Residual Diffusion Bridge Model for Image Restoration

2025-10-27

AI Summary

Existing diffusion bridge models lack a unified theoretical foundation, and global noise operations often corrupt undegraded image regions. To address these issues for general-purpose image restoration, we propose the Residual Diffusion Bridge Model (RDBM). First, grounded in stochastic differential equations, we establish the first unified analytical framework for generalized diffusion bridges, proving that existing bridge models are special cases thereof. Second, we introduce a distributional residual modulation mechanism that enables adaptive noise injection and removal exclusively within degraded regions, thereby preserving intact structural content. Third, we derive closed-form solutions for both forward and reverse processes, enabling efficient sampling. Extensive experiments across diverse image restoration tasks demonstrate that RDBM achieves state-of-the-art qualitative and quantitative performance, significantly improving reconstruction fidelity and visual quality. The code is publicly available.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Diffusion bridge models establish probabilistic paths between arbitrary paired distributions and exhibit great potential for universal image restoration. Most existing methods merely treat them as simple variants of stochastic interpolants, lacking a unified analytical perspective. Besides, they indiscriminately reconstruct images through global noise injection and removal, inevitably distorting undegraded regions due to imperfect reconstruction. To address these challenges, we propose the Residual Diffusion Bridge Model (RDBM). Specifically, we theoretically reformulate the stochastic differential equations of generalized diffusion bridge and derive the analytical formulas of its forward and reverse processes. Crucially, we leverage the residuals from given distributions to modulate the noise injection and removal, enabling adaptive restoration of degraded regions while preserving intact others. Moreover, we unravel the fundamental mathematical essence of existing bridge models, all of which are special cases of RDBM and empirically demonstrate the optimality of our proposed models. Extensive experiments are conducted to demonstrate the state-of-the-art performance of our method both qualitatively and quantitatively across diverse image restoration tasks. Code is publicly available at https://github.com/MiliLab/RDBM.

Problem

• Unifying analytical perspective for diffusion bridge models in image restoration
• Preserving undegraded regions while adaptively restoring damaged areas
• Establishing mathematical framework for generalized diffusion bridge processes

Innovation

• Modulates noise injection using distribution residuals
• Reformulates diffusion bridge stochastic differential equations
• Enables adaptive restoration while preserving intact regions