Continuous normalizing flows (CNFs) are an attractive generative modeling technique, but they have thus far been held back by limitations in their simulation-based maximum likelihood training. In this paper, we introduce a new technique called conditional flow matching (CFM), a simulation-free training objective 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, our CFM objective does not require the source distribution to be Gaussian or require evaluation of its density. Based on this new objective, we also introduce 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. 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. Code is available at https://github.com/atong01/conditional-flow-matching .

翻译：连续规范化流（CNFs）是一种有吸引力的生成建模技术，但此前其基于模拟的最大似然训练受到限制。本文介绍一种名为条件流匹配（CFM）的新技术，这是一种用于CNF的无模拟训练目标。CFM具有类似扩散模型中用于训练随机流的稳定回归目标，同时享有确定性流模型的高效推理优势。与扩散模型及先前CNF训练算法不同，我们的CFM目标不需要源分布为高斯分布，也无需评估其密度。基于这一新目标，我们还引入了最优输运CFM（OT-CFM），该方法可生成更简单的流，训练更稳定，并实现更快的推理，如实验评估所示。使用CFM训练CNF在多种条件生成和无条件生成任务中取得了改进结果，例如推断单细胞动态、无监督图像翻译和薛定谔桥推断。代码见 https://github.com/atong01/conditional-flow-matching 。