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

**Authors:** Raghav Singhal, Mark Goldstein, Rajesh Ranganath  
**arXiv:** [2302.07261](https://arxiv.org/abs/2302.07261)  
**Date:** 2023-02-14  
**Summary page:** https://www.summarizepaper.com/en/paper/2302.07261v2/

## Key points

- Diffusion-based generative models (DBGMs) have been successful in tasks such as image generation, editing, translation, and conditional text-to-image tasks.
- DBGMs perturb data to a target noise distribution and then reverse the process to generate samples.
- The choice of the inference diffusion process greatly impacts both likelihoods and sample quality.
- The authors propose a recipe for maximizing a lower-bound on Multivariate Diffusion Models (MDMs) likelihood without extensive model-specific analysis.
- They demonstrate how to parameterize the diffusion for a specified target noise distribution, enabling optimization of the inference diffusion process.
- Optimizing the diffusion process allows researchers to experiment with a wider range of linear diffusions automatically.
- Two new specific diffusions are introduced and a diffusion process is learned on popular datasets like MNIST, CIFAR10, and ImageNet32.
- Learned MDMs achieve or surpass bits-per-dim (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture.
- Selecting an appropriate inference process is essential for DBGMs' performance.
- This work enables rapid prototyping and evaluation of different multivariate diffusions in DBGMs by providing a method to optimize the inference diffusion process without extensive analysis.

## Summary

Diffusion-based generative models (DBGMs) have been successful in various tasks such as image generation, editing, translation, and conditional text-to-image tasks. These models perturb data to a target noise distribution and then reverse the process to generate samples. The choice of the inference diffusion process greatly impacts both likelihoods and sample quality. In this work, the authors focus on Multivariate Diffusion Models (MDMs) and address the challenge of exploring different multivariate diffusions without requiring extensive model-specific analysis. They propose a recipe for maximizing a lower-bound on MDMs likelihood without the need for model-specific analysis, regardless of the number of auxiliary variables. Additionally, they demonstrate how to parameterize the diffusion for a specified target noise distribution, enabling optimization of the inference diffusion process. By optimizing the diffusion process, researchers can now experiment with a wider range of linear diffusions automatically. To showcase their approach, two new specific diffusions are introduced, and a diffusion process is learned on popular datasets like MNIST, CIFAR10, and ImageNet32. The results show that learned MDMs achieve or surpass bits-per-dim (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture. The study highlights that selecting an appropriate inference process is essential for DBGMs' performance. By providing a method to optimize the inference diffusion process without extensive analysis, this work enables rapid prototyping and evaluation of different multivariate diffusions in DBGMs.