Nonlinear Isometric Manifold Learning for Injective Normalizing Flows

Eike Cramer, Felix Rauh, Alexander Mitsos, Raúl Tempone, Manuel Dahmen

Abstract: To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density estimation and enables training of both parts to high accuracy. Thus, model selection and tuning are simplified compared to existing injective normalizing flows. Applied to data sets on (approximately) flat manifolds, the combined approach generates high-quality data.