Diffusion at the polymer/polymer interface was probed by small-amplitude oscillatory shear measurements carried out on polystyrene (PS)/polystyrene (PS) sandwich-like assembly as a function of the time of welding in the molten state. It was found that the dynamic complex shear modulus G*(t) at a fixed frequency increases with the time of contact in two time regimes. First G*(t) increases proportionally to t(1/2) and then a second regime takes place where G*(t) increases proportionally to t(1/4) At longer times, G*(t) tends asymptotically toward G* of pure polystyrene. The results were interpreted in terms of reptation theory and the time of transition between the two scaling law regimes was found to be in agreement with the time needed for the transition from the Rouse mode to the reptation mode. Special attention was given to the initial state of the polymer surfaces before contact by performing experiments on (i) freshly prepared surfaces, (ii) presheared samples, (iii) fractured samples, and (iv) corona-treated samples. The results showed that the diffusion mechanism is strongly dependent on the initial chain-end distribution at the surface before contact. Diffusion at surfaces with an excess of chain ends proceeds in a Rouse-like mode, whereas for surfaces without excess of chain ends, the diffusion proceeds in a reptational-like dynamics, as was predicted by de Gennes and by Prager and Tirrell.