This work presents an experimental picture of molecular ballistic diffusion on a surface, a process that is difficult to pinpoint because it generally occurs on very short length scales. By combining neutron time-of-flight data with molecular dynamics simulations and density functional theory calculations, we provide a complete description of the ballistic translations and rotations of a polyaromatic hydrocarbon (PAH) adsorbed on the basal plane of graphite. Pyrene, C16H10, adsorbed on graphite is a unique system, where at relative surface coverages of about 10-20% its mean free path matches the experimentally accessible time/space scale of neutron time-of-flight spectroscopy (IN6 at the Institut Laue-Langevin). The comparison between the diffusive behavior of large and small PAHs such as pyrene and benzene adsorbed on graphite brings a strong experimental indication that the interaction between molecules is the dominating mechanism in the surface diffusion of polyaromatic hydrocarbons adsorbed on graphite.