We present quantum dynamics calculations of the diffusion constant of H2 and D2 along a single-walled carbon nanotube at temperatures between 50 and 150 K. We calculate the respective diffusion rates in the low-pressure limit by adapting well-known approaches and methods from the chemical dynamics field using two different potential energy surfaces to model the C-H interaction. Our results predict a usual kinetic isotope effect, with H2 diffusing faster than D2 in the higher temperature range but a reverse trend at temperatures below 50-70 K. These findings are consistent with experimental observation in similar systems and can be explained by the different effective size of both isotopes resulting from their different zero-point energy.