Hybrid Regularization Improves Diffusion-based Inverse Problem Solving

Diffusion models, recognized for their effectiveness as generative priors, have become essential tools for addressing a wide range of visual challenges. Recently, there has been a surge of interest in leveraging Denoising processes for Regularization (DR) to solve inverse problems. However, existing methods often face issues such as mode collapse, which results in excessive smoothing and diminished diversity. In this study, we perform a comprehensive analysis to pinpoint the root causes of gradient inaccuracies inherent in DR. Drawing on insights from diffusion model distillation, we propose a novel approach called Consistency Regularization (CR), which provides stabilized gradients without the need for ODE simulations. Building on this, we introduce Hybrid Regularization (HR), a unified framework that combines the strengths of both DR and CR, harnessing their synergistic potential. Our approach proves to be effective across a broad spectrum of inverse problems, encompassing both linear and nonlinear scenarios, as well as various measurement noise statistics. Experimental evaluations on benchmark datasets, including FFHQ and ImageNet, demonstrate that our proposed framework not only achieves highly competitive results compared to state-of-the-art methods but also offers significant reductions in wall-clock time and memory consumption.

Authors

• Hongkun Dou
• Zeyu Li
• Jinyang Du
• Lijun Yang
• Wen Yao 0001
• Yue Deng 0001

Keywords

• Diffusion models
• inverse problems