Parallel replica dynamics and minimum energy path calculations have been used to study the diffusion mechanisms of H-2 in fcc C-60. Isolated interstitial H-2 molecules bind preferentially in the lattice octahedral (O) sites and diffuse by hopping between O and tetrahedral sites. The simulations reveal an unexpected mechanism involving an H-2 molecule diffusing through an already occupied O site, creating an H-2 dimer, with a lower activation barrier than diffusion into an empty O site. Kinetic Monte Carlo simulations of a lattice model based on these mechanisms indicate that events involving dimers greatly enhance the self-diffusion rates of interstitial H-2 in fee C-60.