  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.
