Isokinetic Flow Matching for Pathwise Straightening of Generative Flows
This addresses the problem of inefficient few-step sampling in generative models for researchers and practitioners, representing a strong specific gain but is incremental as it builds on existing FM methods.
The paper tackled the problem of strong curvature in Flow Matching (FM) that inflates numerical errors and bottlenecks few-step sampling, and introduced Isokinetic Flow Matching (Iso-FM), a lightweight regularizer that penalizes pathwise acceleration, resulting in dramatic improvements such as slashing conditional non-OT FID at 2 steps from 78.82 to 27.13 on CIFAR-10.
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.