Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have been held back by limitations in their simulation-based maximum likelihood training. We introduce the generalized conditional flow matching (CFM) technique, a family of simulation-free training objectives for CNFs. CFM features a stable regression objective like that used to train the stochastic flow in diffusion models but enjoys the efficient inference of deterministic flow models. In contrast to both diffusion models and prior CNF training algorithms, CFM does not require the source distribution to be Gaussian or require evaluation of its density. A variant of our objective is optimal transport CFM (OT-CFM), which creates simpler flows that are more stable to train and lead to faster inference, as evaluated in our experiments. Furthermore, OT-CFM is the first method to compute dynamic OT in a simulation-free way. Training CNFs with CFM improves results on a variety of conditional and unconditional generation tasks, such as inferring single cell dynamics, unsupervised image translation, and Schr\"odinger bridge inference.

翻译：连续正规化流（CNFs）是一种颇具吸引力的生成建模技术，但其基于仿真的最大似然训练方法存在局限性，制约了其发展。本文提出广义条件流匹配（CFM）技术，这是一类无需仿真的CNF训练目标。CFM兼具扩散模型中随机流训练所用的稳定回归目标，以及确定性流模型的高效推理优势。与扩散模型及现有CNF训练算法不同，CFM既不需要源分布为高斯分布，也无需评估其密度。我们的目标函数变体——最优传输CFM（OT-CFM），能够生成更简单的流，这些流在训练中更稳定，并实现更快的推理速度（实验已验证）。此外，OT-CFM是首个以无仿真方式计算动态最优传输的方法。采用CFM训练CNF在多种条件与非条件生成任务中均取得更优效果，包括单细胞动态推断、无监督图像翻译及薛定谔桥推断。