Yunpeng Mei, Xiaowen Zhu, Chenyu Wang, Chenbo Xin, Hongjie Cao, Jiamin Wang, Jie Chen, Gang Wang · 2026 · arXiv
DOI: 10.48550/arXiv.2610.30107 · open-access PDF
Flow matching trains a continuum of velocity regression problems but usually reports a loss averaged over interpolation time, obscuring which regions are limited by intrinsic ambiguity and which remain data-limited. We introduce the Velocity Ambiguity Profile (VAP), $\mathcal{A}_v(t)$, the time-local Bayes-risk floor of velocity prediction, and decompose time-resolved loss as $L_N(t)=\mathcal{A}_v(t)+R(t;N)$, where only the excess term $R(t;N)$ is reducible by more data or a different estimator. For $N$ training samples and a $K$-component mixture in the structured example, we prove two statis
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