Velocity Ambiguity Profiles: Time-Resolved Bayes-Risk Diagnostics for Flow Matching

Key points

• 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.1
• In separated isotropic Gaussian mixtures, the Bayes velocity becomes locally affine, and a label-oracle residual-regression benchmark has parametric excess-risk scale $K\mathcal{A}v(t)/N$, matched within the same separated residual Gaussian-location subproblem.1
• On CIFAR-100 DINOv2 feature flow, guided time sampling reduces uniformly evaluated velocity loss by $6.78%$ and global feature Fréchet distance (FD) by $23.6%$, while class-conditional kernel inception distance (KID) shows no improvement.1
• VAP turns an averaged flow-matching objective into a time-resolved diagnostic for locating ambiguity-limited and data-limited regions.1

Sources (1)

• [1]Velocity Ambiguity Profiles: Time-Resolved Bayes-Risk Diagnostics for Flow Matching
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 21, 05:52 PM

  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.

  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.

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