The primary objective of this article is to investigate the validity of the Knudsen prescription for pore diffusivity. Published experimental data on transient permeation of He-Ar, He-N-2, He-CO2, He-C3H8, and CO2-C3H8 mixtures across mesoporous and macroporous membranes are analyzed using the Maxwell-Stefan (M-S) formulation, combining molecule-wall and molecule-molecule interactions. For He-Ar and He-N-2 mixtures, both components are poorly adsorbed within the pores, and the experimental permeation data can be modeled adequately taking M-S diffusivity for molecule-wall interactions, D-i = D-i,D-Kn, the corresponding Knudsen diffusivity. For He-CO2 and He-C3H8 mixture permeation, the equality D-i = D-i,D-Kn holds only for He. For either CO2 or C3H8, D-i is lower than D-i,D-Kn by a factor ranging from 0.55 to 0.98, depending on the species and operating temperature. The stronger the adsorption strength, the lower the ratio D-i/D-i,D-Kn. The observed lowering in the M-S diffusivity below the Knudsen value, D-i,D-Kn, is in line with the published Molecular Dynamics (MD) data for cylindrical mesopores. The Knudsen prescription is based on the requirement that a molecule experiences diffuse reflection on collision with the pore wall, i.e., the angle of reflection bears no relation to the angle of incidence. Adsorption at the pore wall introduces a bias that makes a molecule hop to a neighboring site on the surface rather than return to the bulk; this bias increases with increasing adsorption strength and has the effect of reducing the pore diffusivity.