optimization across multiple driving objectives. Extensive experiments show that HAD achieves new state-of-the-art performance on both NAVSIM and HUGSIM, outperforming prior arts by a huge margin: +2.3 EPDMS on NAVSIM and +4.9 Route Completion on HUGSIM.

Path-velocity decomposition is an intuitive yet powerful approach to address the complexity of kinodynamic motion planning. The difficult trajectory planning problem is solved in two separate, simpler, steps: first, find a path in the configuration space that satisfies the geometric constraints (path planning), and second, find a time-parameterization of that path satisfying the kinodynamic constraints. A fundamental requirement is that the path found in the first step should be time-parameterizable. Most existing works fulfill this requirement by enforcing quasi-static constraints in the path planning step, resulting in an important loss in completeness. We propose a method that enables path-velocity decomposition to discover truly dynamic motions, i.e. motions that are not quasi-statically executable. At the heart of the proposed method is a new algorithm -- Admissible Velocity Propagation -- which, given a path and an interval of reachable velocities at the beginning of that path, computes exactly and efficiently the interval of all the velocities the system can reach after traversing the path while respecting the system kinodynamic constraints. Combining this algorithm with usual sampling-based planners then gives rise to a family of new trajectory planners that can appropriately handle kinodynamic constraints while retaining the advantages associated with path-velocity decomposition. We demonstrate the efficiency of the proposed method on some difficult kinodynamic planning problems, where, in particular, quasi-static methods are guaranteed to fail.

We propose a Geometry-aware Policy Imitation (GPI) approach that rethinks imitation learning by treating demonstrations as geometric curves rather than collections of state-action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: a progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines a controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across low-dimensional robot states and high-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations as separate models and allows efficient composition of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experiments show that GPI achieves higher success rates than diffusion-based policies while running 20 times faster, requiring less memory, and remaining robust to perturbations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning. Project website: https://yimingli1998.github.io/projects/GPI/

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.

Recent advances in large language models (LLMs) have sparked growing interest in integrating language-driven techniques into trajectory prediction. By leveraging their semantic and reasoning capabilities, LLMs are reshaping how autonomous systems perceive, model, and predict trajectories. This survey provides a comprehensive overview of this emerging field, categorizing recent work into five directions: (1) Trajectory prediction via language modeling paradigms, (2) Direct trajectory prediction with pretrained language models, (3) Language-guided scene understanding for trajectory prediction, (4) Language-driven data generation for trajectory prediction, (5) Language-based reasoning and interpretability for trajectory prediction. For each, we analyze representative methods, highlight core design choices, and identify open challenges. This survey bridges natural language processing and trajectory prediction, offering a unified perspective on how language can enrich trajectory prediction.

We address a fundamental challenge in Reinforcement Learning from Interaction Demonstration (RLID): demonstration noise and coverage limitations. While existing data collection approaches provide valuable interaction demonstrations, they often yield sparse, disconnected, and noisy trajectories that fail to capture the full spectrum of possible skill variations and transitions. Our key insight is that despite noisy and sparse demonstrations, there exist infinite physically feasible trajectories that naturally bridge between demonstrated skills or emerge from their neighboring states, forming a continuous space of possible skill variations and transitions. Building upon this insight, we present two data augmentation techniques: a Stitched Trajectory Graph (STG) that discovers potential transitions between demonstration skills, and a State Transition Field (STF) that establishes unique connections for arbitrary states within the demonstration neighborhood. To enable effective RLID with augmented data, we develop an Adaptive Trajectory Sampling (ATS) strategy for dynamic curriculum generation and a historical encoding mechanism for memory-dependent skill learning. Our approach enables robust skill acquisition that significantly generalizes beyond the reference demonstrations. Extensive experiments across diverse interaction tasks demonstrate substantial improvements over state-of-the-art methods in terms of convergence stability, generalization capability, and recovery robustness.

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 human videos with realistic and controllable motions is a challenging task. While existing methods can generate visually compelling videos, they lack separate control over four key video elements: foreground subject, background video, human trajectory and action patterns. In this paper, we propose a decomposed human motion control and video generation framework that explicitly decouples motion from appearance, subject from background, and action from trajectory, enabling flexible mix-and-match composition of these elements. Concretely, we first build a ground-aware 3D world coordinate system and perform motion editing directly in the 3D space. Trajectory control is implemented by unprojecting edited 2D trajectories into 3D with focal-length calibration and coordinate transformation, followed by speed alignment and orientation adjustment; actions are supplied by a motion bank or generated via text-to-motion methods. Then, based on modern text-to-video diffusion transformer models, we inject the subject as tokens for full attention, concatenate the background along the channel dimension, and add motion (trajectory and action) control signals by addition. Such a design opens up the possibility for us to generate realistic videos of anyone doing anything anywhere. Extensive experiments on benchmark datasets and real-world cases demonstrate that our method achieves state-of-the-art performance on both element-wise controllability and overall video quality.

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.

User profiling and region analysis are two tasks of significant commercial value. However, in practical applications, modeling different features typically involves four main steps: data preparation, data processing, model establishment, evaluation, and optimization. This process is time-consuming and labor-intensive. Repeating this workflow for each feature results in abundant development time for tasks and a reduced overall volume of task development. Indeed, human mobility data contains a wealth of information. Several successful cases suggest that conducting in-depth analysis of population movement data could potentially yield meaningful profiles about users and areas. Nonetheless, most related works have not thoroughly utilized the semantic information within human mobility data and trained on a fixed number of the regions. To tap into the rich information within population movement, based on the perspective that Regions Are Who walk them, we propose a large spatiotemporal model based on trajectories (RAW). It possesses the following characteristics: 1) Tailored for trajectory data, introducing a GPT-like structure with a parameter count of up to 1B; 2) Introducing a spatiotemporal fine-tuning module, interpreting trajectories as collection of users to derive arbitrary region embedding. This framework allows rapid task development based on the large spatiotemporal model. We conducted extensive experiments to validate the effectiveness of our proposed large spatiotemporal model. It's evident that our proposed method, relying solely on human mobility data without additional features, exhibits a certain level of relevance in user profiling and region analysis. Moreover, our model showcases promising predictive capabilities in trajectory generation tasks based on the current state, offering the potential for further innovative work utilizing this large spatiotemporal model.

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.

Generating trajectory data is among promising solutions to addressing privacy concerns, collection costs, and proprietary restrictions usually associated with human mobility analyses. However, existing trajectory generation methods are still in their infancy due to the inherent diversity and unpredictability of human activities, grappling with issues such as fidelity, flexibility, and generalizability. To overcome these obstacles, we propose ControlTraj, a Controllable Trajectory generation framework with the topology-constrained diffusion model. Distinct from prior approaches, ControlTraj utilizes a diffusion model to generate high-fidelity trajectories while integrating the structural constraints of road network topology to guide the geographical outcomes. Specifically, we develop a novel road segment autoencoder to extract fine-grained road segment embedding. The encoded features, along with trip attributes, are subsequently merged into the proposed geographic denoising UNet architecture, named GeoUNet, to synthesize geographic trajectories from white noise. Through experimentation across three real-world data settings, ControlTraj demonstrates its ability to produce human-directed, high-fidelity trajectory generation with adaptability to unexplored geographical contexts.

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.

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.

Multi-agent trajectory prediction at signalized intersections is crucial for developing efficient intelligent transportation systems and safe autonomous driving systems. Due to the complexity of intersection scenarios and the limitations of single-vehicle perception, the performance of vehicle-centric prediction methods has reached a plateau. In this paper, we introduce an Infrastructure-to-Everything (I2X) collaborative prediction scheme. In this scheme, roadside units (RSUs) independently forecast the future trajectories of all vehicles and transmit these predictions unidirectionally to subscribing vehicles. Building on this scheme, we propose I2XTraj, a dedicated infrastructure-based trajectory prediction model. I2XTraj leverages real-time traffic signal states, prior maneuver strategy knowledge, and multi-agent interactions to generate accurate, joint multi-modal trajectory prediction. First, a continuous signal-informed mechanism is proposed to adaptively process real-time traffic signals to guide trajectory proposal generation under varied intersection configurations. Second, a driving strategy awareness mechanism estimates the joint distribution of maneuver strategies by integrating spatial priors of intersection areas with dynamic vehicle states, enabling coverage of the full set of feasible maneuvers. Third, a spatial-temporal-mode attention network models multi-agent interactions to refine and adjust joint trajectory outputs.Finally, I2XTraj is evaluated on two real-world datasets of signalized intersections, the V2X-Seq and the SinD drone dataset. In both single-infrastructure and online collaborative scenarios, our model outperforms state-of-the-art methods by over 30\% on V2X-Seq and 15\% on SinD, demonstrating strong generalizability and robustness.

Distributed blackbox consensus optimization is a fundamental problem in multi-agent systems, where agents must improve a global objective using only local objective queries and limited neighbor communication. Existing methods largely rely on handcrafted update rules and static cooperation patterns, which often struggle to balance local adaptation, global coordination, and communication efficiency in heterogeneous nonconvex environments. In this paper, we take an initial step toward trajectory-driven self-design for distributed black-box consensus optimization. We first redesign the agent-level swarm dynamics with an adaptive internal mechanism tailored to decentralized consensus settings, improving the balance between exploration, convergence, and local escape. Built on top of this adaptive execution layer, we propose Learning to Act and Cooperate (LACMAS), a trajectorydriven framework in which large language models provide sparse highlevel guidance for shaping both agentinternal action behaviors and agentexternal cooperation patterns from historical optimization trajectories. We further introduce a phased cognitive scheduling strategy to activate different forms of adaptation in a resource-aware manner. Experiments on standard distributed black-box benchmarks and real-world distributed tasks show that LAC-MAS consistently improves solution quality, convergence efficiency, and communication efficiency over strong baselines, suggesting a practical route from handcrafted distributed coordination toward self-designing multi-agent optimization systems.

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.

Policy search reinforcement learning allows robots to acquire skills by themselves. However, the learning procedure is inherently unsafe as the robot has no a-priori way to predict the consequences of the exploratory actions it takes. Therefore, exploration can lead to collisions with the potential to harm the robot and/or the environment. In this work we address the safety aspect by constraining the exploration to happen in safe-to-explore state spaces. These are formed by decomposing target skills (e.g., grasping) into higher ranked sub-tasks (e.g., collision avoidance, joint limit avoidance) and lower ranked movement tasks (e.g., reaching). Sub-tasks are defined as concurrent controllers (policies) in different operational spaces together with associated Jacobians representing their joint-space mapping. Safety is ensured by only learning policies corresponding to lower ranked sub-tasks in the redundant null space of higher ranked ones. As a side benefit, learning in sub-manifolds of the state-space also facilitates sample efficiency. Reaching skills performed in simulation and grasping skills performed on a real robot validate the usefulness of the proposed approach.

We propose a novel approach to multi-robot collaboration that harnesses the power of pre-trained large language models (LLMs) for both high-level communication and low-level path planning. Robots are equipped with LLMs to discuss and collectively reason task strategies. They then generate sub-task plans and task space waypoint paths, which are used by a multi-arm motion planner to accelerate trajectory planning. We also provide feedback from the environment, such as collision checking, and prompt the LLM agents to improve their plan and waypoints in-context. For evaluation, we introduce RoCoBench, a 6-task benchmark covering a wide range of multi-robot collaboration scenarios, accompanied by a text-only dataset for agent representation and reasoning. We experimentally demonstrate the effectiveness of our approach -- it achieves high success rates across all tasks in RoCoBench and adapts to variations in task semantics. Our dialog setup offers high interpretability and flexibility -- in real world experiments, we show RoCo easily incorporates human-in-the-loop, where a user can communicate and collaborate with a robot agent to complete tasks together. See project website https://project-roco.github.io for videos and code.

Multi-turn long-horizon planning is critical for foundation model agents, yet how to fundamentally improve it remains unclear. Existing models are trained on uncontrollable and opaque Internet data, making it difficult to identify how planning ability is acquired, shaped, and integrated. To address this challenge, we introduce a unified and controlled multi-turn environment that enables precise control. It allows systematically study long-horizon planning across three stages. (1) Planning ability acquisition during pre-training. We study data format, distribution, and quality. Explicit world model construction through CoT state transition modeling yields stronger long-horizon generalization. Atomic skills alone are insufficient for compositional generalization, whereas a litte long-horizon data works. Moreover, suboptimal trajectories severely impair performance because errors amplify over long horizons. (2) Planning ability shaping via GRPO and OPD post-training. Through mutual information, we distinguish general planning patterns from task-specific planning knowledge. For planning patterns, we identify three application regions of post-training: unnecessary, effective, and unsupported. OPD has a broader effective region than GRPO under low-quality and long-horizon settings, as it provides more consistent update directions. For planning knowledge, distilling unseen procedures from a teacher with different knowledge may impair student's prior world modeling without fully establishing new knowledge. (3) Planning ability integration through MOPD post-training. We show that multi-teacher on-policy distillation (MOPD) integrates capabilities by converging to shared planning-pattern across environments. Compatible patterns enable cross-environment generalization, partially shared patterns support continual learning, while completely conflicting patterns cause severe interference.

We propose ComDrive: the first comfort-oriented end-to-end autonomous driving system to generate temporally consistent and comfortable trajectories. Recent studies have demonstrated that imitation learning-based planners and learning-based trajectory scorers can effectively generate and select safety trajectories that closely mimic expert demonstrations. However, such trajectory planners and scorers face the challenge of generating temporally inconsistent and uncomfortable trajectories. To address these issues, ComDrive first extracts 3D spatial representations through sparse perception, which then serves as conditional inputs. These inputs are used by a Conditional Denoising Diffusion Probabilistic Model (DDPM)-based motion planner to generate temporally consistent multi-modal trajectories. A dual-stream adaptive trajectory scorer subsequently selects the most comfortable trajectory from these candidates to control the vehicle. Experiments demonstrate that ComDrive achieves state-of-the-art performance in both comfort and safety, outperforming UniAD by 17% in driving comfort and reducing collision rates by 25% compared to SparseDrive. More results are available on our project page: https://jmwang0117.github.io/ComDrive/.

Language agents have demonstrated autonomous decision-making abilities by reasoning with foundation models. Recently, efforts have been made to train language agents for performance improvement, with multi-step reasoning and action trajectories as the training data. However, collecting such trajectories still requires considerable human effort, by either artificial annotation or implementations of diverse prompting frameworks. In this work, we propose A^3T, a framework that enables the Autonomous Annotation of Agent Trajectories in the style of ReAct. The central role is an ActRe prompting agent, which explains the reason for an arbitrary action. When randomly sampling an external action, the ReAct-style agent could query the ActRe agent with the action to obtain its textual rationales. Novel trajectories are then synthesized by prepending the posterior reasoning from ActRe to the sampled action. In this way, the ReAct-style agent executes multiple trajectories for the failed tasks, and selects the successful ones to supplement its failed trajectory for contrastive self-training. Realized by policy gradient methods with binarized rewards, the contrastive self-training with accumulated trajectories facilitates a closed loop for multiple rounds of language agent self-improvement. We conduct experiments using QLoRA fine-tuning with the open-sourced Mistral-7B-Instruct-v0.2. In AlfWorld, the agent trained with A^3T obtains a 1-shot success rate of 96%, and 100% success with 4 iterative rounds. In WebShop, the 1-shot performance of the A^3T agent matches human average, and 4 rounds of iterative refinement lead to the performance approaching human experts. A^3T agents significantly outperform existing techniques, including prompting with GPT-4, advanced agent frameworks, and fully fine-tuned LLMs.

We present a fast algorithm for the design of smooth paths (or trajectories) that are constrained to lie in a collection of axis-aligned boxes. We consider the case where the number of these safe boxes is large, and basic preprocessing of them (such as finding their intersections) can be done offline. At runtime we quickly generate a smooth path between given initial and terminal positions. Our algorithm designs trajectories that are guaranteed to be safe at all times, and detects infeasibility whenever such a trajectory does not exist. Our algorithm is based on two subproblems that we can solve very efficiently: finding a shortest path in a weighted graph, and solving (multiple) convex optimal-control problems. We demonstrate the proposed path planner on large-scale numerical examples, and we provide an efficient open-source software implementation, fastpathplanning.

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.

This work presents a novel online model-predictive trajectory planner for robotic manipulators called BoundMPC. This planner allows the collision-free following of Cartesian reference paths in the end-effector's position and orientation, including via-points, within desired asymmetric bounds of the orthogonal path error. The path parameter synchronizes the position and orientation reference paths. The decomposition of the path error into the tangential direction, describing the path progress, and the orthogonal direction, which represents the deviation from the path, is well known for the position from the path-following control in the literature. This paper extends this idea to the orientation by utilizing the Lie theory of rotations. Moreover, the orthogonal error plane is further decomposed into basis directions to define asymmetric Cartesian error bounds easily. Using piecewise linear position and orientation reference paths with via-points is computationally very efficient and allows replanning the pose trajectories during the robot's motion. This feature makes it possible to use this planner for dynamically changing environments and varying goals. The flexibility and performance of BoundMPC are experimentally demonstrated by two scenarios on a 7-DoF Kuka LBR iiwa 14 R820 robot. The first scenario shows the transfer of a larger object from a start to a goal pose through a confined space where the object must be tilted. The second scenario deals with grasping an object from a table where the grasping point changes during the robot's motion, and collisions with other obstacles in the scene must be avoided.

Recent video diffusion models demonstrate strong potential in spatial intelligence tasks due to their rich latent world priors. However, this potential is hindered by their limited controllability and geometric inconsistency, creating a gap between their strong priors and their practical use in 3D/4D tasks. As a result, current approaches often rely on retraining or fine-tuning, which risks degrading pretrained knowledge and incurs high computational costs. To address this, we propose WorldForge, a training-free, inference-time framework composed of three tightly coupled modules. Intra-Step Recursive Refinement introduces a recursive refinement mechanism during inference, which repeatedly optimizes network predictions within each denoising step to enable precise trajectory injection. Flow-Gated Latent Fusion leverages optical flow similarity to decouple motion from appearance in the latent space and selectively inject trajectory guidance into motion-related channels. Dual-Path Self-Corrective Guidance compares guided and unguided denoising paths to adaptively correct trajectory drift caused by noisy or misaligned structural signals. Together, these components inject fine-grained, trajectory-aligned guidance without training, achieving both accurate motion control and photorealistic content generation. Extensive experiments across diverse benchmarks validate our method's superiority in realism, trajectory consistency, and visual fidelity. This work introduces a novel plug-and-play paradigm for controllable video synthesis, offering a new perspective on leveraging generative priors for spatial intelligence.

Modeling and generating human reactions poses a significant challenge with broad applications for computer vision and human-computer interaction. Existing methods either treat multiple individuals as a single entity, directly generating interactions, or rely solely on one person's motion to generate the other's reaction, failing to integrate the rich semantic information that underpins human interactions. Yet, these methods often fall short in adaptive responsiveness, i.e., the ability to accurately respond to diverse and dynamic interaction scenarios. Recognizing this gap, our work introduces an approach tailored to address the limitations of existing models by focusing on text-driven human reaction generation. Our model specifically generates realistic motion sequences for individuals that responding to the other's actions based on a descriptive text of the interaction scenario. The goal is to produce motion sequences that not only complement the opponent's movements but also semantically fit the described interactions. To achieve this, we present MoReact, a diffusion-based method designed to disentangle the generation of global trajectories and local motions sequentially. This approach stems from the observation that generating global trajectories first is crucial for guiding local motion, ensuring better alignment with given action and text. Furthermore, we introduce a novel interaction loss to enhance the realism of generated close interactions. Our experiments, utilizing data adapted from a two-person motion dataset, demonstrate the efficacy of our approach for this novel task, which is capable of producing realistic, diverse, and controllable reactions that not only closely match the movements of the counterpart but also adhere to the textual guidance. Please find our webpage at https://xiyan-xu.github.io/MoReactWebPage.

Controllable video generation has gained significant attention in recent years. However, two main limitations persist: Firstly, most existing works focus on either text, image, or trajectory-based control, leading to an inability to achieve fine-grained control in videos. Secondly, trajectory control research is still in its early stages, with most experiments being conducted on simple datasets like Human3.6M. This constraint limits the models' capability to process open-domain images and effectively handle complex curved trajectories. In this paper, we propose DragNUWA, an open-domain diffusion-based video generation model. To tackle the issue of insufficient control granularity in existing works, we simultaneously introduce text, image, and trajectory information to provide fine-grained control over video content from semantic, spatial, and temporal perspectives. To resolve the problem of limited open-domain trajectory control in current research, We propose trajectory modeling with three aspects: a Trajectory Sampler (TS) to enable open-domain control of arbitrary trajectories, a Multiscale Fusion (MF) to control trajectories in different granularities, and an Adaptive Training (AT) strategy to generate consistent videos following trajectories. Our experiments validate the effectiveness of DragNUWA, demonstrating its superior performance in fine-grained control in video generation. The homepage link is https://www.microsoft.com/en-us/research/project/dragnuwa/

Predicting the future motion of dynamic agents is of paramount importance to ensuring safety and assessing risks in motion planning for autonomous robots. In this study, we propose a two-stage motion prediction method, called R-Pred, designed to effectively utilize both scene and interaction context using a cascade of the initial trajectory proposal and trajectory refinement networks. The initial trajectory proposal network produces M trajectory proposals corresponding to the M modes of the future trajectory distribution. The trajectory refinement network enhances each of the M proposals using 1) tube-query scene attention (TQSA) and 2) proposal-level interaction attention (PIA) mechanisms. TQSA uses tube-queries to aggregate local scene context features pooled from proximity around trajectory proposals of interest. PIA further enhances the trajectory proposals by modeling inter-agent interactions using a group of trajectory proposals selected by their distances from neighboring agents. Our experiments conducted on Argoverse and nuScenes datasets demonstrate that the proposed refinement network provides significant performance improvements compared to the single-stage baseline and that R-Pred achieves state-of-the-art performance in some categories of the benchmarks.

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.

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.

Large Language Models (LLMs) have become integral components in various autonomous agent systems. In this study, we present an exploration-based trajectory optimization approach, referred to as ETO. This learning method is designed to enhance the performance of open LLM agents. Contrary to previous studies that exclusively train on successful expert trajectories, our method allows agents to learn from their exploration failures. This leads to improved performance through an iterative optimization framework. During the exploration phase, the agent interacts with the environment while completing given tasks, gathering failure trajectories to create contrastive trajectory pairs. In the subsequent training phase, the agent utilizes these trajectory preference pairs to update its policy using contrastive learning methods like DPO. This iterative cycle of exploration and training fosters continued improvement in the agents. Our experiments on three complex tasks demonstrate that ETO consistently surpasses baseline performance by a large margin. Furthermore, an examination of task-solving efficiency and potential in scenarios lacking expert trajectory underscores the effectiveness of our approach.

In autonomous driving tasks, trajectory prediction in complex traffic environments requires adherence to real-world context conditions and behavior multimodalities. Existing methods predominantly rely on prior assumptions or generative models trained on curated data to learn road agents' stochastic behavior bounded by scene constraints. However, they often face mode averaging issues due to data imbalance and simplistic priors, and could even suffer from mode collapse due to unstable training and single ground truth supervision. These issues lead the existing methods to a loss of predictive diversity and adherence to the scene constraints. To address these challenges, we introduce a novel trajectory generator named Controllable Diffusion Trajectory (CDT), which integrates map information and social interactions into a Transformer-based conditional denoising diffusion model to guide the prediction of future trajectories. To ensure multimodality, we incorporate behavioral tokens to direct the trajectory's modes, such as going straight, turning right or left. Moreover, we incorporate the predicted endpoints as an alternative behavioral token into the CDT model to facilitate the prediction of accurate trajectories. Extensive experiments on the Argoverse 2 benchmark demonstrate that CDT excels in generating diverse and scene-compliant trajectories in complex urban settings.

Scientific ideation unfolds over multiple stages, including literature search, paper reading, tool use, claim checking, cross-paper synthesis, brainstorming, rejection of weak directions, and iterative writing. Yet most existing resources capture isolated components or final artifacts rather than the process connecting them. We introduce IdeaTrail, a dataset of 1,170 multi-turn trajectories for scientific ideation and proposal generation. Each trajectory follows a research process from evidence gathering to either idea selection or proposal construction, jointly recording tool use, acquired evidence, intermediate artifacts, and reasoning. IdeaTrail is synthesized from human-selected research papers and proposal artifacts through a Generator--Advisor loop. The Generator produces the visible sequence of actions, observations, and artifact edits, while the Advisor uses the full generation context to check grounding, causal order, naturalness, and leakage from hidden targets. This reverse-to-forward design keeps trajectories aligned with real scientific artifacts while retaining the uncertainty, evidence use, and staged convergence characteristic of research practice. IdeaTrail provides both reusable process supervision and a general recipe for constructing scientific-research-agent data.

Predicting future trajectories for other road agents is an essential task for autonomous vehicles. Established trajectory prediction methods primarily use agent tracks generated by a detection and tracking system and HD map as inputs. In this work, we propose a novel method that also incorporates visual input from surround-view cameras, allowing the model to utilize visual cues such as human gazes and gestures, road conditions, vehicle turn signals, etc, which are typically hidden from the model in prior methods. Furthermore, we use textual descriptions generated by a Vision-Language Model (VLM) and refined by a Large Language Model (LLM) as supervision during training to guide the model on what to learn from the input data. Despite using these extra inputs, our method achieves a latency of 53 ms, making it feasible for real-time processing, which is significantly faster than that of previous single-agent prediction methods with similar performance. Our experiments show that both the visual inputs and the textual descriptions contribute to improvements in trajectory prediction performance, and our qualitative analysis highlights how the model is able to exploit these additional inputs. Lastly, in this work we create and release the nuScenes-Text dataset, which augments the established nuScenes dataset with rich textual annotations for every scene, demonstrating the positive impact of utilizing VLM on trajectory prediction. Our project page is at https://moonseokha.github.io/VisionTrap/

Deep research agents aim to solve complex knowledge-intensive tasks through long-horizon planning, evidence gathering, reasoning, and report generation. While recent progress in search agents has demonstrated strong capabilities in information retrieval and answer verification, most existing training datasets remain search-centric, focusing primarily on closed-ended question answering and information localization. As a result, they mainly train information-seeking behavior while providing limited coverage of key deep research capabilities, including evidence integration, knowledge synthesis, planning, file understanding, and structured report generation. In this work, we propose a unified trajectory construction paradigm for deep research agents that combines closed-ended QA and open-ended exploration. The proposed framework consists of graph-grounded task formulation, agentic trajectory rollout, and multi-dimensional trajectory verification, enabling scalable synthesis of high-quality agentic trajectories spanning long-chain complex reasoning, deep research instruction following, report writing, file understanding and generation, and skills usage. Compared with existing search-oriented datasets, our synthesized trajectories place greater emphasis on knowledge synthesis, complex reasoning, and planning. S1-DeepResearch-32B achieves state-of-the-art performance among open-source models of comparable scale across 20 benchmarks spanning five capability dimensions, including complex reasoning, instruction following, report generation, file understanding, and skills usage. On several challenging deep research benchmarks, it approaches the performance of leading proprietary frontier models. These results highlight the importance of jointly modeling information acquisition, knowledge synthesis, and planning-oriented agent behaviors for building effective deep research agents.

Internal modelling of the world -- predicting transitions between previous states X and next states Y under actions Z -- is essential to reasoning and planning for LLMs and VLMs. Learning such models typically requires costly action-labelled trajectories. We propose SWIRL, a self-improvement framework that learns from state-only sequences by treating actions as a latent variable and alternating between Forward World Modelling (FWM) P_θ(Y|X,Z) and an Inverse Dynamics Modelling (IDM) Q_φ(Z|X,Y). SWIRL iterates two phases: (1) Variational Information Maximisation, which updates the FWM to generate next states that maximise conditional mutual information with latent actions given prior states, encouraging identifiable consistency; and (2) ELBO Maximisation, which updates the IDM to explain observed transitions, effectively performing coordinate ascent. Both models are trained with reinforcement learning (specifically, GRPO) with the opposite frozen model's log-probability as a reward signal. We provide theoretical learnability guarantees for both updates, and evaluate SWIRL on LLMs and VLMs across multiple environments: single-turn and multi-turn open-world visual dynamics and synthetic textual environments for physics, web, and tool calling. SWIRL achieves gains of 16% on AURORABench, 28% on ByteMorph, 16% on WorldPredictionBench, and 14% on StableToolBench.

This paper presents a safety-critical approach to the coordination of robots in dynamic environments. To this end, we leverage control barrier functions (CBFs) with the forward reachable set to guarantee the safe coordination of the robots while preserving a desired trajectory via a layered controller. The top-level planner generates a safety-ensured trajectory for each agent, accounting for the dynamic constraints in the environment. This planner leverages high-order CBFs based on the forward reachable set to ensure safety-critical coordination control, i.e., guarantee the safe coordination of the robots during locomotion. The middle-level trajectory planner employs single rigid body (SRB) dynamics to generate optimal ground reaction forces (GRFs) to track the safety-ensured trajectories from the top-level planner. The whole-body motions to adhere to the optimal GRFs while ensuring the friction cone condition at the end of each stance leg are generated from the low-level controller. The effectiveness of the approach is demonstrated through simulation and hardware experiments.

We focus on the utilisation of reactive trajectory imitation controllers for goal-directed mobile robot navigation. We propose a topological navigation graph (TNG) - an imitation-learning-based framework for navigating through environments with intersecting trajectories. The TNG framework represents the environment as a directed graph composed of deep neural networks. Each vertex of the graph corresponds to a trajectory and is represented by a trajectory identification classifier and a trajectory imitation controller. For trajectory following, we propose the novel use of neural object detection architectures. The edges of TNG correspond to intersections between trajectories and are all represented by a classifier. We provide empirical evaluation of the proposed navigation framework and its components in simulated and real-world environments, demonstrating that TNG allows us to utilise non-goal-directed, imitation-learning methods for goal-directed autonomous navigation.

Human trajectory prediction is a practical task of predicting the future positions of pedestrians on the road, which typically covers all temporal ranges from short-term to long-term within a trajectory. However, existing works attempt to address the entire trajectory prediction with a singular, uniform training paradigm, neglecting the distinction between short-term and long-term dynamics in human trajectories. To overcome this limitation, we introduce a novel Progressive Pretext Task learning (PPT) framework, which progressively enhances the model's capacity of capturing short-term dynamics and long-term dependencies for the final entire trajectory prediction. Specifically, we elaborately design three stages of training tasks in the PPT framework. In the first stage, the model learns to comprehend the short-term dynamics through a stepwise next-position prediction task. In the second stage, the model is further enhanced to understand long-term dependencies through a destination prediction task. In the final stage, the model aims to address the entire future trajectory task by taking full advantage of the knowledge from previous stages. To alleviate the knowledge forgetting, we further apply a cross-task knowledge distillation. Additionally, we design a Transformer-based trajectory predictor, which is able to achieve highly efficient two-step reasoning by integrating a destination-driven prediction strategy and a group of learnable prompt embeddings. Extensive experiments on popular benchmarks have demonstrated that our proposed approach achieves state-of-the-art performance with high efficiency. Code is available at https://github.com/iSEE-Laboratory/PPT.

The field of trajectory forecasting has grown significantly in recent years, partially owing to the release of numerous large-scale, real-world human trajectory datasets for autonomous vehicles (AVs) and pedestrian motion tracking. While such datasets have been a boon for the community, they each use custom and unique data formats and APIs, making it cumbersome for researchers to train and evaluate methods across multiple datasets. To remedy this, we present trajdata: a unified interface to multiple human trajectory datasets. At its core, trajdata provides a simple, uniform, and efficient representation and API for trajectory and map data. As a demonstration of its capabilities, in this work we conduct a comprehensive empirical evaluation of existing trajectory datasets, providing users with a rich understanding of the data underpinning much of current pedestrian and AV motion forecasting research, and proposing suggestions for future datasets from these insights. trajdata is permissively licensed (Apache 2.0) and can be accessed online at https://github.com/NVlabs/trajdata

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.

We propose a data augmentation method for offline reinforcement learning, motivated by active positioning problems. Particularly, our approach enables the training of off-policy models from a limited number of suboptimal trajectories. We introduce a trajectory-based augmentation technique that exploits task structure and the geometric relationship between rewards, value functions, and mathematical properties of logging policies. During data collection, our augmentation supports suboptimal logging policies, leading to higher data quality and improved offline reinforcement learning performance. We provide theoretical justification for these strategies and validate them empirically across positioning tasks of varying dimensionality and under partial observability.

Vision Language Models (VLMs) bridge visual perception and linguistic reasoning. In Autonomous Driving (AD), this synergy has enabled Vision Language Action (VLA) models, which translate high-level multimodal understanding into driving behaviors, typically represented as future trajectories. However, existing VLA models mainly generate generic collision-free trajectories. Beyond collision avoidance, adapting to diverse driving styles (e.g., sporty, comfortable) is essential for personalized driving. Moreover, many methods treat trajectory generation as naive token prediction, which can produce kinematically infeasible actions. To address these limitations, we present StyleVLA, a physics-informed VLA framework for generating diverse and physically plausible driving behaviors. We introduce a hybrid loss that combines a kinematic consistency constraint with a continuous regression head to improve trajectory feasibility. To train StyleVLA, built on Qwen3-VL-4B, we construct a large-scale instruction dataset with over 1.2k scenarios, 76k Bird's Eye View (BEV) samples, and 42k First Person View (FPV) samples, with ground-truth trajectories for five driving styles and natural-language instructions. Experiments show that our 4B-parameter StyleVLA significantly outperforms proprietary models (e.g., Gemini-3-Pro) and state-of-the-art VLA models. Using a composite driving score measuring success rate, physical feasibility, and style adherence, StyleVLA achieves 0.55 on BEV and 0.51 on FPV, versus 0.32 and 0.35 for Gemini-3-Pro. These results show that a specialized, physics-informed, lightweight model can surpass closed-source models on domain-specific tasks.

A longstanding challenge for self-driving development is simulating dynamic driving scenarios seeded from recorded driving logs. In pursuit of this functionality, we apply tools from discrete sequence modeling to model how vehicles, pedestrians and cyclists interact in driving scenarios. Using a simple data-driven tokenization scheme, we discretize trajectories to centimeter-level resolution using a small vocabulary. We then model the multi-agent sequence of motion tokens with a GPT-like encoder-decoder that is autoregressive in time and takes into account intra-timestep interaction between agents. Scenarios sampled from our model exhibit state-of-the-art realism; our model tops the Waymo Sim Agents Benchmark, surpassing prior work along the realism meta metric by 3.3% and along the interaction metric by 9.9%. We ablate our modeling choices in full autonomy and partial autonomy settings, and show that the representations learned by our model can quickly be adapted to improve performance on nuScenes. We additionally evaluate the scalability of our model with respect to parameter count and dataset size, and use density estimates from our model to quantify the saliency of context length and intra-timestep interaction for the traffic modeling task.

End-to-end (E2E) autonomous driving presents a promising approach for translating perceptual inputs directly into driving actions. However, prohibitive annotation costs and temporal data quality degradation hinder long-term real-world deployment. While combining imitation learning (IL) and reinforcement learning (RL) is a common strategy for policy improvement, conventional RL training relies on delayed, event-based rewards-policies learn only from catastrophic outcomes such as collisions, leading to premature convergence to suboptimal behaviors. To address these limitations, we introduce GSDrive, a framework that exploits 3D Gaussian Splatting (3DGS) for differentiable, physics-based reward shaping in E2E driving policy improvement. Our method incorporates a flow matching-based trajectory predictor within the 3DGS simulator, enabling multi-mode trajectory probing where candidate trajectories are rolled out to assess prospective rewards. This establishes a bidirectional knowledge exchange between IL and RL by grounding reward functions in physically simulated interaction signals, offering immediate dense feedback instead of sparse catastrophic events. Evaluated on the reconstructed nuScenes dataset, our method surpasses existing simulation-based RL driving approaches in closed-loop experiments. Code is available at https://github.com/ZionGo6/GSDrive.

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.

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

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.

Generative video editing has enabled several intuitive editing operations for short video clips that would previously have been difficult to achieve, especially for non-expert editors. Existing methods focus on prescribing an object's 3D or 2D motion trajectory in a video, or on altering the appearance of an object or a scene, while preserving both the video's plausibility and identity. Yet a method to move an object's 3D motion trajectory in a video, i.e., moving an object while preserving its relative 3D motion, is currently still missing. The main challenge lies in obtaining paired video data for this scenario. Previous methods typically rely on clever data generation approaches to construct plausible paired data from unpaired videos, but this approach fails if one of the videos in a pair can not easily be constructed from the other. Instead, we introduce TrajectoryAtlas, a new data generation pipeline for large-scale synthetic paired video data and a video generator TrajectoryMover fine-tuned with this data. We show that this successfully enables generative movement of object trajectories. Project page: https://chhatrekiran.github.io/trajectorymover

We consider the problem of learning good trajectories for manipulation tasks. This is challenging because the criterion defining a good trajectory varies with users, tasks and environments. In this paper, we propose a co-active online learning framework for teaching robots the preferences of its users for object manipulation tasks. The key novelty of our approach lies in the type of feedback expected from the user: the human user does not need to demonstrate optimal trajectories as training data, but merely needs to iteratively provide trajectories that slightly improve over the trajectory currently proposed by the system. We argue that this co-active preference feedback can be more easily elicited from the user than demonstrations of optimal trajectories, which are often challenging and non-intuitive to provide on high degrees of freedom manipulators. Nevertheless, theoretical regret bounds of our algorithm match the asymptotic rates of optimal trajectory algorithms. We demonstrate the generalizability of our algorithm on a variety of grocery checkout tasks, for whom, the preferences were not only influenced by the object being manipulated but also by the surrounding environment.For more details and a demonstration video, visit: \url{http://pr.cs.cornell.edu/coactive}

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.

Human mobility simulation plays a crucial role in various real-world applications. Recently, to address the limitations of traditional data-driven approaches, researchers have explored leveraging the commonsense knowledge and reasoning capabilities of large language models (LLMs) to accelerate human mobility simulation. However, these methods suffer from several critical shortcomings, including inadequate modeling of urban spaces and poor integration with both individual mobility patterns and collective mobility distributions. To address these challenges, we propose CityGPT-Powered Agentic framework for Mobility Simulation (CAMS), an agentic framework that leverages the language based urban foundation model to simulate human mobility in urban space. CAMS comprises three core modules, including MobExtractor to extract template mobility patterns and synthesize new ones based on user profiles, GeoGenerator to generate anchor points considering collective knowledge and generate candidate urban geospatial knowledge using an enhanced version of CityGPT, TrajEnhancer to retrieve spatial knowledge based on mobility patterns and generate trajectories with real trajectory preference alignment via DPO. Experiments on real-world datasets show that CAMS achieves superior performance without relying on externally provided geospatial information. Moreover, by holistically modeling both individual mobility patterns and collective mobility constraints, CAMS generates more realistic and plausible trajectories. In general, CAMS establishes a new paradigm that integrates the agentic framework with urban-knowledgeable LLMs for human mobility simulation.

Recent advancements in world models have revolutionized dynamic environment simulation, allowing systems to foresee future states and assess potential actions. In autonomous driving, these capabilities help vehicles anticipate the behavior of other road users, perform risk-aware planning, accelerate training in simulation, and adapt to novel scenarios, thereby enhancing safety and reliability. Current approaches exhibit deficiencies in maintaining robust 3D geometric consistency or accumulating artifacts during occlusion handling, both critical for reliable safety assessment in autonomous navigation tasks. To address this, we introduce GeoDrive, which explicitly integrates robust 3D geometry conditions into driving world models to enhance spatial understanding and action controllability. Specifically, we first extract a 3D representation from the input frame and then obtain its 2D rendering based on the user-specified ego-car trajectory. To enable dynamic modeling, we propose a dynamic editing module during training to enhance the renderings by editing the positions of the vehicles. Extensive experiments demonstrate that our method significantly outperforms existing models in both action accuracy and 3D spatial awareness, leading to more realistic, adaptable, and reliable scene modeling for safer autonomous driving. Additionally, our model can generalize to novel trajectories and offers interactive scene editing capabilities, such as object editing and object trajectory control.

Recent Vision-Language-Action (VLA) models for autonomous driving (AD) increasingly utilize chain-of-thought (CoT) supervision to enhance the reasoning capabilities of their Vision-Language Model (VLM) components, yet existing annotation pipelines commonly expose the teacher model to the logged ground-truth (GT) future trajectory. We empirically show that this induces trajectory anchoring bias: teacher models rationalize the revealed outcome rather than infer a decision from scene evidence, producing less causally faithful CoTs and substantially more severe hallucinations, especially in causally challenging scenes. Removing the GT trajectory eliminates this shortcut, but open-ended trajectory generation entangles high-level decision-making with precise geometric synthesis and low-level dynamics. To make trajectory-level driving decisions verifiable without requiring open-ended trajectory synthesis, we introduce Autonomous-Driving Multiple-Choice Question (AD-MCQ), which casts planning as selection among explicit trajectory candidates. Taking this a step further, we propose Deferred Exposure of Future Trajectories for RLVR (DEFT-RLVR) to transform future trajectories from pre-decision anchors into post-decision verification targets. Experimental results show that DEFT-RLVR improves AD reasoning while preserving or even enhancing general visual capabilities. With VLM-only inference and controllable difficulty through candidate construction, AD-MCQ provides a flexible, scalable, and extensible foundation for future research on verifiable AD reasoning.

In this work, we address the challenging problem of long-horizon goal-reaching policy learning from non-expert, action-free observation data. Unlike fully labeled expert data, our data is more accessible and avoids the costly process of action labeling. Additionally, compared to online learning, which often involves aimless exploration, our data provides useful guidance for more efficient exploration. To achieve our goal, we propose a novel subgoal guidance learning strategy. The motivation behind this strategy is that long-horizon goals offer limited guidance for efficient exploration and accurate state transition. We develop a diffusion strategy-based high-level policy to generate reasonable subgoals as waypoints, preferring states that more easily lead to the final goal. Additionally, we learn state-goal value functions to encourage efficient subgoal reaching. These two components naturally integrate into the off-policy actor-critic framework, enabling efficient goal attainment through informative exploration. We evaluate our method on complex robotic navigation and manipulation tasks, demonstrating a significant performance advantage over existing methods. Our ablation study further shows that our method is robust to observation data with various corruptions.

We introduce a method for generating realistic pedestrian trajectories and full-body animations that can be controlled to meet user-defined goals. We draw on recent advances in guided diffusion modeling to achieve test-time controllability of trajectories, which is normally only associated with rule-based systems. Our guided diffusion model allows users to constrain trajectories through target waypoints, speed, and specified social groups while accounting for the surrounding environment context. This trajectory diffusion model is integrated with a novel physics-based humanoid controller to form a closed-loop, full-body pedestrian animation system capable of placing large crowds in a simulated environment with varying terrains. We further propose utilizing the value function learned during RL training of the animation controller to guide diffusion to produce trajectories better suited for particular scenarios such as collision avoidance and traversing uneven terrain. Video results are available on the project page at https://nv-tlabs.github.io/trace-pace .

The symbolic discovery of Ordinary Differential Equations (ODEs) from trajectory data plays a pivotal role in AI-driven scientific discovery. Existing symbolic methods predominantly rely on fixed, pre-collected training datasets, which often result in suboptimal performance, as demonstrated in our case study in Figure 1. Drawing inspiration from active learning, we investigate strategies to query informative trajectory data that can enhance the evaluation of predicted ODEs. However, the butterfly effect in dynamical systems reveals that small variations in initial conditions can lead to drastically different trajectories, necessitating the storage of vast quantities of trajectory data using conventional active learning. To address this, we introduce Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketching (APPS). Instead of directly selecting individual initial conditions, our APPS first identifies an informative region within the phase space and then samples a batch of initial conditions from this region. Compared to traditional active learning methods, APPS mitigates the gap of maintaining a large amount of data. Extensive experiments demonstrate that APPS consistently discovers more accurate ODE expressions than baseline methods using passively collected datasets.

Understanding how transformer representations evolve across layers, not merely what they encode, remains an open problem in mechanistic interpretability. We recast the transformer forward pass as a discrete population trajectory through a high-dimensional representation manifold, drawing on geometric tools from computational neuroscience. Rather than probing for pre-specified features, we characterize trajectory geometry using five metrics computed directly in the ambient space: trajectory length, curvature, a semantic convergence index, layerwise cosine similarity, and representational stability. Across three model families (GPT-2, TinyLlama, Qwen2.5) and five controlled prompt families, we report four findings. First, semantically related prompts converge significantly in middle-to-late layers (peak CI 0.41--0.58, p<0.001, Mann-Whitney U), consistent with attractor-like dynamics. Second, reasoning tasks produce trajectories of greater curvature than lexical variations (0.71--0.83 rad vs. 0.27--0.31 rad), suggesting curvature encodes computational complexity. Third, ambiguous tokens exhibit trajectory bifurcation with up to 5.6x representational separation by the final layer, absent in unambiguous controls. Fourth, layerwise cosine similarity reveals a universal three-phase structure: encoding, elaboration, and output preparation, consistent across all three architectures. All four effects vanish under shuffled-layer and random-embedding controls. We release a fully open-source, model-agnostic pipeline and argue that trajectory geometry constitutes a principled, probe-free lens for mechanistic interpretability.

Teaching robots new skills quickly and conveniently is crucial for the broader adoption of robotic systems. In this work, we address the problem of one-shot imitation from a single human demonstration, given by an RGB-D video recording through a two-stage process. In the first stage which is offline, we extract the trajectory of the demonstration. This entails segmenting manipulated objects and determining their relative motion in relation to secondary objects such as containers. Subsequently, in the live online trajectory generation stage, we first re-detect all objects, then we warp the demonstration trajectory to the current scene, and finally, we trace the trajectory with the robot. To complete these steps, our method makes leverages several ancillary models, including those for segmentation, relative object pose estimation, and grasp prediction. We systematically evaluate different combinations of correspondence and re-detection methods to validate our design decision across a diverse range of tasks. Specifically, we collect demonstrations of ten different tasks including pick-and-place tasks as well as articulated object manipulation. Finally, we perform extensive evaluations on a real robot system to demonstrate the effectiveness and utility of our approach in real-world scenarios. We make the code publicly available at http://ditto.cs.uni-freiburg.de.

Capturing high-dimensional social interactions and feasible futures is essential for predicting trajectories. To address this complex nature, several attempts have been devoted to reducing the dimensionality of the output variables via parametric curve fitting such as the B\'ezier curve and B-spline function. However, these functions, which originate in computer graphics fields, are not suitable to account for socially acceptable human dynamics. In this paper, we present EigenTrajectory (ET), a trajectory prediction approach that uses a novel trajectory descriptor to form a compact space, known here as ET space, in place of Euclidean space, for representing pedestrian movements. We first reduce the complexity of the trajectory descriptor via a low-rank approximation. We transform the pedestrians' history paths into our ET space represented by spatio-temporal principle components, and feed them into off-the-shelf trajectory forecasting models. The inputs and outputs of the models as well as social interactions are all gathered and aggregated in the corresponding ET space. Lastly, we propose a trajectory anchor-based refinement method to cover all possible futures in the proposed ET space. Extensive experiments demonstrate that our EigenTrajectory predictor can significantly improve both the prediction accuracy and reliability of existing trajectory forecasting models on public benchmarks, indicating that the proposed descriptor is suited to represent pedestrian behaviors. Code is publicly available at https://github.com/inhwanbae/EigenTrajectory .

Although the study of human trajectory anomalies is critical for advancing spatial data mining, empirical research remains severely hindered by a pervasive lack of ground-truth datasets. Despite the availability of several real-world and simulated human trajectory collections, these datasets exclusively capture normal mobility patterns and lack annotated anomalies. This specific scarcity is fundamentally driven by the inherent statistical rarity of anomalous events, precluding the feasibility of conventional observational methods. Compounding this challenge, the systematic acquisition of large-scale mobility data is strictly bottlenecked by prohibitive costs and stringent privacy regulations. To overcome these fundamental limitations and establish a reliable human trajectory anomalies dataset with annotated ground truth, we introduce a novel, end-to-end generative framework designed to synthesize realistic trajectory anomalies at scale. Our architecture bridges the gap between purely synthetic mobility data and complex real-world physical constraints by operating directly on baseline simulated trajectories. We employ Large Language Model (LLM) agents to systematically inject semantically meaningful behavioral anomalies such as irregular out-of-distribution check-ins and skipped routine visits. To ensure rigorous spatial validity, the system leverages map-constrained routing reconstruction to recalculate the physical transitions between these LLM agent-modified staypoints. Moreover, to narrow the simulation-to-reality gap, we augment the resulting trajectories with a context-aware spatial noise model, parameterized by environmental and location-specific variables, to accurately emulate heterogeneous GPS sensor degradation.

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.

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.

In this paper, we present empirical evidence of skills and directed exploration emerging from a simple RL algorithm long before any successful trials are observed. For example, in a manipulation task, the agent is given a single observation of the goal state and learns skills, first for moving its end-effector, then for pushing the block, and finally for picking up and placing the block. These skills emerge before the agent has ever successfully placed the block at the goal location and without the aid of any reward functions, demonstrations, or manually-specified distance metrics. Once the agent has learned to reach the goal state reliably, exploration is reduced. Implementing our method involves a simple modification of prior work and does not require density estimates, ensembles, or any additional hyperparameters. Intuitively, the proposed method seems like it should be terrible at exploration, and we lack a clear theoretical understanding of why it works so effectively, though our experiments provide some hints.

Training long-horizon robotic policies in complex physical environments is essential for many applications, such as robotic manipulation. However, learning a policy that can generalize to unseen tasks is challenging. In this work, we propose to achieve one-shot task generalization by decoupling plan generation and plan execution. Specifically, our method solves complex long-horizon tasks in three steps: build a paired abstract environment by simplifying geometry and physics, generate abstract trajectories, and solve the original task by an abstract-to-executable trajectory translator. In the abstract environment, complex dynamics such as physical manipulation are removed, making abstract trajectories easier to generate. However, this introduces a large domain gap between abstract trajectories and the actual executed trajectories as abstract trajectories lack low-level details and are not aligned frame-to-frame with the executed trajectory. In a manner reminiscent of language translation, our approach leverages a seq-to-seq model to overcome the large domain gap between the abstract and executable trajectories, enabling the low-level policy to follow the abstract trajectory. Experimental results on various unseen long-horizon tasks with different robot embodiments demonstrate the practicability of our methods to achieve one-shot task generalization.

As unmanned aerial systems (UASs) increasingly integrate into the US national airspace system, there is an increasing need to characterize how commercial and recreational UASs may encounter each other. To inform the development and evaluation of safety critical technologies, we demonstrate a methodology to analytically calculate all potential relative geometries between different UAS operations performing inspection missions. This method is based on a previously demonstrated technique that leverages open source geospatial information to generate representative unmanned aircraft trajectories. Using open source data and parallel processing techniques, we performed trillions of calculations to estimate the relative horizontal distance between geospatial points across sixteen locations.

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths have been designed principally under the assumption of Euclidean geometry, resulting in straight interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals. In this paper, we propose Metric Flow Matching (MFM), a novel simulation-free framework for conditional flow matching where interpolants are approximate geodesics learned by minimizing the kinetic energy of a data-induced Riemannian metric. This way, the generative model matches vector fields on the data manifold, which corresponds to lower uncertainty and more meaningful interpolations. We prescribe general metrics to instantiate MFM, independent of the task, and test it on a suite of challenging problems including LiDAR navigation, unpaired image translation, and modeling cellular dynamics. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction.

Motion planning under dynamics constraints, i.e., kinodynamic planning, enables safe robot operation by generating dynamically feasible trajectories that the robot can accurately track. For high-\dof robots such as manipulators, sampling-based motion planners are commonly used, especially for complex tasks in cluttered environments. However, enforcing constraints on robot dynamics in such planners requires solving either challenging two-point boundary value problems (BVPs) or propagating robot dynamics over time, both of which are computational bottlenecks that drastically increase planning times. Meanwhile, recent efforts have shown that sampling-based motion planners can generate plans in microseconds using parallelization, but are limited to geometric paths. This paper develops AkinoPDF, a fast parallelized sampling-based kinodynamic motion planning technique for a broad class of differentially flat robot systems, including manipulators, ground and aerial vehicles, and more. Differential flatness allows us to transform the motion planning problem from the original state space to a flat output space, where an analytical time-parameterized solution of the BVP and dynamics integration can be obtained. A trajectory in the flat output space is then converted back to a closed-form dynamically feasible trajectory in the original state space, enabling fast validation via ``single instruction, multiple data" parallelism. Our method is fast, exact, and compatible with any sampling-based motion planner. We extensively verify the effectiveness of our approach in both simulated benchmarks and real experiments with cluttered and dynamic environments, requiring mere microseconds to milliseconds of planning time.

Motion trajectories offer reliable references for physics-based motion learning but suffer from sparsity, particularly in regions that lack sufficient data coverage. To address this challenge, we introduce a self-supervised, structured representation and generation method that extracts spatial-temporal relationships in periodic or quasi-periodic motions. The motion dynamics in a continuously parameterized latent space enable our method to enhance the interpolation and generalization capabilities of motion learning algorithms. The motion learning controller, informed by the motion parameterization, operates online tracking of a wide range of motions, including targets unseen during training. With a fallback mechanism, the controller dynamically adapts its tracking strategy and automatically resorts to safe action execution when a potentially risky target is proposed. By leveraging the identified spatial-temporal structure, our work opens new possibilities for future advancements in general motion representation and learning algorithms.

The ability to accurately predict the trajectory of surrounding vehicles is a critical hurdle to overcome on the journey to fully autonomous vehicles. To address this challenge, we pioneer a novel behavior-aware trajectory prediction model (BAT) that incorporates insights and findings from traffic psychology, human behavior, and decision-making. Our model consists of behavior-aware, interaction-aware, priority-aware, and position-aware modules that perceive and understand the underlying interactions and account for uncertainty and variability in prediction, enabling higher-level learning and flexibility without rigid categorization of driving behavior. Importantly, this approach eliminates the need for manual labeling in the training process and addresses the challenges of non-continuous behavior labeling and the selection of appropriate time windows. We evaluate BAT's performance across the Next Generation Simulation (NGSIM), Highway Drone (HighD), Roundabout Drone (RounD), and Macao Connected Autonomous Driving (MoCAD) datasets, showcasing its superiority over prevailing state-of-the-art (SOTA) benchmarks in terms of prediction accuracy and efficiency. Remarkably, even when trained on reduced portions of the training data (25%), our model outperforms most of the baselines, demonstrating its robustness and efficiency in predicting vehicle trajectories, and the potential to reduce the amount of data required to train autonomous vehicles, especially in corner cases. In conclusion, the behavior-aware model represents a significant advancement in the development of autonomous vehicles capable of predicting trajectories with the same level of proficiency as human drivers. The project page is available at https://github.com/Petrichor625/BATraj-Behavior-aware-Model.

This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be formulated as the problem of stabilizing a path following error system that describes the dynamics of position and possibly orientation errors of a vehicle with respect to a path, with the errors defined in an appropriate reference frame. In spite of the large variety of path following methods described in the literature we show that, in principle, most of them can be categorized in two groups: stabilization of the path following error system expressed either in the vehicle's body frame or in a frame attached to a "reference point" moving along the path, such as a Frenet-Serret (F-S) frame or a Parallel Transport (P-T) frame. With this observation, we provide a unified formulation that is simple but general enough to cover many methods available in the literature. We then discuss the advantages and disadvantages of each method, comparing them from the design and implementation standpoint. We further show experimental results of the path following methods obtained from field trials testing with under-actuated and fully-actuated autonomous marine vehicles. In addition, we introduce open-source Matlab and Gazebo/ROS simulation toolboxes that are helpful in testing path following methods prior to their integration in the combined guidance, navigation, and control systems of autonomous vehicles.

On-Policy Distillation (OPD) improves large language model reasoning by training a student model on trajectories sampled from its own policy under teacher supervision. Although OPD operates on trajectories, its learning signal remains token-level: it identifies deviations through high-loss tokens and repairs them through local reverse-KL correction. We show that this "trajectory-sampled but token-learned" mechanism cannot reliably bridge student trajectories toward teacher trajectories. About 30% of high-loss tokens fall into the low-divergence regime, indicating that many are surface-form mismatches rather than real reasoning forks. Moreover, even truly divergent tokens are difficult to repair with isolated token-level supervision, since reasoning failures often unfold as short-horizon distributional drift. We propose Trajectory-aware OPD (TOPD), which uses near-future trajectory information to identify real divergent states and distribute guidance across multiple future tokens. Experiments show that suppressing non-divergent high-loss tokens improves standard OPD from 47.8% to 48.2% average accuracy, while TOPD further improves performance to 52.2%, with gains on AIME24 from 60.0% to 63.3% and AIME25 from 46.7% to 53.3%.

This work investigates the reproducibility of the paper 'Explaining RL decisions with trajectories'. The original paper introduces a novel approach in explainable reinforcement learning based on the attribution decisions of an agent to specific clusters of trajectories encountered during training. We verify the main claims from the paper, which state that (i) training on less trajectories induces a lower initial state value, (ii) trajectories in a cluster present similar high-level patterns, (iii) distant trajectories influence the decision of an agent, and (iv) humans correctly identify the attributed trajectories to the decision of the agent. We recover the environments used by the authors based on the partial original code they provided for one of the environments (Grid-World), and implemented the remaining from scratch (Seaquest, HalfCheetah, Breakout and Q*Bert). While we confirm that (i), (ii), and (iii) partially hold, we extend on the largely qualitative experiments from the authors by introducing a quantitative metric to further support (iii), and new experiments and visual results for (i). Moreover, we investigate the use of different clustering algorithms and encoder architectures to further support (ii). We could not support (iv), given the limited extent of the original experiments. We conclude that, while some of the claims can be supported, further investigations and experiments could be of interest. We recognise the novelty of the work from the authors and hope that our work paves the way for clearer and more transparent approaches.

Predicting how a person's first-person view will evolve (what action will follow, what plan completes a task, whether an in-progress shot will score) is fundamentally under-specified: the same context admits many plausible futures, and a model trained to minimize prediction error is forced to hedge or average across them, getting it wrong either way. Two findings shape our approach. First, the future camera trajectory, the path the head carves through space, lets the model commit to one of those futures: it carries the operator's intent in a form fine enough to determine how an action will unfold, substantially outperforming language as a conditioning signal. Second, this same intent makes the trajectory itself partially predictable from the context at hand, enough that trajectory need not be observed at test time to recover most of the gain. We instantiate these findings as TrajPilot, a model that predicts candidate future trajectories from egocentric context and uses them to pilot action prediction in an action-aligned embedding space where language shapes the structure but is never used as a conditioning input. TrajPilot beats VLM and structured-planner baselines on procedural planning across Ego-Exo4D atomic, Ego-Exo4D Keystep, Ego4D GoalStep, and EgoPER, with the trajectory advantage widening with horizon (exactly where prior planners collapse) and holding under RGB-only camera-pose estimation. With the goal masked at inference, the same model performs goal-free anticipation, beating VLM baselines on Ego-Exo4D atomic and extending to EPIC-Kitchens-100 and basketball shot-outcome prediction.

Robust pedestrian trajectory forecasting is crucial to developing safe autonomous vehicles. Although previous works have studied adversarial robustness in the context of trajectory forecasting, some significant issues remain unaddressed. In this work, we try to tackle these crucial problems. Firstly, the previous definitions of robustness in trajectory prediction are ambiguous. We thus provide formal definitions for two kinds of robustness, namely label robustness and pure robustness. Secondly, as previous works fail to consider robustness about all points in a disturbance interval, we utilise a probably approximately correct (PAC) framework for robustness verification. Additionally, this framework can not only identify potential counterexamples, but also provides interpretable analyses of the original methods. Our approach is applied using a prototype tool named TrajPAC. With TrajPAC, we evaluate the robustness of four state-of-the-art trajectory prediction models -- Trajectron++, MemoNet, AgentFormer, and MID -- on trajectories from five scenes of the ETH/UCY dataset and scenes of the Stanford Drone Dataset. Using our framework, we also experimentally study various factors that could influence robustness performance.

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative modeling. In these settings, we assume access to cross-sectional samples that are uncorrelated over time, rather than full trajectories of samples. In order to better understand the systems under observation, we would like to learn a model of the underlying process that allows us to propagate samples in time and thereby simulate entire individual trajectories. In this work, we propose Action Matching, a method for learning a rich family of dynamics using only independent samples from its time evolution. We derive a tractable training objective, which does not rely on explicit assumptions about the underlying dynamics and does not require back-propagation through differential equations or optimal transport solvers. Inspired by connections with optimal transport, we derive extensions of Action Matching to learn stochastic differential equations and dynamics involving creation and destruction of probability mass. Finally, we showcase applications of Action Matching by achieving competitive performance in a diverse set of experiments from biology, physics, and generative modeling.

Terminal agents have demonstrated strong potential for autonomous command-line execution, yet their training remains constrained by the scarcity of high-quality and diverse execution trajectories. Existing approaches mitigate this bottleneck by synthesizing large-scale terminal task instances for trajectory sampling. However, they primarily focus on scaling the number of tasks while providing limited control over the diversity of execution trajectories that agents actually experience during training. In this paper, we present SkillSynth, an automated framework for terminal task synthesis built on a scenario-mediated skill graph. SkillSynth first constructs a large-scale skill graph, where scenarios serve as intermediate transition nodes that connect diverse command-line skills. It then samples paths from this graph as abstractions of real-world workflows, and uses a multi-agent harness to instantiate them into executable task instances. By grounding task synthesis in graph-sampled workflow paths, SkillSynth explicitly controls the diversity of minimal execution trajectories required to solve the synthesized tasks. Experiments on Terminal-Bench demonstrate the effectiveness of SkillSynth. Moreover, task instances synthesized by SkillSynth have been adopted to train Hy3 Preview, contributing to its enhanced agentic capabilities in terminal-based settings.

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

Predicting the trajectories of road agents is essential for autonomous driving systems. The recent mainstream methods follow a static paradigm, which predicts the future trajectory by using a fixed duration of historical frames. These methods make the predictions independently even at adjacent time steps, which leads to potential instability and temporal inconsistency. As successive time steps have largely overlapping historical frames, their forecasting should have intrinsic correlation, such as overlapping predicted trajectories should be consistent, or be different but share the same motion goal depending on the road situation. Motivated by this, in this work, we introduce HPNet, a novel dynamic trajectory forecasting method. Aiming for stable and accurate trajectory forecasting, our method leverages not only historical frames including maps and agent states, but also historical predictions. Specifically, we newly design a Historical Prediction Attention module to automatically encode the dynamic relationship between successive predictions. Besides, it also extends the attention range beyond the currently visible window benefitting from the use of historical predictions. The proposed Historical Prediction Attention together with the Agent Attention and Mode Attention is further formulated as the Triple Factorized Attention module, serving as the core design of HPNet.Experiments on the Argoverse and INTERACTION datasets show that HPNet achieves state-of-the-art performance, and generates accurate and stable future trajectories. Our code are available at https://github.com/XiaolongTang23/HPNet.

Tool-calling agents are increasingly deployed in real-world customer-facing workflows. Yet most studies on tool-calling agents focus on idealized settings with general, fixed, and well-specified tasks. In real-world applications, user requests are often (1) ambiguous, (2) changing over time, or (3) infeasible due to policy constraints, and training and evaluation data that cover these diverse, complex interaction patterns remain under-represented. To bridge the gap, we present Trajectory2Task, a verifiable data generation pipeline for studying tool use at scale under three realistic user scenarios: ambiguous intent, changing intent, and infeasible intents. The pipeline first conducts multi-turn exploration to produce valid tool-call trajectories. It then converts these trajectories into user-facing tasks with controlled intent adaptations. This process yields verifiable task that support closed-loop evaluation and training. We benchmark seven state-of-the-art LLMs on the generated complex user scenario tasks and observe frequent failures. Finally, using successful trajectories obtained from task rollouts, we fine-tune lightweight LLMs and find consistent improvements across all three conditions, along with better generalization to unseen tool-use domains, indicating stronger general tool-calling ability.

Demystifying the interactions among multiple agents from their past trajectories is fundamental to precise and interpretable trajectory prediction. However, previous works mainly consider static, pair-wise interactions with limited relational reasoning. To promote more comprehensive interaction modeling and relational reasoning, we propose DynGroupNet, a dynamic-group-aware network, which can i) model time-varying interactions in highly dynamic scenes; ii) capture both pair-wise and group-wise interactions; and iii) reason both interaction strength and category without direct supervision. Based on DynGroupNet, we further design a prediction system to forecast socially plausible trajectories with dynamic relational reasoning. The proposed prediction system leverages the Gaussian mixture model, multiple sampling and prediction refinement to promote prediction diversity, training stability and trajectory smoothness, respectively. Extensive experiments show that: 1)DynGroupNet can capture time-varying group behaviors, infer time-varying interaction category and interaction strength during trajectory prediction without any relation supervision on physical simulation datasets; 2)DynGroupNet outperforms the state-of-the-art trajectory prediction methods by a significant improvement of 22.6%/28.0%, 26.9%/34.9%, 5.1%/13.0% in ADE/FDE on the NBA, NFL Football and SDD datasets and achieve the state-of-the-art performance on the ETH-UCY dataset.

Modeling and reproducing crowd behaviors are important in various domains including psychology, robotics, transport engineering and virtual environments. Conventional methods have focused on synthesizing momentary scenes, which have difficulty in replicating the continuous nature of real-world crowds. In this paper, we introduce a novel method for automatically generating continuous, realistic crowd trajectories with heterogeneous behaviors and interactions among individuals. We first design a crowd emitter model. To do this, we obtain spatial layouts from single input images, including a segmentation map, appearance map, population density map and population probability, prior to crowd generation. The emitter then continually places individuals on the timeline by assigning independent behavior characteristics such as agents' type, pace, and start/end positions using diffusion models. Next, our crowd simulator produces their long-term locomotions. To simulate diverse actions, it can augment their behaviors based on a Markov chain. As a result, our overall framework populates the scenes with heterogeneous crowd behaviors by alternating between the proposed emitter and simulator. Note that all the components in the proposed framework are user-controllable. Lastly, we propose a benchmark protocol to evaluate the realism and quality of the generated crowds in terms of the scene-level population dynamics and the individual-level trajectory accuracy. We demonstrate that our approach effectively models diverse crowd behavior patterns and generalizes well across different geographical environments. Code is publicly available at https://github.com/InhwanBae/CrowdES .

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.

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.

Trajectory-Guided image-to-video (I2V) generation aims to synthesize videos that adhere to user-specified motion instructions. Existing methods typically rely on computationally expensive fine-tuning on scarce annotated datasets. Although some zero-shot methods attempt to trajectory control in the latent space, they may yield unrealistic motion by neglecting 3D perspective and creating a misalignment between the manipulated latents and the network's noise predictions. To address these challenges, we introduce Zo3T, a novel zero-shot test-time-training framework for trajectory-guided generation with three core innovations: First, we incorporate a 3D-Aware Kinematic Projection, leveraging inferring scene depth to derive perspective-correct affine transformations for target regions. Second, we introduce Trajectory-Guided Test-Time LoRA, a mechanism that dynamically injects and optimizes ephemeral LoRA adapters into the denoising network alongside the latent state. Driven by a regional feature consistency loss, this co-adaptation effectively enforces motion constraints while allowing the pre-trained model to locally adapt its internal representations to the manipulated latent, thereby ensuring generative fidelity and on-manifold adherence. Finally, we develop Guidance Field Rectification, which refines the denoising evolutionary path by optimizing the conditional guidance field through a one-step lookahead strategy, ensuring efficient generative progression towards the target trajectory. Zo3T significantly enhances 3D realism and motion accuracy in trajectory-controlled I2V generation, demonstrating superior performance over existing training-based and zero-shot approaches.

We introduce a vocabulary for automated research systems built from one or more agents to make their design choices easier to describe and compare. The vocabulary specifies 1) who the agents are, 2) what operations are available in the system, 3) who may invoke them, 4) how agents communicate, 5) what information is visible within and across runs, 6) how the next action is chosen, 7) how a run begins, and 8) how outputs are evaluated. A trajectory records one run from the input task to the returned artifact. Because agents, operations, and initialization may be stochastic, repeated runs on the same task induce a distribution over trajectories rather than a single behavior. Our vocabulary turns structural design questions, such as when agents should communicate, gain or lose a capability, or carry information across runs, into testable choices. It also makes the evaluator a component of the system, since reported gains depend on how closely the proxy score matches true quality. That separation also splits the vague complaint that these systems lack taste into two failures with different solutions. Generative taste is the rate at which a system proposes novel trajectories before any score is observed, and evaluative taste is the gap between the proxy score and the quality it should match. We instantiate the vocabulary on recent autoresearch systems to illustrate that it covers designs that differ widely in structure.

Trajectory prediction has been a crucial task in building a reliable autonomous driving system by anticipating possible dangers. One key issue is to generate consistent trajectory predictions without colliding. To overcome the challenge, we propose an efficient masked autoencoder for trajectory prediction (Traj-MAE) that better represents the complicated behaviors of agents in the driving environment. Specifically, our Traj-MAE employs diverse masking strategies to pre-train the trajectory encoder and map encoder, allowing for the capture of social and temporal information among agents while leveraging the effect of environment from multiple granularities. To address the catastrophic forgetting problem that arises when pre-training the network with multiple masking strategies, we introduce a continual pre-training framework, which can help Traj-MAE learn valuable and diverse information from various strategies efficiently. Our experimental results in both multi-agent and single-agent settings demonstrate that Traj-MAE achieves competitive results with state-of-the-art methods and significantly outperforms our baseline model.

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.

Accumulating substantial volumes of real-world driving data proves pivotal in the realm of trajectory forecasting for autonomous driving. Given the heavy reliance of current trajectory forecasting models on data-driven methodologies, we aim to tackle the challenge of learning general trajectory forecasting representations under limited data availability. We propose a pipeline-level solution to mitigate the issue of data scarcity in trajectory forecasting. The solution is composed of two parts: firstly, we adopt HD map augmentation and trajectory synthesis for generating driving data, and then we learn representations by pre-training on them. Specifically, we apply vector transformations to reshape the maps, and then employ a rule-based model to generate trajectories on both original and augmented scenes; thus enlarging the driving data without collecting additional real ones. To foster the learning of general representations within this augmented dataset, we comprehensively explore the different pre-training strategies, including extending the concept of a Masked AutoEncoder (MAE) for trajectory forecasting. Without bells and whistles, our proposed pipeline-level solution is general, simple, yet effective: we conduct extensive experiments to demonstrate the effectiveness of our data expansion and pre-training strategies, which outperform the baseline prediction model by large margins, e.g. 5.04%, 3.84% and 8.30% in terms of MR_6, minADE_6 and minFDE_6. The pre-training dataset and the codes for pre-training and fine-tuning are released at https://github.com/yhli123/Pretraining_on_Synthetic_Driving_Data_for_Trajectory_Prediction.

We present Kinodynamic RRT*, an incremental sampling-based approach for asymptotically optimal motion planning for robots with linear differential constraints. Our approach extends RRT*, which was introduced for holonomic robots (Karaman et al. 2011), by using a fixed-final-state-free-final-time controller that exactly and optimally connects any pair of states, where the cost function is expressed as a trade-off between the duration of a trajectory and the expended control effort. Our approach generalizes earlier work on extending RRT* to kinodynamic systems, as it guarantees asymptotic optimality for any system with controllable linear dynamics, in state spaces of any dimension. Our approach can be applied to non-linear dynamics as well by using their first-order Taylor approximations. In addition, we show that for the rich subclass of systems with a nilpotent dynamics matrix, closed-form solutions for optimal trajectories can be derived, which keeps the computational overhead of our algorithm compared to traditional RRT* at a minimum. We demonstrate the potential of our approach by computing asymptotically optimal trajectories in three challenging motion planning scenarios: (i) a planar robot with a 4-D state space and double integrator dynamics, (ii) an aerial vehicle with a 10-D state space and linearized quadrotor dynamics, and (iii) a car-like robot with a 5-D state space and non-linear dynamics.