通过抑制生成路径加速度，实现快速高质量图像生成。
Isokinetic Flow Matching for Pathwise Straightening of Generative Flows
- 引入无雅可比矩阵的等速正则化，直接惩罚路径加速度。
- 2步生成时FID从78.82降至27.13，4步达最优FID 10.23。
- 无需额外编码器或二阶自动微分，可即插即用。
流匹配（FM）构建线性条件概率路径，但因轨迹叠加导致学习到的边缘速度场存在强曲率，严重增大数值截断误差，限制少步采样性能。为此，本文提出等速流匹配（Iso-FM），一种轻量级、无雅可比矩阵的动态正则化方法，直接惩罚路径加速度。通过自引导的有限差分近似材料导数Dv/Dt，Iso-FM在不依赖辅助编码器或昂贵二阶自动微分的情况下，实现局部速度一致性。作为单阶段FM训练的纯插件式增强，Iso-FM显著提升少步生成效果。在CIFAR-10（DiT-S/2）上，2步条件非OT FID从78.82降至27.13（相对效率提升2.9倍），4步达到最优观测FID 10.23。这些结果确立了加速度正则化作为快速生成采样的原理性、高计算效率机制。
原文摘要 · Abstract (English)
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.
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