  Molecular hydrogen is a fascinating candidate for quantum fluid showing
bosonic and fermionic superfluidity. We have studied diffusion dynamics of thin
films of H$_2$, HD and D$_2$ adsorbed on a glass substrate by measurements of
elasticity. The elasticity shows multiple anomalies well below bulk triple
point. They are attributed to three different diffusion mechanisms of
admolecules and their "freezing" into localized state: classical thermal
diffusion of vacancies, quantum tunneling of vacancies, and diffusion of
molecules in the uppermost surface. The surface diffusion is active down to 1
K, below which the molecules become localized. This suggests that the surface
layer of hydrogen films is on the verge of quantum phase transition to
superfluid state.
