s × N Flow-matching VLA deployment · training-free

Coupling Execution Horizon and Sampling Depth

in Flow-Matching Vision-Language-Action Policies

Jiabing Yang1,2,5, Yuan Xu1,2, Yixiang Chen1,2, Qisen Ma1,2, Peiyan Li1,2, Kai Wang1,2, Chenhang Cui3, Tao Yu1,2,
Zichen Wen4, Wen Ye1,2, Bowen Fang1,2, Ziheng He1,2, Xiangnan Wu1,2, Yingda Li1,2, Yan Huang1,2,5,†, Liang Wang1,2

1School of Artificial Intelligence, University of Chinese Academy of Sciences 2New Laboratory of Pattern Recognition (NLPR), Institute of Automation, Chinese Academy of Sciences 3National University of Singapore 4Shanghai Jiao Tong University 5FiveAges †Corresponding author

01Overview

Two deployment knobs, one coupled choice

TL;DR

Abstract

02Phenomenon

Fewer steps hurt fast replanning and help long open-loop runs

The sign reversal
Backbone
π0 on LIBERO-Long in one pictureThe 2 × 2 of Table I: each line follows one execution horizon from the default 10 steps to 2 steps.
Table I
The full horizon × depth grid
Backbone
03Mechanism

Truncation shrinks the cloud, not its centre

Figure 2.

Deployment: N Euler steps, then s actions open loop

x of k plus one equals x of k minus delta tau times the velocity field at x of k, tau k and the observation; delta tau equals one over N and tau k equals one minus k over N
the executed action a k equals the predicted action for k from t to t plus s minus one

Every evaluation of vθ is a full forward pass of the backbone, so N is also the number of function evaluations per query. The policy is queried again at t + s with a fresh observation and fresh noise.

Proposition 1 · Euler truncation contraction (Gaussian target)

the marginal velocity is affine: alpha of tau times x minus one minus tau times mu, minus mu, with alpha of tau given by the Gaussian gain
the expectation of the emitted chunk equals mu for all N
the covariance equals rho of N times sigma zero squared times the identity, with rho of N the product over steps of one minus alpha of tau k over N, squared, over sigma zero squared
rho of N equals one minus c over N plus order N to the minus two, with c equal to two plus the integral of alpha squared

The mean is integrated exactly for every N; the spread is multiplied by g(N) = √ρ(N), which is 0 at N = 1 and approaches 1 at the rate 1 − c/N.

Euler contraction, live

Euler steps N
Variance gain g(N) = √ρ(N)
exact for a Gaussian target
(a) Cloud radius vs. sampling depth
(b) Open-loop spread over the horizon
04Results

Higher success at a fraction of the latency

Backbone
Interaction per suiteEach panel follows the short and the long horizon from the default depth to two steps; lines that cross reverse the sign of the depth effect.
Table I
Success vs. per-step latencyLIBERO average; the latency is per control step, amortized over the executed actions.

05Analysis

It is the redraws, not just less noise

Causal interventions on π0 / LIBERO-LongTwo-step minus ten-step success at s = 5 and s = 20 for each condition; the interaction is the change between them.
Table III

    06Rollouts

    Same scene, four deployments

    07Citation

    BibTeX

    @article{yang2026coupling,
  title   = {Coupling Execution Horizon and Sampling Depth in Flow-Matching VLA Policies},
  author  = {Yang, Jiabing and Xu, Yuan and Chen, Yixiang and Ma, Qisen and Li, Peiyan and Wang, Kai and Cui, Chenhang and Yu, Tao and Wen, Zichen and Ye, Wen and Fang, Bowen and He, Ziheng and Wu, Xiangnan and Li, Yingda and Huang, Yan and Wang, Liang},
  journal = {arXiv preprint},
  year    = {2026}
}