Stable Velocity: A Variance Perspective on Flow Matching

• URL: http://arxiv.org/abs/2602.05435v1
• Date: Thu, 05 Feb 2026 08:25:05 GMT
• Title: Stable Velocity: A Variance Perspective on Flow Matching
• Abstract summary: We propose Stable Velocity, a unified framework that improves both training and sampling.<n>For training, we introduce Stable Velocity Matching (StableVM), an unbiased variance-reduction objective.<n>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.
• Score: 47.91689941155031
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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