等速流匹配用于生成流的路径直线化
Isokinetic Flow Matching for Pathwise Straightening of Generative Flows
AI总结：
本文提出等速流匹配方法，通过直接惩罚路径加速度来减少生成流中的曲率，提升少步生成效率，在CIFAR-10数据集上显著降低FID分数。
摘要：
流匹配（FM）构建线性条件概率路径，但学习的边缘速度场因轨迹叠加而产生强曲率，严重放大数值截断误差，限制了少步采样。为解决此问题，我们引入等速流匹配（Iso-FM），一种轻量、无雅可比矩阵的动态正则化器，直接惩罚路径加速度。通过使用自引导的有限差分近似计算材料导数Dv/Dt，Iso-FM在不需辅助编码器或昂贵的二阶自动微分的情况下，强制局部速度一致性。作为单阶段FM训练的纯插件添加，Iso-FM显著提升了少步生成。在CIFAR-10（DiT-S/2）上，Iso-FM在2步时将条件非OT FID从78.82降至27.13，效率提升2.9倍，并在4步时达到最佳观测FID 10.23。这些结果确立了加速正则化作为原理上可行且计算高效的快速生成采样机制。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
