EPiC-ly Fast Particle Cloud Generation with Flow-Matching and Diffusion
Erik Buhmann Cedric Ewen Darius A. Faroughy Tobias Golling Gregor Kasieczka Matthew Leigh Guillaume Quétant John Andrew Raine Debajyoti Sengupta David Shih
Jets at the LHC, typically consisting of a large number of highly correlated
particles, are a fascinating laboratory for deep generative modeling. In this
paper, we present two novel methods that generate LHC jets as point clouds
efficiently and accurately. We introduce \epcjedi, which combines
score-matching diffusion models with the Equivariant Point Cloud (EPiC)
architecture based on the deep sets framework. This model offers a much faster
alternative to previous transformer-based diffusion models without reducing the
quality of the generated jets. In addition, we introduce \epcfm, the first
permutation equivariant continuous normalizing flow (CNF) for particle cloud
generation. This model is trained with {\it flow-matching}, a scalable and
easy-to-train objective based on optimal transport that directly regresses the
vector fields connecting the Gaussian noise prior to the data distribution. Our
experiments demonstrate that \epcjedi and \epcfm both achieve state-of-the-art
performance on the top-quark JetNet datasets whilst maintaining fast generation
speed. Most notably, we find that the \epcfm model consistently outperforms all
the other generative models considered here across every metric. Finally, we
also introduce two new particle cloud performance metrics: the first based on
the Kullback-Leibler divergence between feature distributions, the second is
the negative log-posterior of a multi-model ParticleNet classifier.