The diffusion of hydrogen adsorbed inside layered MoS2 crystals has been studied by means of quasi-elastic neutron scattering, neutron spin-echo spectroscopy, nuclear reaction analysis, and X-ray photoelectron spectroscopy. The neutron time-of-flight and neutron spin-echo measurements demonstrate fast diffusion of hydrogen molecules parallel to the basal planes of the two dimensional crystal planes. At room temperature and above, this intra-layer diffusion is of a similar speed to the surface diffusion that has been observed in earlier studies for hydrogen atoms on Pt surfaces. A significantly slower hydrogen diffusion was observed perpendicular to the basal planes using nuclear reaction analysis.