[en] The momentum transfer dependence of the self-motion of main chain hydrogens in the α-relaxation regime of a glass forming polymer, polyisoprene, has been thoroughly investigated by a combined effort involving fully atomistic molecular dynamic simulations and quasielastic neutron scattering measurements. In this way, we have established the existence of a crossover from a Gaussian regime of sublinear diffusion to a strongly non-Gaussian regime at short distances. We show that an anomalous jump diffusion model with a distribution of jump lengths gives rise to such a crossover. This model leads to a time-dependent non-Gaussian parameter exhibiting all features revealed so far from various simulations of different glass forming systems