System-Embedded Diffusion Bridge Models

2025-06-30

AI Summary

This paper addresses linear inverse problems under incomplete or noisy measurements by proposing a novel supervised diffusion bridge method. The core innovation lies in explicitly incorporating the known linear measurement operator into the matrix-valued stochastic differential equation (SDE) coefficients of the diffusion process—rather than treating it as a black box or a post-processing module. This design enables seamless integration of system-structural priors with data-driven modeling within the score-based generative modeling framework. Experiments demonstrate substantial improvements in reconstruction accuracy across diverse linear inverse tasks, including compressed sensing, image deblurring, and computed tomography (CT) reconstruction. Notably, the method exhibits strong robustness to system mismatch between training and testing conditions, effectively mitigating deployment bias. These properties underscore its practical applicability in real-world imaging and inverse problem settings.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Recovering signals from incomplete or noisy measurements
• Integrating known linear measurement systems into models
• Improving generalization under system misspecification

Innovation

• Embed linear measurement system into SDE
• Supervised bridge with structural information
• Robust generalization under system misspecification