  Simulating showers of particles in highly-granular detectors is a key
frontier in the application of machine learning to particle physics. Achieving
high accuracy and speed with generative machine learning models would enable
them to augment traditional simulations and alleviate a major computing
constraint. This work achieves a major breakthrough in this task by, for the
first time, directly generating a point cloud of a few thousand space points
with energy depositions in the detector in 3D space without relying on a
fixed-grid structure. This is made possible by two key innovations: i) Using
recent improvements in generative modeling we apply a diffusion model to
generate photon showers as high-cardinality point clouds. ii) These point
clouds of up to $6,000$ space points are largely geometry-independent as they
are down-sampled from initial even higher-resolution point clouds of up to
$40,000$ so-called Geant4 steps. We showcase the performance of this approach
using the specific example of simulating photon showers in the planned
electromagnetic calorimeter of the International Large Detector (ILD) and
achieve overall good modeling of physically relevant distributions.
