System-Embedded Diffusion Bridge Models

Bartlomiej Sobieski, Matthew Tivnan, Yuang Wang, Siyeop yoon, Pengfei Jin, Dufan Wu, Quanzheng Li, Przemyslaw Biecek

Keywords: diffusion, generative, inverse, problems, image, translation, restoration, linear, system, bridge

TL;DR: We propose a new diffusion bridge method that embeds the linear measurement system into the SDE coefficients, enabling direct use of system information and improving performance across diverse inverse problem benchmarks.

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.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 5521