jats:titleAbstract</jats:title> jats:pWe investigate how a Generative Adversarial Network could be used to generate a list of particle four-momenta from LHC proton collisions, allowing one to define a generative model that could abstract from the irregularities of typical detector geometries. As an example of application, we show how such an architecture could be used as a generator of LHC parasitic collisions (pileup). We present two approaches to generate the events: unconditional generator and generator conditioned on missing transverse energy. We assess generation performances in a realistic LHC data-analysis environment, with a pileup mitigation algorithm applied.</jats:p>