Conformal Embedding Flows: Tractable Density Estimation on Learned Manifolds

Brendan Leigh Ross, Jesse C Cresswell

Keywords: generative modelling, normalizing flows, injective flows, image generation, manifold learning

TL;DR: We introduce Conformal Embedding Flows which can model data confined to unknown low-dimensional manifolds while preserving tractable likelihoods.

Abstract: Normalizing flows are generative models that provide tractable density estimation by transforming a simple distribution into a complex one. However, flows cannot directly model data supported on an unknown low-dimensional manifold. We propose Conformal Embedding Flows, which learn low-dimensional manifolds with tractable densities. We argue that composing a standard flow with a trainable conformal embedding is the most natural way to model manifold-supported data. To this end, we present a series of conformal building blocks and demonstrate experimentally that flows can model manifold-supported distributions without sacrificing tractable likelihoods.