The problem of diffusion in pore networks of a certain class is considered, and a procedure for estimating effective diffusivities is formulated. The effective-medium theory is used to obtain an effective conductance for the network, which is then used to determine the effective diffusivity starting from first physical principles and utilizing the observation that a network of pores of uniform conductance satisfies the smooth field approximation. Comparison of the estimated intraparticle diffusivities with those obtained from the exact solution of the transport equation for large networks reveals high accuracy and reliability of the method. Results for a number of pore networks show that the smooth field assumption should not be employed arbitrarily since it always predicts higher effective diffusion coefficients than the exact ones, by more than one order of magnitude in some cases.