Statistical inference problems arise in numerous machine learning and signal/image processing tasks. Bayesian inference provides a powerful framework for solving such problems, but posterior estimation can be computationally challenging. In this talk, we present a stochastic plug and play sampling algorithm that leverages variable splitting to efficiently sample from a posterior distribution. The algorithm draws inspiration from the alternating direction method of multipliers (ADMM), and subdivides the challenging task of posterior sampling into two simpler sampling problems. The first problem is dependent on the forward model, while the second corresponds to a denoising problem that can be readily accomplished through a deep generative model. Specifically, we demonstrate our method using diffusion-based generative models. By sampling the parameter to infer and the hyperparameters of the problem efficiently, the generated samples can be used to approximate Bayesian estimators of the parameters. Unlike optimization methods, the proposed approach provides confidence intervals at a relatively low computational cost. To evaluate the effectiveness of our proposed samplers, we conduct simulations on four commonly studied signal processing problems and compare their performance to recent state-of-the-art optimization and MCMC algorithms.