Outlier-Robust Diffusion Solvers for Inverse Problems

2026-05-10

AI Summary

This work addresses the vulnerability of diffusion models to measurement outliers in inverse problems, which often leads to significant performance degradation. To enhance robustness, the authors propose a novel optimization framework that first purifies the observed data through explicit noise estimation and then formulates an iteratively reweighted least squares objective based on the Huber loss. The resulting optimization problem is efficiently solved using the conjugate gradient method, eliminating the need for meticulous learning rate tuning. This approach represents the first integration of Huber loss with diffusion models and demonstrates consistently superior robustness against outliers across multiple image datasets and both linear and nonlinear inverse problems, outperforming existing diffusion-based methods.

Abstract

Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based methods typically struggle against outliers, which are common in real-world measurements. In this work, to tackle IPs with outliers, we first refine the measurement via explicit noise estimation to mitigate the effect of noise. Subsequently, we formulate an iteratively reweighted least squares objective based on the Huber loss to address the outliers. We propose a method utilizing gradient descent to approximately solve the corresponding optimization problem for the robust objective. To avoid delicate tuning of the learning rate required by the gradient descent method, we further employ the conjugate gradient method with an efficient strategy for updating. Extensive experiments on multiple image datasets for linear and nonlinear tasks under various conditions demonstrate that our proposed methods exhibit robustness to outliers and outperform recent DM-based methods in most cases.

Problem

• outlier-robust
• diffusion models
• inverse problems
• Huber loss
• noise estimation

Innovation

• outlier-robust
• diffusion models
• inverse problems
• Huber loss
• conjugate gradient