Graphically Structured Diffusion Models

Christian Dietrich Weilbach, William Harvey, Frank Wood

Keywords: diffusion models, amortized inference, graphical models, invariances, sparsity, probabilistic programming

TL;DR: We propose a diffusion model architecture incorporating statistical independencies and exchangeability for more scalable amortized inference.

Abstract: We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy.

Publication Venue: ICML 2023

Submission Number: 3