Stable Velocity: A Variance Perspective on Flow Matching

TL;DR

This paper introduces Stable Velocity, a framework that reduces variance in flow matching, leading to more stable training and faster sampling in generative models, validated on large-scale image and video datasets.

Contribution

It proposes Stable Velocity, including StableVM and VA-REPA for training, and StableVS for sampling, to improve efficiency and stability in flow matching-based generative models.

Findings

Achieves over 2x faster sampling without quality loss.

Demonstrates consistent training improvements on large datasets.

Validates approach on diverse models like SD3.5, Flux, and Qwen-Image.

Abstract

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.