The diffusion kinetics of dye molecules (C.I. Direct Yellow 12) adsorbed in porous cellulose membranes is investigated. A solid diffusion model with concentration-dependent diffusivity (SDCDD model) is utilized to fit the experimental uptake curves (UCs) and concentration profiles (CPs). The experimental equilibrium data are well fitted by the Freundlich as well as the Redlich-Peterson model. On the basis of the Redlich-Peterson isotherm equation, the SDCDD model is able to simulate the experimental UCs and CPs for a wide variety of conditions. The simulations reveal a high sensitivity of the SDCDD model to variations in the course of the sorption isotherm. This property entails that the Freundlich model, although equivalent to the Redlich-Peterson equation with respect to fitting the equilibrium data, is not able to reflect the concentration dependence of CPs. The SDCDD model (in association with the Redlich-Peterson isotherm) is demonstrated to be the necessary alternative of the parallel diffusion model proposed by Yoshida et al.