Accelerating accurate simulations of calorimeter showers with normalizing flows and probability density distillation

Recently, we introduced caloflow, a high-fidelity generative model for geant4 calorimeter shower emulation based on normalizing flows. Here, we present caloflow v2, an improvement on our original framework that speeds up shower generation by a further factor of 500 relative to the original. The improvement is based on a technique called probability density distillation, originally developed for speech synthesis in the machine learning literature, and which we develop further by introducing a set of powerful new loss terms. We demonstrate that caloflow v2 preserves the same high fidelity as the original using qualitative (average images, histograms of high-level features) and quantitative (classifier metric between geant4 and generated samples) measures. The result is a generative model for calorimeter showers that matches the state of the art in speed (a factor of ${10}^{4}$ faster than geant4) and greatly surpasses the previous state of the art in fidelity.