In high energy physics (HEP), jets are collections of correlated particles produced ubiquitously in particle collisions such as those at the CERN Large Hadron Collider (LHC). Machine-learning-based generative models, such as generative adversarial networks (GANs), have the potential to significantly accelerate LHC jet simulations. However, despite jets having a natural representation as a set of particles in momentum-space, a.k.a. a particle cloud, to our knowledge there exist no generative models applied to such a dataset. We introduce a new particle cloud dataset (JetNet), and, due to similarities between particle and point clouds, apply to it existing point cloud GANs. Results are evaluated using (1) the 1-Wasserstein distance between high- and low-level feature distributions, (2) a newly developed Fréchet ParticleNet Distance, and (3) the coverage and (4) minimum matching distance metrics. Existing GANs are found to be inadequate for physics applications, hence we develop a new message passing GAN (MPGAN), which outperforms existing point cloud GANs on virtually every metric and shows promise for use in HEP. We propose JetNet as a novel point-cloud-style dataset for the machine learning community to experiment with, and set MPGAN as a benchmark to improve upon for future generative models.