Isokinetic Flow Matching for Pathwise Straightening

Tauhid Khan

Keywords: Generative Models, Flow Matching, Rectified Flow, Optimal Transport, Acceleration Regularization, Few-Step Generation, Sampling Efficiency, Eulerian Dynamics, Diffusion Transformers

TL;DR: Iso-FM adds a single Jacobian-free penalty to standard Flow Matching training that suppresses material acceleration ($Dv/Dt$) along learned trajectories, straightening the velocity field so that coarse ODE solvers need far fewer steps

Abstract: Flow Matching (FM) constructs linear conditional probability paths, but the learned marginal velocity field exhibits curvature due to trajectory superposition, inflating numerical truncation errors and bottlenecking few-step sampling. We introduce \textbf{Isokinetic Flow Matching (Iso-FM)}, a lightweight, Jacobian-free regularizer that penalizes pathwise acceleration via a self-guided finite-difference approximation of the material derivative $Dv/Dt$. Operating as a plug-and-play addition to single-stage FM training, Iso-FM requires only standard forward evaluations and stop-gradient targets. On CIFAR-10 (DiT-S/2), Iso-FM reduces conditional non-OT FID@2 from 78.82 to 27.13, a $2.9\times$ relative efficiency gain and achieves a best-observed FID@4 of 10.23. These results demonstrate that acceleration regularization is a principled, compute-efficient mechanism for improving the quality--NFE trade-off in flow-based generative models.

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Submission Number: 98