稳定速度：基于方差视角的流匹配研究

摘要

尽管流匹配方法具有优雅的理论形式，但其对单样本条件速度的依赖会导致高方差训练目标，从而破坏优化稳定性并减缓收敛速度。通过显式刻画这种方差特性，我们发现了两个关键区域：1）在先验分布附近的高方差区域，该区域的优化极具挑战性；2）在数据分布附近的低方差区域，此处条件速度与边际速度几乎重合。基于这一发现，我们提出了稳定速度（Stable Velocity）这一统一框架，可同时改进训练与采样过程。在训练方面，我们引入了无偏方差缩减目标——稳定速度匹配（StableVM），以及方差感知表示对齐（VA-REPA）方法，后者能在低方差区域自适应增强辅助监督。在推理方面，我们证明低方差区域的动力学过程存在闭式简化形式，由此实现了无需微调的加速采样方法——稳定速度采样（StableVS）。在ImageNet 256×256数据集及SD3.5、Flux、Qwen-Image、Wan2.2等大型预训练文本-图像/文本-视频模型上的大量实验表明，该方法能持续提升训练效率，并在低方差区域内实现超过2倍的采样加速，且不损失样本质量。代码已开源：https://github.com/linYDTHU/StableVelocity。

English

While flow matching is elegant, its reliance on single-sample conditional velocities leads to high-variance training targets that destabilize optimization and slow convergence. By explicitly characterizing this variance, we identify 1) a high-variance regime near the prior, where optimization is challenging, and 2) a low-variance regime near the data distribution, where conditional and marginal velocities nearly coincide. Leveraging this insight, we propose Stable Velocity, a unified framework that improves both training and sampling. For training, we introduce Stable Velocity Matching (StableVM), an unbiased variance-reduction objective, along with Variance-Aware Representation Alignment (VA-REPA), which adaptively strengthen auxiliary supervision in the low-variance regime. For inference, we show that dynamics in the low-variance regime admit closed-form simplifications, enabling Stable Velocity Sampling (StableVS), a finetuning-free acceleration. Extensive experiments on ImageNet 256times256 and large pretrained text-to-image and text-to-video models, including SD3.5, Flux, Qwen-Image, and Wan2.2, demonstrate consistent improvements in training efficiency and more than 2times faster sampling within the low-variance regime without degrading sample quality. Our code is available at https://github.com/linYDTHU/StableVelocity.

稳定速度：基于方差视角的流匹配研究

Stable Velocity: A Variance Perspective on Flow Matching

摘要

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