The time dependence of the diffusion process at the interface between two thin films of protonated and deuterated poly(methyl methacrylate) (PMMA) is studied. By neutron reflection, we investigate both the form and the width of the interface between the two polymer layers with subnanometer resolution. At small diffusion times the movement of chain segments across the interface is followed in detail. Different characteristic time regimes for the broadening of the interface are distinguished. In addition, the form of the interfacial profile changes during the diffusion process and deviates at small diffusion times significantly from an error function profile, which would be assumed for normal Fickian diffusion. The results are discussed within the predictions of the reptation model and are compared : to experiments with polystyrene films.