Denoising Normalizing FlowDownload PDF

May 21, 2021 (edited Nov 05, 2021)NeurIPS 2021 PosterReaders: Everyone
  • Keywords: Normalizing Flow, Manifold Learning, Density Estimation
  • TL;DR: We propose an NF for simultaneous manifold and density-on-manifold learning.
  • Abstract: Normalizing flows (NF) are expressive as well as tractable density estimation methods whenever the support of the density is diffeomorphic to the entire data-space. However, real-world data sets typically live on (or very close to) low-dimensional manifolds thereby challenging the applicability of standard NF on real-world problems. Here we propose a novel method - called Denoising Normalizing Flow (DNF) - that estimates the density on the low-dimensional manifold while learning the manifold as well. The DNF works in 3 steps. First, it inflates the manifold - making it diffeomorphic to the entire data-space. Secondly, it learns an NF on the inflated manifold and finally it learns a denoising mapping - similarly to denoising autoencoders. The DNF relies on a single cost function and does not require to alternate between a density estimation phase and a manifold learning phase - as it is the case with other recent methods. Furthermore, we show that the DNF can learn meaningful low-dimensional representations from naturalistic images as well as generate high-quality samples.
  • Supplementary Material: pdf
  • Code Of Conduct: I certify that all co-authors of this work have read and commit to adhering to the NeurIPS Statement on Ethics, Fairness, Inclusivity, and Code of Conduct.
  • Code:
15 Replies