  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 ML 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 of 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.
