Conformal Embedding Flows: Tractable Density Estimation on Learned ManifoldsDownload PDF

Published: 15 Jun 2021, Last Modified: 05 May 2023INNF+ 2021 spotlighttalkReaders: Everyone
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.
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