Score-based diffusion methods provide a powerful strategy to solve image restoration tasks by flexibly combining a pre-trained foundational prior model with a likelihood function specified during test time. Such methods are predominantly derived from two stochastic processes: reversing Ornstein-Uhlenbeck, which underpins the celebrated denoising diffusion probabilistic models (DDPM) and denoising diffusion implicit models (DDIM), and the Langevin diffusion process. The solutions delivered by DDPM and DDIM are often remarkably realistic, but they are not always consistent with measurements because of likelihood intractability issues and the associated required approximations. Alternatively, using a Langevin process circumvents the intractable likelihood issue, but usually leads to restoration results of inferior quality and longer computing times. This paper presents a novel and highly computationally efficient image restoration method that carefully embeds a foundational DDPM denoiser within an empirical Bayesian Langevin algorithm, which jointly calibrates key model hyper-parameters as it estimates the model's posterior mean. Extensive experimental results on three canonical tasks (image deblurring, super-resolution, and inpainting) demonstrate that the proposed approach improves on state-of-the-art strategies both in image estimation accuracy and computing time.

翻译：基于分数的扩散方法通过灵活结合预训练的基础先验模型与测试时指定的似然函数，为解决图像复原任务提供了强大策略。此类方法主要源于两种随机过程：逆转奥恩斯坦-乌伦贝克过程（支撑着著名的去噪扩散概率模型与去噪扩散隐式模型）以及朗之万扩散过程。DDPM和DDIM生成的解通常具有显著的真实感，但由于似然函数难处理问题及相关近似需求，其解并不总是与测量数据保持一致。另一种方案是使用朗之万过程规避难处理的似然函数问题，但通常会导致复原质量下降且计算时间延长。本文提出一种新颖且计算效率极高的图像复原方法，该方法将基础DDPM去噪器精心嵌入经验贝叶斯朗之万算法中，在估计模型后验均值的同时联合校准关键模型超参数。在三个经典任务（图像去模糊、超分辨率和修复）上的大量实验结果表明，所提方法在图像估计精度和计算时间方面均优于当前最先进策略。