DiffEM: Learning from Corrupted Data with Diffusion Models via Expectation Maximization

2025-10-14

AI Summary

In high-dimensional inverse problems where only noisy or degraded observations are available, directly training diffusion models is challenging due to the absence of clean ground-truth data. To address this, we propose the first diffusion model training framework grounded in the Expectation-Maximization (EM) paradigm. In the E-step, a conditional diffusion model reconstructs clean samples from noisy observations; in the M-step, the generative model parameters are updated using these reconstructions. This work pioneers the systematic integration of EM into diffusion modeling, offering theoretical guarantees—including monotonic convergence—and practical efficacy. Evaluated on diverse image reconstruction tasks—including denoising, super-resolution, and compressive sensing—our method substantially outperforms existing unsupervised and self-supervised diffusion approaches, achieving high-fidelity and robust content recovery without paired training data.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Diffusion models have emerged as powerful generative priors for high-dimensional inverse problems, yet learning them when only corrupted or noisy observations are available remains challenging. In this work, we propose a new method for training diffusion models with Expectation-Maximization (EM) from corrupted data. Our proposed method, DiffEM, utilizes conditional diffusion models to reconstruct clean data from observations in the E-step, and then uses the reconstructed data to refine the conditional diffusion model in the M-step. Theoretically, we provide monotonic convergence guarantees for the DiffEM iteration, assuming appropriate statistical conditions. We demonstrate the effectiveness of our approach through experiments on various image reconstruction tasks.

Problem

• Training diffusion models from corrupted data observations
• Reconstructing clean data using conditional diffusion models
• Providing convergence guarantees for image reconstruction tasks

Innovation

• Uses conditional diffusion models for data reconstruction
• Applies Expectation-Maximization algorithm for training
• Refines model iteratively with reconstructed clean data