Solving Inverse Problems using Diffusion with Fast Iterative Renoising

2025-01-29

AI Summary

This work addresses imaging inverse problems—including linear inversion and phase retrieval—by proposing DDfire, an unsupervised diffusion-based solving framework. To overcome inaccurate early-stage score gradient estimation and poor alignment with the noise assumptions of pretrained diffusion models, we introduce iterative renoising: at each diffusion inversion step, we repeatedly re-estimate and re-add white Gaussian noise consistent with the model’s training distribution, thereby enforcing continuous score matching under measurement constraints while preserving the learned prior. Coupled with colored noise shaping and measurement-driven score estimation, DDfire significantly improves gradient fidelity in early reverse steps. Experiments demonstrate that DDfire achieves state-of-the-art reconstruction quality across multiple inverse problems using only 20, 100, or 1000 network evaluations—substantially accelerating convergence and enhancing robustness compared to existing methods.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Imaging inverse problems can be solved in an unsupervised manner using pre-trained diffusion models. In most cases, that involves approximating the gradient of the measurement-conditional score function in the reverse process. Since the approximations produced by existing methods are quite poor, especially early in the reverse process, we propose a new approach that re-estimates and renoises the image several times per diffusion step. Renoising adds carefully shaped colored noise that ensures the pre-trained diffusion model sees white-Gaussian error, in accordance with how it was trained. We demonstrate the effectiveness of our"DDfire"method at 20, 100, and 1000 neural function evaluations on linear inverse problems and phase retrieval.

Problem

• Image Inversion
• Accuracy Improvement
• Complex Image Recovery

Innovation

• DDfire
• Noise Clearing and Augmentation
• Image Inversion Problems