Abstract: The interest in using Denoising Diffusion Models (DDM) as priors for solving Bayesian inverse problems has increased rapidly in recent time. However, sampling from the resulting posterior distribution is a challenge. To address this problem, previous works have proposed approximations to skew the drift term of the diffusion. In this work, we take a different approach and utilize the specific structure of the DDM prior to define a set of intermediate and simpler posterior sampling problems, resulting in a lower approximation error compared to previous methods. We empirically demonstrate the reconstruction capability of our method for general linear inverse problems on the basis of synthetic examples and various image restoration tasks.