The transport of adsorbates in microporous random networks is examined in the presence of an arbitrary nonlinear local isotherm. The transport model is developed by means of a correlated random walk theory, assuming pore mouth equilibrium at an intersection in the network and a local chemical potential gradient driving force. The results demonstrate more rapid increase of the transport coefficient with adsorbed concentration than straightforward use of the classical Darken equation. Application of the theory to experimental data for diffusion of carbon dioxide in carbolac, with various local isotherm choices, shows good agreement when the activation energy associated with the mobility based on a chemical potential gradient driving force is taken as the Henry's law region isosteric heat of adsorption. Furthermore, a combination of transport and equilibrium data can discriminate better among competing isotherms than the latter data alone.