Among the different geometrical descriptions of the pore networks of porous materials, a common one is that of cylindrical pores arranged on a regular lattice. Lattice calculations of diffusivities and other transport parameters are expected to gain increasing interest, both because of their tractability and because of continuing developments in techniques for characterizing porous solids in terms of models of this type. In this study we consider two approaches to the prediction of the apparent molecular and Knudsen diffusivities of diluted simple-cubic lattices: the MC-REMA method of Zhang and Seaton, which explicitly incorporates the geometry and connectivity of the network and is known to give accurate results, and the simple capillary model of Mualem and Friedman, which is computationally very fast. The MC-REMA calculations show that the diffusion coefficients increase both with increasing coordination number and decreasing coefficient of variation of the pore-size distribution. The influence of the coordination number, Zeta, is found to be more pronounced for small values of Zeta, while the effect of the width of the pore-size distribution is less significant at both extremes of highly uniform and highly distributed pore sizes. The simple capillary model of Mualem and Friedman is shown to give a good representation of the accurate MC-REMA results, after correlating a single adjustable parameter to Zeta and the coefficient of variation of the pore-size distribution.