Beckmann Transport Models: From Autonomous Flows to One-Step Maps

We propose an instantiation of flow matching that relies on a time-independent velocity field (an \emph{autonomous flow}) to exactly map between two distributions, so long as the target is singular, i.e.\ supported on a lower-dimensional data manifold. We also show that the one-step generative map associated with this flow is the unique solution of a simple conservation equation, which can be used to learn the map directly from samples. These autonomous flows and maps give a dynamical meaning to the flux constraint of Beckmann's transportation problem. Their construction provides a unifying framework that recovers, for instance, the closed-form Poisson-flow generative model and equilibrium matching with a quadratic flow-matching regression loss. We illustrate how this theory corrects inconsistencies in existing methods and demonstrate the effectiveness of the autonomous flow and the one-step map on ImageNet 256x256.

World Action Planner: Generalizable Decision-Making with Action-Conditioned World Models

Building generalizable agents for diverse applications remains a fundamental challenge. While imitation learning-based policies succeed in specific training environments, they often fail to generalize to novel scenes and tasks. In this work, we propose World Action Planner, a robot planning system that leverages the reasoning capabilities of Vision-Language Models (VLMs) and the physical grounding of a multi-task pose-image conditioned world model. Our system enables an agent to propose initial action plans and iteratively refine them via optimization and search, reasoning over imagined world model rollouts. We demonstrate that our approach achieves superior performance across compositional tasks, new layouts, and zero-shot generalization scenarios, significantly outperforming state-of-the-art end-to-end policy models such as VLAs and WAMs. Project website at worldactionplanner.github.io

Explorative Modeling: Unlocking a Third Pretraining Axis and End-to-End Generation

The deep learning revolution, kicked off by AlexNet, taught us that end-to-end training beats decomposing a problem into hand-designed stages. Generative modeling, however, has remained the exception-despite generative models being remarkably capable, they are still not trained end-to-end. This is because, at its core, generative modeling is about handling distributions with many modes, and existing scalable approaches handle this the same way, by factoring the generation procedure, which prevents end-to-end generation. In this work, we introduce Explorative Modeling, a new paradigm that instead factors the training loop, exploring K candidate matches between model generations and data, and training on the best, so predictions commit to modes rather than blurring them. We find Explorative Models (XMs) useful in two settings. First, increasing exploration adds a third pretraining axis beyond parameters and data for existing generative models-where scaling exploration monotonically improves performance across both continuous and discrete domains (images, video, and language). Notably, gains from exploration increase with scale, climbing from 7% to 36% as data scales and from 13% to 23% as models grow, with efficiency gains more than doubling at 3x the compute. Concretely, exploration improves FLOP efficiency by 4.1x, sample efficiency by 6.2x, parameter efficiency by 47%, lifts the strongest of image-generation recipes to a near-state-of-the-art 1.43 FID on ImageNet without guidance, enables scaling how end-to-end existing models are, and unlocks scaling generalization. Second, XMs enable end-to-end reconstructive generative modeling, matching diffusion on control tasks with 16-256x fewer inference steps. Together, these results establish XMs as both a new pretraining axis for existing generative models and a standalone end-to-end generative modeling paradigm.

From Interface to Inference: Eliciting Any-Order Inference from Any-Order Models

Many discrete reasoning tasks, such as code generation, are inherently non-causal: programmers move between high-level structure and local details, a process we call any-order inference. For autoregressive language models, which lack a native any-order interface, non-causal abilities such as infilling and next-edit prediction require hand-designed mechanisms. Can we instead design models that natively support any-order inference? Masked diffusion models have recently emerged as compelling candidates, as their any-order training objective naturally offers an any-order prediction interface. This interface, however, does not automatically yield any-order inference. We demonstrate that this interface-inference gap stems from positional uncertainty: fixed-canvas, token-level models may know what semantic component should appear without knowing where to place it. In light of this, we propose two complementary approaches: (1) Insertion-based masked diffusion, building on FlexMDM (Kim et al, 2025), relaxes fixed-position commitments via insertions, enabling generation across non-contiguous regions. (2) Latent-space masked diffusion shifts prediction to coarser semantic segments, enabling search over latent generation orders. Empirically, we train a 7B FlexMDM for Python coding and a 125M LatentMDM for GSM8K and show that both approaches induce distinct any-order inference behaviors and improve downstream performance. We release our codebase at https://github.com/SeunggeunKimkr/genuine-any-order.

Ordered Action Tokens for Visuomotor Policy Learning

Action tokenization maps continuous robot action chunks to discrete tokens and has become an important interface for modern visuomotor policies. Existing approaches either rely on analytical discretization methods that produce prohibitively long token sequences or learned latent tokenizers that lack structure, limiting their compatibility with downstream policies. In this work, we identify three desiderata for action tokenization - high compression, total decodability, and an ordered token space - and introduce Ordered Action Tokenization (OAT), a learned action tokenizer that satisfies all three. OAT discretizes action chunks into an ordered sequence of tokens using a transformer with registers, finite scalar quantization, and ordering-inducing training mechanisms. By training each token prefix to decode into a valid action chunk, OAT places coarse control information in early tokens and uses later tokens to refine residual detail, yielding an anytime tradeoff between inference cost and action fidelity. We validate OAT in two prevailing uses of action tokens: autoregressive policies that generate tokens for control, and token co-training policies that use token losses to shape the vision-language model context consumed by a flow-based action expert. Across three policy backbones and more than 60 tasks spanning five simulation benchmarks and real-world settings, OAT consistently delivers strong policy performance while offering significantly greater flexibility at inference time.

Masked Visual Actions for Unified World Modeling

Video models absorb rich priors over how the visual world moves, interacts, and responds to contact, making them promising substrates for robotic world modeling. The central challenge is how to communicate action to such models in a form aligned with the visual space in which they learned these interaction priors, yet still grounded in physical manipulation. We introduce Masked Visual Actions, a pixel-space control interface that expresses action as a partially revealed trajectory of an arbitrary entity in a video. Revealing robot motion makes the model act as a forward dynamics model that predicts the scene's response to low-level robot actions, while revealing desired object motion makes the same model recover robot behavior consistent with that outcome. Finetuned with only 15 hours of masked examples from real videos and simulation, a single checkpoint achieves strong visual fidelity and controllability across diverse scenes and multiple embodiments. In downstream manipulation settings, the model produces imagined rollouts whose outcomes correlate with real-world execution for policy evaluation, improves decision making by ranking candidate futures in model-based planning, and supports inverse modeling by synthesizing robot motion from desired object motion.

DriftWorld: Fast World Modeling through Drifting

Predictive world models enable robots to plan by imagining the outcomes of their actions, but their value for control hinges on generating many rollouts quickly. This creates a bottleneck for diffusion-based world models: multistep sampling makes each rollout expensive, limiting large-scale action search at inference time. We introduce DriftWorld, an action-conditioned world model based on drifting generative models. Rather than denoising iteratively at inference, DriftWorld learns an action-conditioned drift during training, allowing it to generate future frames from the current observation and a candidate action sequence in a single forward pass at 30+ fps, which is 17x faster on average than diffusion based baselines. We evaluate DriftWorld on standard vision-based robotic manipulation benchmarks, including Bridge-V2, RT-1, Language Table, Push-T, and Robomimic. By producing rollouts that are both accurate and fast, DriftWorld achieves state-of-the-art decision-making performance with far less inference time than diffusion-based world model baselines. Beyond online control, DriftWorld can also serve as an offline simulator for ranking real-world robot policies, with rollout-based scores correlating with ground truth at up to 0.99. These results show that drifting models are a strong fit for robot world modeling, where fast, high-quality imagination directly supports planning and policy evaluation.

B-spline Policy: Accelerating Manipulation Policies via B-spline Action Representations

In this work, we present B-spline Policy (BSP), an action representation designed for accelerating robot manipulation policies. Rather than predicting discrete-time action chunks, BSP parameterizes actions as continuous B-spline curves defined by a set of knots and control points. This representation yields smooth, time-continuous trajectories that can be temporally scaled and executed by low-level controllers at higher frequencies and speeds. We show that B-spline-parameterized actions can be seamlessly integrated into standard policy learning pipelines by directly predicting B-spline parameters. Experiments on simulated and real-world tasks demonstrate that BSP significantly reduces task completion time, achieving substantial improvements over baseline methods while maintaining strong success rates. More results: https://b-spline-policy.github.io

Formal Disco: Scalable Open-Ended Generation of Formally Verified Programs

The cost of producing code is rapidly diminishing with increasingly capable AI agents, while quality assurance of generated programs has not kept pace. Formal verification provides the strongest possible guarantees, but the ability of AI models to work with verification-aware languages is hindered by the scarcity of human-written examples of programs in those languages. To tackle this prevalent data scarcity issue, we propose Formal Disco: a distributed system for coordination of LLM-based workers that can be easily applied to open-ended synthetic data generation at scale. We use Formal Disco to share tasks and programs between three classes of workers: "initiators", which read random READMEs from open-source repositories and documentation snippets to sketch a related verified program, "fixers" which take compiler and verifier feedback and attempt to resolve issues, and "extenders" that take working programs and propose patches to expand them. Formal Disco records all agent-generated traces and uses them both for initial distillation from a stronger model as well as self-improvement. We also propose a principle of maximum entropy for synthetic program generation, and use entropy maximization via iterative supervised fine-tuning to learn to generate increasingly diverse programs over time. We release large datasets of synthetic verified programs in three languages - Dafny, Verus, and Frama-C -, and fine-tune open models for verification-relevant tasks, often matching or exceeding the performance of Claude Opus 4.5. Overall, our work offers a path to create synthetic data at scale for formal reasoning domains and overcome the long-standing data barrier.

MemoBench: Benchmarking World Modeling in Dynamically Changing Environments

Video generation models aspire to simulate dynamic environments, and several benchmarks now evaluate memory consistency across frames. However, most assess consistency only while the target remains in view, and the few that force objects out of view evaluate static scenes where nothing changes during occlusion. To bridge this gap, we introduce MemoBench, a diagnostic benchmark built around the disappear-and-reappear paradigm in dynamically changing environments: a target object undergoes a physical process, disappears from view, and must be correctly recovered in its updated state upon reappearance. We curate 360 ground-truth clips spanning synthetic and real-world scenes, and design an evaluation suite combining automated metrics with VQA-based assessment across four diagnostic pillars. Evaluation of eight state-of-the-art models reveals key insights and open challenges regarding memory consistency under the disappear-and-reappear paradigm.