Using diffusion models to solve inverse problems is a growing field of research. Current methods assume the degradation to be known and provide impressive results in terms of restoration quality and diversity. In this work, we leverage the efficiency of those models to jointly estimate the restored image and unknown parameters of the degradation model. In particular, we designed an algorithm based on the well-known Expectation-Minimization (EM) estimation method and diffusion models. Our method alternates between approximating the expected log-likelihood of the inverse problem using samples drawn from a diffusion model and a maximization step to estimate unknown model parameters. For the maximization step, we also introduce a novel blur kernel regularization based on a Plug \& Play denoiser. Diffusion models are long to run, thus we provide a fast version of our algorithm. Extensive experiments on blind image deblurring demonstrate the effectiveness of our method when compared to other state-of-the-art approaches.

翻译：利用扩散模型求解逆问题是当前一个快速发展的研究领域。现有方法通常假定退化模型已知，在恢复质量和多样性方面取得了令人瞩目的成果。本研究充分利用这些模型的高效性，联合估计恢复图像和退化模型中的未知参数。具体而言，我们基于经典的期望最大化（EM）估计方法与扩散模型设计了一种算法。该方法交替进行以下步骤：利用扩散模型生成的样本近似逆问题的期望对数似然，以及通过最大化步骤估计未知模型参数。针对最大化步骤，我们还引入了一种基于即插即用（Plug & Play）去噪器的新型模糊核正则化方法。由于扩散模型运行耗时，我们进一步提出了算法的快速版本。在盲图像去模糊任务上的大量实验表明，相较于其他最新方法，本方法具有显著的优越性。