Quasielastic neutron scattering measurements are combined with molecular dynamics simulations to extract the self-diffusion coefficient of hydrogen in the metal organic frameworks MIL-47(V) and MIL-53(Cr). We find that the diffusivity of hydrogen at low loading is about 2 orders of magnitude higher than in zeolites. Such a high mobility has never been experimentally observed before in any nanoporous materials, although it was predicted in carbon nanotubes. Either 1D or 3D diffusion mechanisms are elucidated depending on the chemical features of the MIL framework.