流匹配不确定性的几何本质与自由代理
The Geometry of Flow-Matching Uncertainty: A Cost-free Uncertainty Proxy and Its Application in Flow-based VLA Failure Detection
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中文总结 AI 辅助
该研究针对流匹配（FM）不确定性估计方法的缺陷，提出去噪加速度（accel）作为高泛化无成本的不确定性代理，可提前识别FM生成动作的失败，性能优于相关基线。
中文摘要 AI 辅助
流匹配（Flow Matching, FM）已成为现代具身模型的流行动作头范式。然而，作为条件生成模型，它未明确暴露固有不确定性，即使误判场景或遇到分布外（OOD）输入也会生成错误动作块。因此，确定FM生成动作何时可信对安全部署至关重要，但现有实时控制的不确定性估计方法存在额外训练预算、高计算开销、泛化能力低等问题。本研究对速度场中的FM不确定性给出几何解释，表明不确定性表现为与理想仿射各向同性收缩场的偏差。基于此，引入去噪加速度（denoising acceleration, accel），这是一种高泛化且无成本的不确定性代理，通过单次前向传播测量去噪轨迹的弯曲程度，无需额外模型评估、训练或重采样。理论与实验均证明accel是FM不确定性的忠实代理，还测试了其在线故障检测的实用性，结果显示accel能在失败回滚终止前很好地识别，在现实部署预算下，其性能在各场景中匹配甚至优于成本高昂的基于重采样和训练的基线。代码和演示可在：this https URL获取。
英文摘要
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.
