Nonlinear gradient-driven diffusion was studied in concentrated polystyrene (PS)/ethylbenzene (EB) solutions using vapor sorptions with a finite driving force. The nonlinear sorptions were carried out on thin films (congruent to 2.05, 3.50 mu m thick) at conditions where non-Fickian, "viscoelastic" effects appear. These data were modeled with the nonlinear diffusion equation studied by Tang. Four dimensionless material parameters in the model were determined from a limited amount of linear-response, differential sorption data on PS/EB mixtures measured in the same range of experimental conditions as for the nonlinear sorptions. The nonlinear model successfully predicts the observed nonlinear response either above or below the glass transition (T-g). In order to simultaneously capture the nonlinear response both above and below T-g, the abrupt change in the concentration dependence of physical properties at T-g must be accounted for.