System-Embedded Diffusion Bridge Models

Przemyslaw Biecek (Netezza Polska) · Pengfei Jin (Massachusetts General Hospital, Harvard University) · Quanzheng Li (Massachusetts General Hospital， Harvard Medical School) · Bartlomiej Sobieski (University of Warsaw, Centre for Credible AI) · Matthew Tivnan (Massachusetts General Hospital, Harvard University) · Yuang Wang (Massachusetts General Hospital, Harvard University) · Siyeop yoon (Massachusetts General Hospital, Harvard Medical School) · Dufan Wu (The Ohio State University)

consistent improvementsinverse problemslinear inverse problemslinear measurement systemmatrix-valued sdemeasurement modelrobust generalization score-based generative models stochastic processessupervised bridge methodssystem misspecificationsystem-embedded diffusion bridge modelstraining and deploymentunsupervised approaches

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.