Isokinetic Flow Matching for Pathwise Straightening

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.