  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 such as blur kernel. 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.
