Multi-Resolution Continuous Normalizing Flows

TL;DR

This paper introduces a Multi-Resolution Continuous Normalizing Flow model that improves image generation efficiency and quality at higher resolutions, while maintaining exact likelihood computation and invertibility.

Contribution

The paper proposes a novel multi-resolution extension to CNFs, enabling efficient high-resolution image modeling with fewer parameters and no change in likelihood calculations.

Findings

Comparable likelihood values across datasets

Improved performance at higher resolutions

Fewer parameters needed for high-quality generation

Abstract

Recent work has shown that Neural Ordinary Differential Equations (ODEs) can serve as generative models of images using the perspective of Continuous Normalizing Flows (CNFs). Such models offer exact likelihood calculation, and invertible generation/density estimation. In this work we introduce a Multi-Resolution variant of such models (MRCNF), by characterizing the conditional distribution over the additional information required to generate a fine image that is consistent with the coarse image. We introduce a transformation between resolutions that allows for no change in the log likelihood. We show that this approach yields comparable likelihood values for various image datasets, with improved performance at higher resolutions, with fewer parameters, using only 1 GPU. Further, we examine the out-of-distribution properties of (Multi-Resolution) Continuous Normalizing Flows, and find that they are similar to those of other likelihood-based generative models.