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

Jiabing Yang; Yuan Xu; Yixiang Chen; Qisen Ma; Peiyan Li; Kai Wang; Chenhang Cui; Tao Yu

cs.ROOct 23, 2026

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

Authors: Jiabing Yang, Yuan Xu, Yixiang Chen, Qisen Ma, Peiyan Li, Kai Wang, Chenhang Cui, Tao Yu,

Organizations: School of Artificial Intelligence, University of Chinese Academy of Sciences. · New Laboratory of Pattern Recognition (NLPR), Institute of Automation, Chinese Academy of Sciences. · FiveAges. · National University of Singapore. ·

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/

Figures & tables

Fig. 1: Sign-reversing coupling between execution horizon

s

and sampling depth

N

. Shallow sampling (

N{=}2

) degrades performance under rapid replanning but yields systematic gains under extended open-loop execution. Curves show paired marginal contrasts

Y_{s,2}-Y_{s,N_{0}}

on LIBERO-Long across matched seeds (mean

\pm

sample SD), where solid markers indicate horizons with unanimous sign agreement across all three seeds.

Fig. 2: Overview of computational-execution co-design in flow-matching Vision-Language-Action policies. Top: The policy conditions on multimodal observation $o_{t}$ and integrates linear probability flow with $N$ forward Euler steps from prior noise $x^{(0)}\sim\mathcal{N}(0,I)$ to generate action chunk $\hat{\mathbf{a}}_{t}$ , committing to an open-loop prefix of length $s$ on the robot before replanning at $t+s$ . Bottom: The coupling mechanism. Early solver truncation ( $N{=}2$ ) contracts sample dispersion around the conditional centroid ( $R(2)<R(10)$ ). Under rapid replanning ( $s{=}5$ ), high-frequency closed-loop feedback exploits sample diversity; under extended commitment ( $s{=}20$ ), coarse integration suppresses compounding lateral drift, reversing solver degradation and delivering up to $5.6\times$ inference speedups.

Suite

\pi_{0}

[ 1 ] [

H{=}50

]

\pi_{0.5}

[ 2 ] [

H{=}10

]

GR00T-N1.7 [ 28 ] [

H{=}16

]

(5,10)

(5,2)

(20,10)

(20,2)

\mathcal{I}

(5,10)

(5,2)

(10,10)

(10,2)

\mathcal{I}

(2,4)

(2,2)

(8,4)

(8,2)

\mathcal{I}

Spatial

97.1_{\pm 0.3}

\mathbf{97.7}_{\pm 0.4}

93.8_{\pm 0.5}

95.3_{\pm 0.3}

\mathbf{+0.9}_{\pm 0.6}

98.5_{\pm 0.4}

98.5_{\pm 0.4}

98.3_{\pm 0.6}

\mathbf{98.7}_{\pm 0.6}

\mathbf{+0.3}_{\pm 1.2}^{\dagger}

\mathbf{97.0}_{\pm 0.5}

96.9_{\pm 0.6}

96.7_{\pm 0.5}

96.5_{\pm 0.4}

\mathbf{-0.1}_{\pm 0.4}^{\dagger}

Object

98.1_{\pm 0.5}

97.9_{\pm 0.8}

97.1_{\pm 0.7}

\mathbf{99.1}_{\pm 0.5}

\mathbf{+2.1}_{\pm 1.5}

97.8_{\pm 0.3}

98.5_{\pm 0.6}

99.1_{\pm 0.6}

\mathbf{99.5}_{\pm 0.2}

\mathbf{-0.4}_{\pm 0.2}

97.1_{\pm 0.9}

96.5_{\pm 0.8}

98.9_{\pm 0.3}

\mathbf{99.1}_{\pm 0.3}

\mathbf{+0.7}_{\pm 0.4}

Goal

93.3_{\pm 1.0}

93.9_{\pm 1.2}

93.9_{\pm 0.1}

\mathbf{97.3}_{\pm 0.6}

\mathbf{+2.7}_{\pm 1.2}

98.3_{\pm 1.1}

97.9_{\pm 0.5}

98.0_{\pm 0.6}

\mathbf{98.5}_{\pm 0.5}

\mathbf{+0.8}_{\pm 0.5}

94.4_{\pm 0.5}

94.4_{\pm 1.1}

\mathbf{95.9}_{\pm 0.7}

95.5_{\pm 0.5}

\mathbf{-0.4}_{\pm 0.5}^{\dagger}

Long

81.2_{\pm 0.7}

78.5_{\pm 1.5}

86.9_{\pm 2.5}

\mathbf{90.5}_{\pm 0.6}

\mathbf{+6.4}_{\pm 2.1}

93.1_{\pm 0.4}

93.1_{\pm 0.5}

94.8_{\pm 1.0}

\mathbf{95.3}_{\pm 0.8}

\mathbf{+0.5}_{\pm 1.6}^{\dagger}

84.4_{\pm 0.3}

78.9_{\pm 0.9}

\mathbf{91.3}_{\pm 2.4}

89.5_{\pm 0.8}

\mathbf{+3.6}_{\pm 1.4}

Average

92.4_{\pm 0.6}

92.0_{\pm 0.5}

92.9_{\pm 0.8}

\mathbf{95.5}_{\pm 0.1}

\mathbf{+3.0}_{\pm 0.8}

96.9_{\pm 0.4}

97.0_{\pm 0.2}

97.6_{\pm 0.2}

\mathbf{98.0}_{\pm 0.5}

\mathbf{+0.3}_{\pm 0.5}^{\dagger}

93.2_{\pm 0.3}

91.7_{\pm 0.5}

\mathbf{95.7}_{\pm 0.6}

95.1_{\pm 0.3}

\mathbf{+0.9}_{\pm 0.4}

TABLE I: Factorial Horizon–Depth Evaluation on the LIBERO Benchmark (Mean Success Rate %). For each model, we contrast the short-horizon pair (

s_{\mathrm{short}}

) and long-horizon pair (

s_{\mathrm{long}}

\Delta_{\mathrm{short}}

and

\Delta_{\mathrm{long}}

denote the paired marginal effect of reducing solver depth; Interaction

\mathcal{I}=\Delta_{\mathrm{long}}-\Delta_{\mathrm{short}}

reflects the sign-reversing coupling across execution regimes (

\dagger

denotes interaction contrasts constrained by baseline task ceiling effects).

Fig. 3: Success rates across the joint execution horizon ( $s$ ) vs. sampling depth ( $N$ ) grid on LIBERO-Long (500 rollouts per cell; $\pi_{0}$ and $\pi_{0.5}$ from seed 7, GR00T-N1.7 averaged over seeds 7/8/9; color scales normalized per panel). (a) For $\pi_{0}$ , optimal sampling depth shifts shallower as $s$ expands. (b) $\pi_{0.5}$ is restricted by its 10-action prediction head. (c) GR00T-N1.7 supervises 16 actions, peaking near its released configuration $(8,4)$ .

Task Name	$\pi_{0}$ [ $H{=}50$ ]						$\pi_{0.5}$ [ $H{=}50$ ]
Task Name	$(10,10)$	$(10,2)$	$(25,10)$	$(25,2)$	$(50,10)$	$(50,2)$	$(10,10)$	$(10,2)$	$(25,10)$	$(25,2)$	$(50,10)$	$(50,2)$
Hanging Mug	8.0	2.0	6.0	13.0	5.0	8.0	30.0	26.0	19.0	20.0	6.0	8.0
Open Microwave	10.0	9.0	31.0	4.0	37.0	15.0	58.0	14.0	77.0	61.0	57.0	44.0
Place Can in Basket	34.0	38.0	43.0	44.0	30.0	29.0	69.0	75.0	74.0	78.0	52.0	60.0
Place Shoe	41.0	47.0	62.0	68.0	42.0	40.0	64.0	57.0	66.0	70.0	63.0	53.0
Move Playing Card Away	57.0	74.0	61.0	68.0	42.0	46.0	96.0	76.0	88.0	83.0	73.0	72.0

TABLE II: Horizon–Depth Evaluation on RoboTwin 2.0 across 50 Bimanual Tasks (Mean Success Rate %) evaluated across execution horizons (

s\in\{10,25,50\}

H{=}50

) and two sampling depths (

100

rollouts per task). Multi-task checkpoints are jointly fine-tuned across all 50 tasks.

Fig. 4: Geometric mechanism of horizon–depth coupling. (a) Cloud radius vs. sampling depth on

\pi_{0}

(Proposition 1 curve fitted on

N\geq 2

). Single-step Euler deviates by retaining a non-zero approximation residual. (b) Open-loop trajectory spread accumulated over horizon

s

. Deep sampling (

N{=}10

) generates

2.1\times

wider lateral dispersion than

N{=}2

while preserving nominal path direction.

Experimental Condition	Short Horizon ( $s{=}5$ )			Long Horizon ( $s{=}20$ )			Interaction $\mathcal{I}$
Experimental Condition	Deep ( $N{=}10$ )	Shallow ( $N{=}2$ )	Diff ( $\Delta_{5}$ )	Deep ( $N{=}10$ )	Shallow ( $N{=}2$ )	Diff ( $\Delta_{20}$ )	Interaction $\mathcal{I}$
Standard Sampling (Default)	$81.2\pm 0.7$	$78.5\pm 1.5$	$-2.7\pm 1.0$	$86.9\pm 2.5$	$90.5\pm 0.6$	$+3.7\pm 2.4$	$\mathbf{+6.4\pm 2.1}$
Intervention 1: 1D Dispersion Rescaling (Matched Endpoint Radius $\alpha_{N}$ )
Scaled Noise Prior	$79.8\pm 0.9$	$70.9\pm 1.7$	$-8.9\pm 2.5$	$88.3\pm 1.3$	$77.8\pm 0.7$	$-10.5\pm 0.9$	$-1.5\pm 1.6$
Intervention 2: Noise Freezing across Replans (Redraw Stochasticity Ablation)
Frozen Noise Source ( $x^{(0)}_{t}\equiv x^{(0)}_{0}$ )	$42.3\pm 2.3$	$72.9\pm 0.6$	$\mathbf{+30.6\pm 2.5}$	$75.0\pm 1.7$	$89.3\pm 0.4$	$\mathbf{+14.3\pm 1.9}$	$\mathbf{-16.3\pm 4.3}$

TABLE III: Causal Diagnostic Interventions on

\pi_{0}

/LIBERO-Long. Success rates (%) are mean

\pm

sample SD across matched seeds

7/8/9

\Delta_{s}=Y_{s,2}-Y_{s,10}

; interaction contrast

\mathcal{I}=\Delta_{20}-\Delta_{5}

Fig. 5: Physical Franka platform (left), five evaluated manipulation tasks (top right), and real-world factorial results across three VLA backbones (bottom right). Over 40 matched rollouts per cell across four configurations ( $(s{=}10,N_{0})$ , $(s{=}10,2)$ , $(s{=}H,N_{0})$ , and $(s{=}H,2)$ ), all four quasi-static tasks consistently replicate the sign reversal; shallow sampling degrades success under rapid replanning ( $s{=}10$ ) but systematically outperforms deep sampling under full-horizon commitment ( $s{=}H$ ). On the dynamic turntable task, tracking moving targets requires high feedback rates, rendering open-loop execution horizon the dominant failure mode.

Flow-Based VLA Models

See all 29 papers

TemporalFlow-VLA: Learning Physically Grounded Execution History for Long-Horizon Robot Manipulation
Aug 27, 2026Jiarui Yang, Yehao Lu, Yuning Su +9Robot Learning Long-Horizon Robotic Manipulation
The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China. · Zhejiang University, Hangzhou, China. · Simon Fraser University, Burnaby, BC, Canada. +1
Fewer Steps, Better Actions: Rethinking Flow-Matching Inference for VLA Policies
Sep 18, 2026Zhipeng Tang, Xinda Chen, Weining Rao +5Flow-Based VLA Models Efficient VLA Model Inference
Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · Zhongke Haichuan Intelligent
ReactVLA: Fast and Lightweight Reactive Robot Manipulation via Improved Mean Flow Action Generation
Jun 12, 2026Yanzhao Guo, Wenkai Chen, Jianwei ZhangLanguage-Conditioned Robot Manipulation Efficient VLM Inference
Shanghai Jiao Tong University · Technical Aspects of Multimodal Systems (TAMS), Department of Informatics, Universität Hamburg

Aug 27, 2026J/K move · Enter open · S save

TemporalFlow-VLA: Learning Physically Grounded Execution History for Long-Horizon Robot Manipulation

Jiarui Yang, Yehao Lu, Yuning Su, Yu Zhong+8

The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China. · Zhejiang University, Hangzhou, China. · Simon Fraser University, Burnaby, BC, Canada.+1

Robot Learning Long-Horizon Robotic Manipulation Vision-Language-Action Models

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Vision-language-action (VLA) models leverage pretrained vision-language representations for robot control, yet simply adding historical frames does not reliably capture recent physical change. This is especially problematic in multi-stage manipulation, where visually similar states may require different actions depending on prior execution. To address this challenge, we present TemporalFlow-VLA, which learns compact execution history through physically grounded temporal supervision. Using recorded robot states, robot geometry, and calibrated cameras, we construct robot-surface temporal flow as a training-only target and supervise two execution-aligned temporal queries that provide structured history to the action expert. The geometric supervision path is not evaluated at deployment. TemporalFlow-VLA achieves 97.63 +/- 0.26% average success on LIBERO, including 96.60 +/- 0.87% on LIBERO Long, and 85.5%/84.2% Clean/Randomized success across 12 RoboTwin tasks. It shows its clearest advantage over prior methods on longer-horizon, multi-stage manipulation. Controlled history interventions show that action prediction depends on both historical content and temporal order. With asynchronous feature caching, temporal conditioning maintains single-frame-level server-side sampling latency without additional historical-encoding overhead. Overall, TemporalFlow-VLA provides a compact, physically grounded interface for exploiting ordered execution history without explicit motion estimation or geometric processing at deployment.

Abstract

Flow-Based VLA Models

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TemporalFlow-VLA: Learning Physically Grounded Execution History for Long-Horizon Robot Manipulation

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