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, we show that when the true OT plan is available, our OT-CFM method approximates dynamic OT. 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：连续归一化流（CNFs）是一种有吸引力的生成建模技术，但其基于模拟的最大似然训练方法存在局限性，阻碍了其发展。我们引入广义条件流匹配（CFM）技术，这是一类无需模拟的CNFs训练目标函数。CFM具有与扩散模型中训练随机流相似的稳定回归目标，同时保留了确定性流模型的高效推理优势。与扩散模型及先前的CNF训练算法不同，CFM不要求源分布为高斯分布，也无需计算其密度。我们目标函数的一个变体是最优传输CFM（OT-CFM），它能生成更简单的流，训练更稳定且推理速度更快（如实验评估所示）。此外，我们证明当真实最优传输方案可用时，我们的OT-CFM方法能够近似动态最优传输。使用CFM训练CNFs显著改进了各种条件生成和无条件生成任务的结果，包括单细胞动态推断、无监督图像翻译和薛定谔桥推断。