  We introduce a novel machine learning method developed for the fast
simulation of calorimeter detector response, adapting vector-quantized
variational autoencoder (VQ-VAE). Our model adopts a two-stage generation
strategy: initially compressing geometry-aware calorimeter data into a discrete
latent space, followed by the application of a sequence model to learn and
generate the latent tokens. Extensive experimentation on the Calo-challenge
dataset underscores the efficiency of our approach, showcasing a remarkable
improvement in the generation speed compared with conventional method by a
factor of 2000. Remarkably, our model achieves the generation of calorimeter
showers within milliseconds. Furthermore, comprehensive quantitative
evaluations across various metrics are performed to validate physics
performance of generation.
