FlowS: One-Step Motion Prediction via Local Transport Conditioning

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.