The short-time interdiffusion between bilayers of protonated and deuterated polystyrene was measured using neutron reflectivity. The moments of the segment density profiles were used as a model-independent means of characterizing the interdiffusion. It is shown that for diffusion times between the Rouse relaxation time and the reptation time of a single chain, the concentration profile at the polymer/polymer interface can be described by a sharp gradient at the interface with a relatively long range decay away from it. With increasing molecular weight, the decay length increased substantially as expected for reptating chains. Furthermore, the effective diffusion coefficient is shown to decrease for all times less than the estimated reptation time and reduce to the bulk value at longer times. Critical slowing down effects of isotropic origin at the interface are shown to be of no consequences in these studies.