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

Improving and generalizing flow-based generative models with minibatch optimal transport