Learning Diffusion Priors from Observations by Expectation Maximization

2024/05/22 by François Rozet, Rozet, François, Gérôme Andry +5 · 1 voice · 26 citations
Computer Science · Mathematics · #Artificial intelligence #Bayesian probability #Computer science #Diffusion #Domain Adaptation and Few-Shot Learning #Econometrics #Economics #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning in Healthcare #Mathematical optimization #Mathematics #Maximization #Physics #Prior probability #Thermodynamics #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.2405.13712

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2024/05/22 · arxiv published 2024/05/22 · openalex created_date 2025/10/10 · arxiv updated 2025/10/31 · openalex updated_date 2026/07/28

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.

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• Noisy MRI Reconstruction via MAP Estimation with an Implicit Deep-Denoiser Prior
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• AION-1: Omnimodal Foundation Model for Astronomical Sciences
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• Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Sampling
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• Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulation
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• Noise-Robust Conditional Flow Matching: Generating Clean Samples from Noisy Datasets
• Exact Posterior Score Estimation for Solving Linear Inverse Problems
• Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation

Discussions

• It is only useful when the training data is noisy or incomplete. See eg. arxiv.org/abs/2405.13712 where train diffusion models from sparse images only. [bsky, 0 points, 1 comments]

Related

• DiffEM: Learning from Corrupted Data with Diffusion Models via Expectation Maximization
• Learning Diffusion Model from Noisy Measurement using Principled Expectation-Maximization Method
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• An Expectation-Maximization Algorithm for Training Clean Diffusion Models from Corrupted Observations