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

• URL: http://arxiv.org/abs/2302.07261v1
• Date: Tue, 14 Feb 2023 18:57:04 GMT
• Title: Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions
• Authors: Raghav Singhal, Mark Goldstein, Rajesh Ranganath
• Abstract summary: Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this inference diffusion process to generate samples. We show how to maximize a lower-bound on the likelihood for any number of auxiliary variables. We then demonstrate how to parameterize the diffusion for a specified target noise distribution.
• Score: 22.04182099405728
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this inference diffusion process to generate samples. The choice of inference diffusion 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.

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