The Geometry of Flow-Matching Uncertainty: A Cost-free Uncertainty Proxy and Its Application in Flow-based VLA Failure Detection

• URL: http://arxiv.org/abs/2607.27933v3
• Date: Thu, 06 Aug 2026 08:12:13 GMT
• Title: The Geometry of Flow-Matching Uncertainty: A Cost-free Uncertainty Proxy and Its Application in Flow-based VLA Failure Detection
• Abstract summary: Flow matching (FM) has become a popular action head paradigm for modern embodied models.<n>We show that uncertainty manifests as deviation from an ideal affine-isotropic contraction field.<n>We introduce denoising acceleration ($mathrmaccel$), a cost-free uncertainty proxy that measures the bending of the trajectory from a single forward pass.
• Score: 40.15880250907137
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Flow matching (FM) has become a popular action head paradigm for modern embodied models. However, as a conditional generative model, it does not explicitly expose its inherent uncertainty, producing faulty action chunks even when it misinterprets the scene or encounters out-of-distribution (OOD) inputs. Therefore, determining when an FM-generated action can be trusted is essential for safe deployment, yet existing uncertainty estimation methods on real-time control suffer from several issues: extra training budget, high computational overhead, and low generalization ability. In this work, we provide a geometric interpretation of FM uncertainty in the velocity field, showing that uncertainty manifests as deviation from an ideal affine-isotropic contraction field. Building on this observation, we introduce denoising acceleration ($\mathrm{accel}$), a highly-generalizable and cost-free uncertainty proxy that measures the bending of the denoising trajectory from a single forward pass, without additional model evaluations, training, or resampling. We theoretically and empirically demonstrate that $\mathrm{accel}$ is a faithful proxy for FM uncertainty and further test its utility in online failure detection. Results show that $\mathrm{accel}$ identifies failing rollouts well before termination, matching or even outperforming costly resampling- and training-based baselines across settings under realistic deployment budget. Code and demos available at: https://github.com/rrrrrrzy/fm-geometry.

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