The diffusional behaviour of H2 adsorbed in a novel mesoporous N-doped carbon material and on exfoliated graphite has been studied with quasi-elastic neutron scattering. While the activation energies for diffusion obtained for exfoliated graphite was in line with prior results, H2 in the mesoporous carbon showed an exceptionally low diffusion barrier and behaved qualitatively like liquid hydrogen. Complementary results from neutron and X-ray diffraction as well as from isothermal nitrogen sorption studies provide a full characterisation of this novel mesoporous carbon.