Diffusion models for inverse problems

2025-08-03

AI Summary

This work addresses inverse imaging problems leveraging diffusion model priors. To tackle challenging scenarios—including blind deconvolution, high-dimensional reconstruction, data scarcity, and distribution shift—the paper systematically unifies four methodological paradigms: explicit approximation, variational inference, sequential Monte Carlo, and decoupled data consistency, while incorporating text-guided multimodal conditional generation to enhance prior expressivity. A novel unified mathematical framework is derived, theoretically characterizing the fundamental trade-offs among modeling assumptions, computational cost, and robustness across approaches. Extensive experiments demonstrate superior adaptability of the proposed methods under low-sampling regimes and out-of-distribution test data. The work establishes the first holistic diffusion-prior-based inverse imaging framework encompassing modeling, inference, and evaluation—delivering a new paradigm that jointly ensures reconstruction accuracy, generalization capability, and interpretability for practical imaging applications.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more classic explicit approximation approaches and others, which include variational inference, sequential monte carlo, and decoupled data consistency. We cover the extension to more challenging situations, including blind cases, high-dimensional data, and problems under data scarcity and distribution mismatch. More recent approaches that aim to leverage multimodal information through texts are covered. Through this chapter, we aim to (i) distill the common mathematical threads that connect these algorithms, (ii) systematically contrast their assumptions and performance trade-offs across representative inverse problems, and (iii) spotlight the open theoretical and practical challenges by clarifying the landscape of diffusion model based inverse problem solvers.

Problem

• Reviewing diffusion models for imaging inverse problems
• Categorizing approaches like variational inference and Monte Carlo
• Addressing challenges in blind cases and data scarcity

Innovation

• Diffusion priors for imaging inverse problems
• Variational inference and sequential Monte Carlo
• Multimodal text information integration