In this paper, we present a novel method for pile-up removal of $pp$ interactions using variational inference with diffusion models, called vipr. Instead of using classification methods to identify which particles are from the primary collision, a generative model is trained to predict the constituents of the hard-scatter particle jets with pile-up removed. This results in an estimate of the full posterior over hard-scatter jet constituents, which has not yet been explored in the context of pile-up removal, yielding a clear advantage over existing methods especially in the presence of imperfect detector efficiency. We evaluate the performance of vipr in a sample of jets from simulated $t\bar{t}$ events overlain with pile-up contamination. vipr outperforms softdrop and has comparable performance to puppiml in predicting the substructure of the hard-scatter jets over a wide range of pile-up scenarios.