将测量系统信息嵌入扩散模型，提升逆问题求解精度与鲁棒性。
System-Embedded Diffusion Bridge Models
- 在扩散过程中显式融入已知线性测量系统的矩阵系数
- 在多种线性逆问题上表现更优，且对系统建模误差具有强鲁棒性
- 适合需要高可靠性的实际应用，如医学成像与信号恢复
求解逆问题——从不完整或噪声测量中恢复信号——是科学与工程的基础任务。基于分数的生成模型（SGMs）近期成为该任务的强大框架。现有方法分为两类：无监督方法依赖预训练生成模型适配逆问题，需已知测量模型；有监督桥接方法通过成对干净与损坏数据训练随机过程，但通常忽略系统结构信息。本文提出系统嵌入扩散桥模型（SDB），一种新型有监督桥接方法，将已知线性测量系统以矩阵形式嵌入到随机微分方程（SDE）的系数中。这种合理整合在多种线性逆问题上均带来一致性能提升，并在训练与部署阶段系统建模存在偏差时仍表现出强泛化能力，为真实场景应用提供了可行方案。
原文摘要 · Abstract (English)
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.
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