Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions

TL;DR

This paper introduces a method for automatically optimizing multivariate diffusion processes in generative models, enabling rapid experimentation and improved sample quality across various datasets.

Contribution

It provides a general recipe for maximizing likelihood bounds for any number of auxiliary variables without model-specific analysis, and demonstrates automatic diffusion optimization.

Findings

Learned MDMs match or surpass fixed diffusions in BPDs.

Introduces two new diffusion processes.

Successfully applies to MNIST, CIFAR10, and ImageNet32 datasets.

Abstract

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality. For example, extending the inference process with auxiliary variables leads to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study Multivariate Diffusion Models (MDMs). For any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDMs likelihood without requiring any model-specific analysis. We then demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over all linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST, CIFAR10, and ImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture.