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Abstract: 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 Schrödinger bridge inference.

Speaker: Alexander Tong - https://www.alextong.net/

Twitter Hannes:   / hannesstaerk  
Twitter Dominique:   / dom_beaini  

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Chapters

00:00 - Intro
02:03 - Background on diffusion + flow models
10:31 - Why do diffusion models beat CNFs?
11:42 - Main idea: how can we train a CNF like a diffusion model?
18:25 - Flow matching
32:38 - Conditional flow matching
38:18 - Properties of flow depend on the choice of the probability path
47:40 - Score and flow matching
57:34 - Main takeaways
58:32 - Q+A