Velocity Ambiguity Profiles split flow-matching loss by interpolation time
Original title: Velocity Ambiguity Profiles: Time-Resolved Bayes-Risk Diagnostics for Flow Matching
Guided time sampling cuts DINOv2 feature velocity loss 6.78% and Fréchet distance 23.6%, with no class-conditional KID gain.
The paper defines the Velocity Ambiguity Profile, the time-local Bayes-risk floor of velocity prediction in flow matching, and splits time-resolved loss into that floor plus a reducible excess. Only the excess term shrinks with more data or a different estimator. Proofs cover a nonparametric local-regression rate and a parametric excess-risk scale for separated isotropic Gaussian mixtures. On CIFAR-100 DINOv2 feature flow, guided time sampling lowers uniformly evaluated velocity loss and global feature Fréchet distance, while class-conditional kernel inception distance does not improve.
- Loss is written as ambiguity floor plus excess risk reducible by data or estimator.
- Gaussian-mixture theory gives excess-risk scale K times ambiguity over N.
- CIFAR-100 DINOv2 flow: velocity loss down 6.78% and FD down 23.6%.
- Class-conditional KID shows no improvement under the same sampling.
From the original article
1 min read at arxiv.orgFlow 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.
By Yunpeng Mei · arxiv.org
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