# FlowS: One-Step Motion Prediction via Local Transport Conditioning

arXiv: https://arxiv.org/abs/2604.26065 · HTML: https://mlsanity.com/paper/2604.26065/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 29 of its 33 references that are in the map.
- First posted on arXiv 28 Apr 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [DiffusionDrive: Truncated Diffusion Model for End-to-End Autonomous Driving](https://mlsanity.com/paper/2411.15139/) (2024)
- [Wayformer: Motion Forecasting via Simple & Efficient Attention Networks](https://mlsanity.com/paper/2207.05844/) (2022)
- [Motion Transformer with Global Intention Localization and Local Movement Refinement](https://mlsanity.com/paper/2209.13508/) (2022)
- [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [MotionLM: Multi-Agent Motion Forecasting as Language Modeling](https://mlsanity.com/paper/2309.16534/) (2023)
- [MTR++: Multi-Agent Motion Prediction with Symmetric Scene Modeling and Guided Intention Querying](https://mlsanity.com/paper/2306.17770/) (2023)
- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [GoalFlow: Goal-Driven Flow Matching for Multimodal Trajectories Generation in End-to-End Autonomous Driving](https://mlsanity.com/paper/2503.05689/) (2025)
- [HDGT: Heterogeneous Driving Graph Transformer for Multi-Agent Trajectory Prediction via Scene Encoding](https://mlsanity.com/paper/2205.09753/) (2022)
- [Consistency Flow Matching: Defining Straight Flows with Velocity Consistency](https://mlsanity.com/paper/2407.02398/) (2024)
- [Real-Time Motion Prediction via Heterogeneous Polyline Transformer with Relative Pose Encoding](https://mlsanity.com/paper/2310.12970/) (2023)
- [Scenario Dreamer: Vectorized Latent Diffusion for Generating Driving Simulation Environments](https://mlsanity.com/paper/2503.22496/) (2025)
- [Reasoning Multi-Agent Behavioral Topology for Interactive Autonomous Driving](https://mlsanity.com/paper/2409.18031/) (2024)
- [BridgeDrive: Diffusion Bridge Policy for Closed-Loop Trajectory Planning in Autonomous Driving](https://mlsanity.com/paper/2509.23589/) (2025)
- [EDA: Evolving and Distinct Anchors for Multimodal Motion Prediction](https://mlsanity.com/paper/2312.09501/) (2023)
- [MGTR: Multi-Granular Transformer for Motion Prediction with LiDAR](https://mlsanity.com/paper/2312.02409/) (2023)
- [TrajFlow: Multi-modal Motion Prediction via Flow Matching](https://mlsanity.com/paper/2506.08541/) (2025)
- [ModeSeq: Taming Sparse Multimodal Motion Prediction with Sequential Mode Modeling](https://mlsanity.com/paper/2411.11911/) (2024)
- [RMP-YOLO: A Robust Motion Predictor for Partially Observable Scenarios even if You Only Look Once](https://mlsanity.com/paper/2409.11696/) (2024)
- [IMPACT: Behavioral Intention-aware Multimodal Trajectory Prediction with Adaptive Context Trimming](https://mlsanity.com/paper/2504.09103/) (2025)
- [FlowDrive: Energy Flow Field for End-to-End Autonomous Driving](https://mlsanity.com/paper/2509.14303/) (2025)
- [FlowDrive: moderated flow matching with data balancing for trajectory planning](https://mlsanity.com/paper/2509.21961/) (2025)

## Abstract (arXiv)

Generative motion prediction must satisfy three simultaneous requirements for real-world autonomy: high accuracy, diverse multimodal futures, and strictly bounded latency. Diffusion models meet the first two but violate the third, requiring tens to hundreds of denoising steps. We identify a conditioning strategy that resolves this tension: textitsingle-step integration is accurate when the underlying transport problem is local. A model that must both discover the correct behavioral mode and traverse a long displacement in one step accumulates large discretization errors; conditioning the base distribution to lie near plausible futures reduces the problem to short-range refinement, the regime where a single Euler step suffices. We instantiate this local transport conditioning in FlowS, a conditional flow matching framework with two mechanisms. First, an online, scene-conditioned learned prior emits K calibrated anchor trajectories per agent, each already near a plausible future, converting mode discovery into local correction. Second, a step-consistent displacement field enforces semigroup self-consistency, guaranteeing that a single step inherits multi-step accuracy. Crucially, anchoring this field at learned priors along straight-line paths yields a stable, low-variance training target, unlike prior self-consistency methods that suffer from high-variance bootstrap signals on curved diffusion paths. On the Waymo Open Motion Dataset, FlowS achieves state-of-the-art Soft mAP (0.4804) and mAP (0.4703) with ensemble at 75,FPS with single-step inference, demonstrating that local transport conditioning makes one-step generative motion prediction practical for safety-critical autonomy. Code and pretrained models will be released upon acceptance.