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.