Density estimation on low-dimensional manifolds: an inflation-deflation approach

Normalizing flows (NFs) are universal density estimators based on neural networks. However, this universality is limited: the density's support needs to be diffeomorphic to a Euclidean space. In this paper, we propose a novel method to overcome this limitation without sacrificing universality. The proposed method inflates the data manifold by adding noise in the normal space, trains an NF on this inflated manifold, and, finally, deflates the learned density. Our main result provides sufficient conditions on the manifold and the …

data inflation low manifold networks neural networks noise normal novel paper space support trains