A number of experiments have shown that hydrogen molecules can migrate on films of solid hydrogen. This was thought to be a diffusive process but recent experimental findings have led others to a different conclusion, so a question remains about the process by which the hydrogen molecules migrate over their own solid surface. We report new measurements using a hole-burning technique which confirm these recent experiments but we interpret them differently. We have developed a model for the recovery of the hydrogen which accounts for these results and shows that the H2 does move diffusively. The diffusion is thermally activated and we have determined the diffusion constant, D0=4.03×10−4±2.5×10−5 m2s−1, and the activation energy, E=43±7 K, for hydrogen.