We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

翻译：我们提出了一种基于连续归一化流（CNFs）的生成建模新范式，使得能够以前所未有的规模训练CNFs。具体而言，我们引入了流匹配（FM）的概念，这是一种基于回归固定条件概率路径的向量场、无需模拟的CNF训练方法。流匹配适用于将噪声与数据样本相互转换的高斯概率路径的一般族系——该族系将现有扩散路径作为特例纳入其中。有趣的是，我们发现将流匹配与扩散路径结合使用，可为训练扩散模型提供更鲁棒且更稳定的替代方案。此外，流匹配开辟了使用非扩散概率路径训练CNFs的途径。一个特别值得关注的实例是利用最优传输（OT）位移插值定义条件概率路径。这些路径比扩散路径更高效，能实现更快的训练与采样速度，并带来更优的泛化性能。在ImageNet数据集上使用流匹配训练CNFs，无论是在似然性还是样本质量方面，均持续优于基于扩散的替代方法，并且能够利用现成的数值常微分方程求解器实现快速可靠的样本生成。