Generative Control as Optimization: Time Unconditional Flow Matching for Adaptive and Robust Robotic Control

arXiv cs.RO / 4/28/2026

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Key Points

The paper argues that diffusion/flow-matching approaches for robotic imitation learning are structurally inefficient because their inference uses a fixed integration schedule regardless of how complex the current state is.
It proposes Generative Control as Optimization (GeCO), which replaces trajectory integration with iterative optimization by learning a stationary velocity field in action-sequence space where expert behaviors act as stable attractors.
At test time, GeCO adaptively allocates compute based on convergence: it exits early for easy states and performs more refinement for harder ones.
The stationary geometry also provides a training-free safety signal, using the velocity-field norm at the optimized action as an out-of-distribution detector that stays low for in-distribution states and rises for anomalies.
The authors validate GeCO on simulation benchmarks and show it scales to pi0-series Vision-Language-Action (VLA) models, positioning it as a plug-and-play replacement for standard flow-matching heads that improves success rate and efficiency.

Abstract

Diffusion models and flow matching have become a cornerstone of robotic imitation learning, yet they suffer from a structural inefficiency where inference is often bound to a fixed integration schedule that is agnostic to state complexity. This paradigm forces the policy to expend the same computational budget on trivial motions as it does on complex tasks. We introduce Generative Control as Optimization (GeCO), a time-unconditional framework that transforms action synthesis from trajectory integration into iterative optimization. GeCO learns a stationary velocity field in the action-sequence space where expert behaviors form stable attractors. Consequently, test-time inference becomes an adaptive process that allocates computation based on convergence--exiting early for simple states while refining longer for difficult ones. Furthermore, this stationary geometry yields an intrinsic, training-free safety signal, as the field norm at the optimized action serves as a robust out-of-distribution (OOD) detector, remaining low for in-distribution states while significantly increasing for anomalies. We validate GeCO on standard simulation benchmarks and demonstrate seamless scaling to pi0-series Vision-Language-Action (VLA) models. As a plug-and-play replacement for standard flow-matching heads, GeCO improves success rates and efficiency with an optimization-native mechanism for safe deployment. Video and code can be found at https://hrh6666.github.io/GeCO/