Unsupervised learning of deep-neural-networks (DNNs) for image quality enhancement can overcome the real-world challenge of the lack of high-quality training images. Typical DNNs for weakly/un-supervised image restoration make strong assumptions that are often infeasible or undesirable in clinical scenarios, e.g., they (a) demand multiple acquired degraded instances per scene, (b) simulate degraded instances assuming independent identically-distributed noise per pixel, (c) demand pre-training large diffusion models on large sets of high(er)-quality images, or (d) ignore uncertainty estimation in their outputs. We propose a novel Bayesian DNN framework for unsupervised image quality enhancement incorporating (i) stochastic perturbations at multiple stages within the DNN architecture, for regularization and data-driven automatic generation of realistic degraded instances, (ii) variational/distribution modeling in latent space, (iii) novel Monte-Carlo expectation maximization of DNN parameters using Langevin diffusion in latent space, and (iv) novel low-density sampling for perturbations using normalized Langevin diffusion. Results on publicly available datasets demonstrates the benefits of our DNN framework over existing methods in CT, MRI, and PET.