We report quasielastic neutron scattering experiments exploring the alpha relaxation in polyisoprene over an unprecedented range in momentum transfer. Corroborating and validating earlier molecular dynamics simulations, the measurements reveal a crossover from a Gaussian regime of sublinear diffusion to a strongly non-Gaussian regime at short distances. We show that a consistent interpretation in terms of a distribution of finite jumps underlying the alpha process is possible. This model leads to a time-dependent non-Gaussian parameter exhibiting all features revealed so far from various simulations.