  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.
