Coupling Execution Horizon and Sampling Depth in Flow-Matching VLA Policies

Abstract

Flow-matching Vision-Language-Action (VLA) models generate expressive continuous trajectories for robotic manipulation, yet balancing real-time responsiveness with execution stability remains a persistent challenge. Standard deployment workflows typically treat numerical solver depth and execution horizon as decoupled choices. The horizon amortizes inference latency, while solver depth is kept high to preserve integration fidelity. In this paper, we reveal a fundamental compute-execution coupling in flow-matching VLAs governed by a systematic sign reversal. While coarse numerical integration degrades precision under rapid replanning, it markedly improves task performance under extended open-loop commitment. Geometrically, numerical truncation contracts lateral action dispersion around an invariant trajectory centroid, serving as an implicit regularizer that suppresses compounding open-loop drift. Across LIBERO, RoboTwin 2.0, and real-world Franka manipulation on representative VLA backbones including $π_0$, $π_{0.5}$, and GR00T, exploiting this joint coupling consistently achieves superior task success while drastically lowering inference latency, entirely training-free and without architectural modifications. These findings establish numerical sampling depth as an operational variance regulator, shifting its role from a static precision budget to an active deployment knob in robot learning. Project page: https://jiabingyang01.github.io/Horizon-Depth-VLA/