Principled Design of Diffusion-based Optimizers for Inverse Problems

2026-05-12

AI Summary

Diffusion models face challenges in solving inverse problems due to slow inference and the need for task-specific hyperparameter tuning, which hinders their practical deployment. This work proposes a reparameterization strategy that induces invariance, enabling hyperparameters to generalize across tasks. Building upon the RED-diff framework, the authors introduce OptDiff—an optimization pipeline that integrates convex optimization techniques to accelerate inference. By combining score-based diffusion models, posterior sampling reconstruction, a carefully designed noise schedule, and adaptive posterior weighting, the method achieves substantial improvements in both inference speed and reconstruction quality across image restoration tasks such as deblurring and super-resolution, effectively balancing computational efficiency with performance.

Abstract

Score-based diffusion models achieve state-of-the-art performance for inverse problems, but their practical deployment is hindered by long inference times and cumbersome hyperparameter tuning. While pretrained diffusion models can be reused across tasks without retraining, inference-time hyperparameters such as the noise schedule and posterior sampling weights typically require ad-hoc adjustment for each problem setup. We propose principled reparameterizations that induce invariances, allowing the same hyperparameters to be reused across multiple problems without re-tuning. In addition, building on the RED-diff framework, which reformulates posterior sampling as an optimization problem, we further develop the OptDiff pipeline. OptDiff provides a simplified tuning framework that facilitates the integration of convex optimization tools to accelerate inference. Experiments on image reconstruction, deblurring, and super-resolution show substantial speedups and improved image quality.

Problem

• inverse problems
• diffusion models
• hyperparameter tuning
• inference time
• posterior sampling

Innovation

• diffusion models
• inverse problems
• hyperparameter invariance
• convex optimization
• OptDiff