Solving inverse problems -- recovering signals from incomplete or noisy measurements -- is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main paradigms have formed: unsupervised approaches that adapt pretrained generative models to inverse problems, and supervised bridge methods that train stochastic processes conditioned on paired clean and corrupted data. While the former typically assume knowledge of the measurement model, the latter have largely overlooked this structural information. We introduce System embedded Diffusion Bridge Models (SDBs), a new class of supervised bridge methods that explicitly embed the known linear measurement system into the coefficients of a matrix-valued SDE. This principled integration yields consistent improvements across diverse linear inverse problems and demonstrates robust generalization under system misspecification between training and deployment, offering a promising solution to real-world applications.

翻译：解决逆问题——从不完全或有噪声的测量中恢复信号——是科学与工程领域的一项基础任务。基于分数的生成模型（SGMs）近年来已成为完成此任务的一个强大框架。目前形成了两种主要范式：一是将预训练的生成模型适配于逆问题的无监督方法，二是基于成对干净与受损数据训练条件随机过程的监督桥方法。前者通常假设已知测量模型，而后者在很大程度上忽略了这一结构信息。我们提出了系统嵌入扩散桥模型（SDBs），这是一类新的监督桥方法，它将已知的线性测量系统显式地嵌入到一个矩阵值随机微分方程（SDE）的系数中。这种原理性的整合在多种线性逆问题中带来了一致的性能提升，并在训练与部署之间存在系统误设的情况下展现出稳健的泛化能力，为实际应用提供了一个有前景的解决方案。