发表机构
Nanjing University; Renmin University of China（南京大学; 中国人民大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出SDDBMs，一种正则化扩散桥的通用框架，以非退化高斯终端边际替代硬端点约束，涵盖现有多种扩散桥模型，图像修复实验显示其数值稳定性与生成质量更优。
AI 中文摘要
扩散桥模型利用杜布的\boldsymbol{h}-变换构建任意端点分布间的随机传输，在图像到图像的翻译与修复中展现出强大潜力。然而，现有多数桥模型依赖硬端点条件，强制终端状态精确匹配规定目标，这种硬约束会引发终端边界奇异：终端律坍缩为狄拉克测度，且所得漂移系数在端点附近病态。本文提出软去噪扩散桥模型（SDDBMs），这是一种直接在终端约束层面正则化扩散桥的通用框架。SDDBMs不施加精确端点，而是在变换路径测度下规定非退化高斯终端边际，带有灵活的终端中心与方差。从该规定边际出发，我们开发了软桥的完整闭式构造，包括高斯终端重加权、软\boldsymbol{h}-函数、诱导高斯前向边际以及无\boldsymbol{x}_0动态。理论上，SDDBMs提供了统一的概率视角，涵盖现有扩散桥模型（包括DDBMs、GOUB和UniDB）作为特定参数选择下的特例。在图像修复任务上的大量实验表明，SDDBMs相较于现有基于桥的方法，实现了更高的数值稳定性与更优的生成质量。
英文摘要
Diffusion bridge models leverage Doob's \(h\)-transform to construct stochastic transports between arbitrary endpoint distributions, and have shown strong potential in image-to-image translation and restoration. However, most existing bridge models rely on hard endpoint conditioning, which forces the terminal state to match a prescribed target exactly. This hard constraint induces terminal-boundary singularities: the terminal law collapses to a Dirac measure, and the resulting drift coefficients become ill-conditioned near the endpoint. In this paper, we propose Soft Denoising Diffusion Bridge Models (SDDBMs), a generalized framework that regularizes diffusion bridges directly at the level of their terminal constraints. Instead of imposing an exact endpoint, SDDBMs prescribe a non-degenerate Gaussian terminal marginal under the transformed path measure, with a flexible terminal center and variance. Starting from this prescribed marginal, we develop a complete closed-form construction of the soft bridge, including the Gaussian terminal reweighting and soft \(h\)-function, the induced Gaussian forward marginals and \(\mathbf{x}_0\)-free dynamics. Theoretically, SDDBMs provide a unified probabilistic perspective that encompasses existing diffusion bridge models, including DDBMs, GOUB, and UniDB, as special cases under specific parameter choices. Extensive experiments on image restoration tasks demonstrate that SDDBMs achieve improved numerical stability and superior generation quality over existing bridge-based methods.
