A one-parameter model for species flux through pores in a crystalline monolayer or multilayer film is developed. The model is based on surface diffusion of the species on the upstream surface of the monolayer and one-directional diffusion of the species into the pores of the monolayer. It is found that the Fickian diffusivity depends on the concentration of adsorbed species on surface sites and on the pore coverage. The model contains an important parameter, the rate constant of activation, which is function of the diffusing species and film surface properties. The model is compared with experimental data on ion and gas flux through single and multilayer films. Good agreement between theory and experiment is found with all sets of the data with the rate constant as a sole adjustable parameter.