We have used quasielastic neutron scattering to derive the self- and transport diffusion coefficients of hydrogen molecules adsorbed in $\mathrm{Na}X$ zeolite. For ${\mathrm{H}}_{2}$, incoherent scattering is dominant so that self-diffusion is measured. For ${\mathrm{D}}_{2}$, the coherent and incoherent contributions are of the same order of magnitude so that both collective and individual motions can be characterized. At low ${\mathrm{D}}_{2}$ concentration, the self- and transport diffusivities have similar values. For higher loadings, the transport diffusivity increases rapidly and exceeds the self-diffusivity. Only close to the saturation of the zeolite does the transport diffusivity start to decrease. To our knowledge this is the first time that transport and self-diffusion coefficients have been measured simultaneously for an adsorbed molecule. In contrast to numerous examples where discrepancies have been stated, these results are in agreement with each other.