2022-06-28-ben-hamu22a.md

title	booktitle	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Matching Normalizing Flows and Probability Paths on Manifolds	Proceedings of the 39th International Conference on Machine Learning	Continuous Normalizing Flows (CNFs) are a class of generative models that transform a prior distribution to a model distribution by solving an ordinary differential equation (ODE). We propose to train CNFs on manifolds by minimizing probability path divergence (PPD), a novel family of divergences between the probability density path generated by the CNF and a target probability density path. PPD is formulated using a logarithmic mass conservation formula which is a linear first order partial differential equation relating the log target probabilities and the CNF’s defining vector field. PPD has several key benefits over existing methods: it sidesteps the need to solve an ODE per iteration, readily applies to manifold data, scales to high dimensions, and is compatible with a large family of target paths interpolating pure noise and data in finite time. Theoretically, PPD is shown to bound classical probability divergences. Empirically, we show that CNFs learned by minimizing PPD achieve state-of-the-art results in likelihoods and sample quality on existing low-dimensional manifold benchmarks, and is the first example of a generative model to scale to moderately high dimensional manifolds.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	ben-hamu22a	0	Matching Normalizing Flows and Probability Paths on Manifolds	1749	1763	1749-1763	1749	false	Ben-Hamu, Heli and Cohen, Samuel and Bose, Joey and Amos, Brandon and Nickel, Maximillian and Grover, Aditya and Chen, Ricky T. Q. and Lipman, Yaron	given family Heli Ben-Hamu given family Samuel Cohen given family Joey Bose given family Brandon Amos given family Maximillian Nickel given family Aditya Grover given family Ricky T. Q. Chen given family Yaron Lipman	2022-06-28		Proceedings of the 39th International Conference on Machine Learning	162	inproceedings	date-parts 2022 6 28	https://proceedings.mlr.press/v162/ben-hamu22a/ben-hamu22a.pdf