Velocity Scaling in Flow Matching

Computer Science > Computer Vision and Pattern Recognition arXiv:2610.10823 (cs) [Submitted on 7 Oct 2026] Title: Velocity Scaling in Flow Matching Authors: Youssef Saied, François Fleuret.

计算机科学 > 计算机视觉与模式识别 arXiv:2610.10823 (cs) [提交于 2026 年 10 月 7 日] 标题：流匹配中的速度缩放 作者：Youssef Saied, François Fleuret。

Abstract: Scaling a learned flow-matching velocity field $v_\theta$ by a gain $\gamma(t)$ was recently shown to greatly improve generation quality. Prior work argued that velocity fields trained with mean-squared error (MSE) systematically underestimate velocity magnitude and that scaling corrects this error.

摘要：最近的研究表明，通过增益 $\gamma(t)$ 对学习到的流匹配速度场 $v_\theta$ 进行缩放，可以显著提高生成质量。先前的研究认为，使用均方误差 (MSE) 训练的速度场会系统性地低估速度幅值，而缩放操作可以纠正这一误差。

We show that MSE training does not create a velocity-magnitude deficit. We find instead that velocity scaling reduces population time lag: sampled states at model time $t$ resemble training states from an earlier time. Velocity scaling and moving model time back are two ways to address this population time lag.

我们证明了 MSE 训练并不会导致速度幅值不足。相反，我们发现速度缩放减少了总体时间滞后：模型在时间 $t$ 采样的状态类似于较早时间的训练状态。速度缩放和将模型时间回溯是解决这种总体时间滞后的两种方法。

Across architectures and model sizes, measuring population time lag and using it to select a gain greatly improves generation quality, reducing FID from 28.0 to 12.2 (estimated by linear interpolation between FID measurements at neighboring gains) on ImageNet-256 at NFE 25 without guidance.

在各种架构和模型规模下，测量总体时间滞后并利用其选择增益，可以极大地提高生成质量。在不使用引导的情况下，于 ImageNet-256 数据集上（NFE 为 25），FID 从 28.0 降低至 12.2（通过相邻增益下的 FID 测量值进行线性插值估算）。