Moser Flow: Divergence-based Generative Modeling on Manifolds

Understand

We are interested in learning generative models for complex geometries described via manifolds, such as spheres, tori, and other implicit surfaces.

• Current extensions of existing (Euclidean) generative models are restricted to specific geometries and typically suffer from high computational costs.
• We introduce Moser Flow (MF), a new class of generative models within the family of continuous normalizing flows (CNF).
• MF also produces a CNF via a solution to the change-of-variable formula, however differently from other CNF methods, its model (learned) density is parameterized as the source (prior) density minus the divergence of a neural network (NN).