A new inverse problem approach is formulated for the determination of the concentration dependence of the diffusion coefficient from uptake data. A model based on Fick’s law is assumed to hold for the process for which the governing partial differential equation, which has to be inverted, is ill-posed. The inversion is achieved using a combination of orthogonal collocation and regularization techniques. It is seen that it is possible to deduce the diffusivity-concentration relationship from a single uptake curve without any a priori knowledge of the form of the relationship. The application of the technique is demonstrated for both simulated data as well as actual experimental data for the uptake of iodine from the vapor phase by activated carbon. In all the cases considered, the method is seen to provide stable and convergent solutions, even when the data to be inverted are noisy.