The diffusivity D of pure substances in idealized zeolite crystals is analyzed on the basis of the hopping model and its various extensions. Forces between neigboring molecules are taken into account as well as multiple adsorption in cages and the possibility of extended jumps. Finally, the case of correlated jumps is considered. For each model, D is approximated for small concentrations and in the saturation limit. Only the model with cages permitting at least three molecules is capable of reproducing the prevalent observed behavior.