Outlier-Robust Diffusion Solvers for Inverse Problems
For practitioners solving inverse problems with real-world noisy data, this work provides a robust diffusion-based method that outperforms existing approaches in outlier scenarios.
Diffusion model-based methods for inverse problems fail under outlier-corrupted measurements. The authors propose a robust solver combining explicit noise estimation and iteratively reweighted least squares with Huber loss, solved via conjugate gradient, achieving state-of-the-art performance on multiple image datasets under various outlier conditions.
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.