  Plug-and-Play (PnP) algorithms are a class of iterative algorithms that
address image inverse problems by combining a physical model and a deep neural
network for regularization. Even if they produce impressive image restoration
results, these algorithms rely on a non-standard use of a denoiser on images
that are less and less noisy along the iterations, which contrasts with recent
algorithms based on Diffusion Models (DM), where the denoiser is applied only
on re-noised images. We propose a new PnP framework, called Stochastic
deNOising REgularization (SNORE), which applies the denoiser only on images
with noise of the adequate level. It is based on an explicit stochastic
regularization, which leads to a stochastic gradient descent algorithm to solve
ill-posed inverse problems. A convergence analysis of this algorithm and its
annealing extension is provided. Experimentally, we prove that SNORE is
competitive with respect to state-of-the-art methods on deblurring and
inpainting tasks, both quantitatively and qualitatively.
