Learning Diffusion Priors from Observations by Expectation Maximization
This addresses a bottleneck for researchers and practitioners in fields like medical imaging or remote sensing where clean data is scarce, though it is incremental as it builds on existing diffusion model frameworks.
The authors tackled the problem of training diffusion models without clean data by introducing DiEM, a method based on expectation-maximization that learns from incomplete and noisy observations, resulting in proper diffusion models suitable for downstream tasks.
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.