Learning Diffusion Priors from Observations by Expectation Maximization

TL;DR

This paper introduces DiEM, a new EM-based method for training diffusion models solely from incomplete and noisy data, enabling their use as priors in Bayesian inverse problems without requiring large clean datasets.

Contribution

DiEM is the first approach to train proper diffusion priors from incomplete and noisy observations using expectation-maximization, improving applicability in data-scarce scenarios.

Findings

DiEM effectively trains diffusion models from noisy, incomplete data.

The proposed posterior sampling scheme enhances diffusion model performance.

Empirical results demonstrate DiEM's superiority over existing methods.

Abstract

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we present DiEM, a novel method based on the expectation-maximization algorithm for training diffusion models from incomplete and noisy observations only. Unlike previous works, DiEM leads to proper diffusion models, which is crucial for downstream tasks. As part of our methods, we propose and motivate an improved posterior sampling scheme for unconditional diffusion models. We present empirical evidence supporting the effectiveness of our approach.