Stable Velocity: A Variance Perspective on Flow Matching

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 $256\times256$ 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 $2\times$ faster sampling within the *low-variance regime* without degrading sample quality. Our code is available at https://github.com/linYDTHU/StableVelocity.

Modern generative models can create high-quality images and videos, but training them efficiently remains challenging. One reason is that the learning signals they rely on can be very noisy, especially in the early stages of generation, which makes training unstable and slow. In this work, we analyze where this noise comes from and show that it is much higher when the model starts from random inputs, but becomes much lower as the model gets closer to real data. Based on this observation, we propose a new method called Stable Velocity that improves both training and generation. During training, our method reduces noise in the learning signals and focuses more on the parts of the process that are easier to learn. During generation, we take advantage of simpler dynamics in the low-noise region to speed up sampling without additional training. Our approach consistently makes training more efficient and can generate images and videos more than twice as fast, while maintaining the same quality.