Matching Normalizing Flows and Probability Paths on Manifolds

Understand

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.