Isokinetic Flow Matching for Pathwise Straightening of Generative Flows

TL;DR

Iso-FM introduces a Jacobian-free regularizer for flow matching that significantly accelerates generative sampling by reducing path curvature and numerical errors.

Contribution

It proposes Isokinetic Flow Matching, a lightweight regularizer that enforces local velocity consistency without second-order derivatives, improving few-step generation in flow models.

Findings

Reduces CIFAR-10 FID at 2 steps from 78.82 to 27.13

Achieves a best FID of 10.23 at 4 steps

Dramatically improves efficiency of flow-based generative models

Abstract

Flow Matching (FM) constructs linear conditional probability paths, but the learned marginal velocity field inevitably exhibits strong curvature due to trajectory superposition. This curvature severely inflates numerical truncation errors, bottlenecking few-step sampling. To overcome this, we introduce Isokinetic Flow Matching (Iso-FM), a lightweight, Jacobian-free dynamical regularizer that directly penalizes pathwise acceleration. By using a self-guided finite-difference approximation of the material derivative Dv/Dt, Iso-FM enforces local velocity consistency without requiring auxiliary encoders or expensive second-order autodifferentiation. Operating as a pure plug-and-play addition to single-stage FM training, Iso-FM dramatically improves few-step generation. On CIFAR-10 (DiT-S/2), Iso-FM slashes conditional non-OT FID at 2 steps from 78.82 to 27.13 - a 2.9x relative efficiency gain - and reaches a best-observed FID at 4 steps of 10.23. These results firmly establish acceleration regularization as a principled, compute-efficient mechanism for fast generative sampling.