The idea of using generative models to perform posterior sampling for imaging inverse problems has elicited attention from the computational imaging community. The main limitation of the existing generative model-based posterior sampling methods is that they do not provide any information about how uncertain the generative model is. In this work, we propose a quick-to-adopt framework that can transform a given generative model-based posterior sampling method into a statistical model that can quantify the generative model uncertainty. The proposed framework is built upon the principles of Bayesian neural networks with latent variables and uses ensembling to capture the uncertainty on the parameters of a generative model. We evaluate the proposed framework on the computed tomography reconstruction problem and demonstrate its capability to quantify generative model uncertainty with an illustrative example. We also show that the proposed method can improve the quality of the reconstructions and the predictive uncertainty estimates of the generative model-based posterior sampling method used within the proposed framework.