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.

翻译：扩散桥模型在任意配对分布之间建立概率路径，展现出通用图像复原的巨大潜力。现有方法大多仅将其视为随机插值器的简单变体，缺乏统一的分析视角。此外，它们通过全局噪声注入与去除不加区分地重建图像，不可避免地因不完美重建而扭曲未退化区域。为应对这些挑战，我们提出残差扩散桥模型（RDBM）。具体而言，我们从理论上重构广义扩散桥的随机微分方程，并推导其前向与反向过程的解析公式。关键的是，我们利用给定分布的残差来调制噪声注入与去除，从而实现对退化区域的自适应复原，同时保持其他完好区域不变。此外，我们揭示了现有桥模型的基本数学本质，它们均为RDBM的特例，并通过实验证明了所提模型的最优性。大量实验定性与定量地验证了我们的方法在多种图像复原任务中的先进性能。代码公开于 https://github.com/MiliLab/RDBM。