π0-EqM: Equilibrium Matching for Closed-Loop Vision-Language-Action Control

Huanming Liu1,*, Congsheng Xu2,*, Jianmin Ji1,†, and Yao Mu2,†

1University of Science and Technology of China    2Shanghai Jiao Tong University

* Equal contribution. † Corresponding authors.

Paper arXiv
pi0-EqM overview
Overview of π0-EqM. We replace only the action decoder in π0 and cast action generation as iterative equilibrium solving, enabling adaptive stopping and warm starts. An executable intermediate action may appear before full numerical convergence.

Abstract

Currently, Vision-Language-Action (VLA) models have become the most adopted paradigm for robotic manipulation for its great potential for task generalization. While most generative flow-matching action decoders for VLA control are often deployed with fixed sampling horizons, limiting state-dependent compute and temporal reuse across control cycles.

We present π0-EqM, which replaces the flow-matching expert in π0 with an Equilibrium Matching (EqM) decoder while leaving the upstream VLA stack unchanged. Under a matched 300-step budget, π0-EqM improves RoboTwin average success from 40.4% to 50.2% across 19 tasks and remains competitive on LIBERO, with its clearest gain on LIBERO-10 (87.0%).

Two threshold scans reveal a task-dependent non-monotonic relation between residual and success, which we term the stationarity-executability gap. The results suggest that inference depth in iterative VLA control is part of policy design and introduce an energy-based VLA perspective that may inform future work on composable action generation across tasks and embodiments.

Method

Action Decoding as Iterative Inference

Rather than treating decoding as a fixed-cost black box, we view it as iterative inference whose depth is a controllable policy variable. EqM provides the mathematical scaffolding for this view.

Equilibrium Matching for VLA Control

Unlike diffusion or flow-matching policies that parameterize time-indexed score or velocity fields, EqM learns a time-invariant conditional vector field. The roots of this field correspond to the target equilibrium action chunks.

Adaptive Inference Depth

The normalized lookahead residual exposes state-dependent test-time compute without changing the upstream VLA stack.

Structural Warm-Start

Because EqM decoding is independent of a fixed noise schedule, we can exploit temporal coherence between consecutive control cycles.

Results

Under a matched 300-step budget, π0-EqM improves 12 tasks, degrades 5, and ties 2, raising the average success rate from 40.4 to 50.2.

40.4 → 50.2 RoboTwin average success
85.2 → 87.0 LIBERO-10 success
+9.8 RoboTwin average improvement

RoboTwin

Task π0 π0-EqM Δ

LIBERO

Suite π0 π0-EqM Δ
LIBERO-Spatial96.897.2+0.4
LIBERO-Object98.898.4-0.4
LIBERO-Goal95.894.8-1.0
LIBERO-1085.287.0+1.8
Average94.1594.35+0.20

Threshold Scans

Threshold scans reveal task-dependent non-monotonicity. The preferred threshold is task dependent, so the same residual threshold changes both solver cost and closed-loop behavior.

Threshold scans on two RoboTwin tasks
Threshold scans on two RoboTwin tasks.
EqM inference trajectory on click_alarmclock
Qualitative EqM inference trajectory on click_alarmclock, showing early attraction, semantic shaping, and over-refinement.

Evaluation Videos

We evaluate on the 19-task RoboTwin benchmark. Representative rollouts from the included videos are shown below.

BibTeX

@misc{liu2026pi0eqmequilibriummatchingclosedloop,
  title={$\pi_0$-EqM: Equilibrium Matching for Closed-Loop Vision-Language-Action Control},
  author={Huanming Liu and Congsheng Xu and Jianmin Ji and Yao Mu},
  year={2026},
  eprint={2605.23128},
  archivePrefix={arXiv},
  primaryClass={cs.RO},
  url={https://arxiv.org/abs/2605.23128},
}