A Stability Benchmark of Generative Regularizers for Inverse Problems

2026-05-11

AI Summary

This work systematically evaluates the stability and reliability of generative priors—such as diffusion models—in imaging inverse problems under imperfect conditions, including out-of-distribution data, inaccuracies in the forward operator, and mismatches in noise models. We introduce the first comprehensive framework for assessing the stability of generative regularization methods, conducting extensive numerical experiments to analyze key properties such as convergence and robustness, and comparing them against state-of-the-art variational optimization approaches. Our findings demonstrate that while generative priors can achieve near-optimal reconstruction in certain tasks, they may exhibit instability or even failure under specific perturbations, thereby delineating their practical applicability boundaries and inherent limitations.

Abstract

Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect settings. Typical definitions of stability encompass the notion of ''convergent regularization'', robustness to out-of-distribution data, and to inaccuracies in the forward operator or noise model. We evaluate these properties numerically. Furthermore, we benchmark generative approaches against modern optimization-based methods inspired by the widely used variational techniques. Our results give insights for which settings and applications generative priors can deliver state-of-the-art reconstructions, and on those in which they fall short or may even be problematic.

Problem

• inverse problems
• generative priors
• stability
• imaging
• robustness

Innovation

• generative priors
• stability benchmark
• inverse problems
• convergent regularization
• robustness