Residual Diffusion Bridge Model for Image Restoration

TL;DR

The paper introduces the Residual Diffusion Bridge Model (RDBM), a novel approach for image restoration that adaptively reconstructs degraded regions by leveraging residuals, with theoretical analysis and state-of-the-art experimental results.

Contribution

It provides a unified analytical framework for diffusion bridge models, introduces residual-based modulation for adaptive restoration, and demonstrates the optimality and superior performance of RDBM.

Findings

RDBM achieves state-of-the-art results across various image restoration tasks.

Theoretical reformulation clarifies the mathematical foundation of diffusion bridge models.

Residual modulation improves restoration quality by adaptively handling degraded regions.

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.