Generative machine learning has risen into the public consciousness in a remarkably short time due to eye-catching advances in text and image generation. Beyond the hype of these accessible applications, the underlying techniques also hold enormous potential for serious scientific pursuits in data intensive disciplines like EHEP.  Generative models at their core are not merely sample generators, but distribution learners, and understanding the distributions of backgrounds and experimental data is the entire premise of EHEP. In this talk I will introduce the technical foundations of deep generative modelling and describe where and when it should be used, with examples taken from the physics programmes of ATLAS, SuperCDMS, and MATHUSLA. In particular, I will dig into recent developments for calorimeter shower simulation which are designed to supplement the physics-based simulations of GEANT4. Deep generative models show a computational speedup of up to 75,000x which promises to largely alleviate the computational bottlenecks forecasted by the ATLAS collaboration. Outside of the ATLAS experiment, similar applications have been much less explored, presenting many opportunities for graduate students to establish new lines of research while developing skills that are transferable and in-demand in industry.