System-Embedded Diffusion Bridge Models

TL;DR

This paper introduces System embedded Diffusion Bridge Models (SDBs), a new supervised approach that explicitly incorporates known measurement systems into stochastic processes, improving inverse problem solutions and robustness.

Contribution

The paper proposes SDBs, a novel class of supervised diffusion models that embed measurement system knowledge directly into the SDE coefficients, enhancing performance and generalization.

Findings

Consistent improvements across various linear inverse problems.

Robust generalization under system misspecification.

Effective integration of measurement models into diffusion processes.

Abstract

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.