Diffusion Normalizing Flow

TL;DR

This paper introduces diffusion normalizing flow, a new generative model combining normalizing flows and diffusion models via neural SDEs, achieving efficient sampling and high-quality data generation.

Contribution

It proposes a novel diffusion normalizing flow method that leverages neural SDEs to improve sampling efficiency and model complex distributions with sharp boundaries.

Findings

Competitive performance in high-dimensional density estimation

Efficient sampling with fewer discretization steps

Ability to model distributions with sharp boundaries

Abstract

We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform the data into Gaussian random noise, and a backward SDE that gradually removes the noise to sample from the data distribution. By jointly training the two neural SDEs to minimize a common cost function that quantifies the difference between the two, the backward SDE converges to a diffusion process the starts with a Gaussian distribution and ends with the desired data distribution. Our method is closely related to normalizing flow and diffusion probabilistic models and can be viewed as a combination of the two. Compared with normalizing flow, diffusion normalizing flow is able to learn distributions with sharp boundaries. Compared with diffusion probabilistic models, diffusion normalizing flow requires fewer discretization steps and thus has better sampling efficiency. Our algorithm demonstrates competitive performance in both high-dimension data density estimation and image generation tasks.