The dependence of hopping diffusion on lattice topology and occupancy by the diffusing molecules is studied using Monte-Carlo simulations. For poorly connected lattices, such as ZSM-5/silicalite, the self-diffusivity deviates strongly from the linear mean-held result, especially at high occupancies. A time-correlation formalism is derived to predict these deviations which are proportional to the accumulated correlation between the displacement at some time and the first attempted hop. Renormalized deviations depend on lattice topology, but not on occupancy, so that the curves for various occupancies can be collapsed on to a single curve which can be well approximated by a stretched exponential. The results show that a mean-field theory with correlated time steps should work adequately for well-connected lattices, but poor performance is predicted for such poorly connected lattices as ZSM-5.