DFlow: A Generative Model Combining Denoising AutoEncoder and Normalizing Flow for High Fidelity Waveform Generation

Normalizing flows (NF) are expressive as well as tractable density estimation methods whenever the support of the density is diffeomorphic to the entire dataspace. However, real-world data sets typically live on (or very close to) lowdimensional manifolds thereby challenging the applicability of standard NF on realworld 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.