A numerical approach based on Tikhonov regularization is developed to invert torque curves from time-dependent small amplitude oscillatory shear (SAOS) experiments in which diffusion occurs to determine the diffusion coefficient. Diffusion of a solvent into a polymer melt for example causes the measured torque to decrease over time and is thus dependent on diffusion kinetics and the concentration profile. Our numerical approach provides a general method for retrieving local viscosity profiles during diffusion with reasonable accuracy, depending only on the linear viscoelastic constitutive equation and a general power law dependency of the diffusion process on time. This approach also allows us to identify the type of diffusion (Fickian, pseudo-Fickian, anomalous, and glassy) and estimate the diffusion coefficient without the a priori identification of a specific diffusion model. Retrieving local viscosity profiles from torque measurements in the presence of a concentration gradient is an ill-posed problem of the second type and requires Tikhonov regularization. The robustness of our approach is demonstrated using a number of virtual experiments, with data sets from Fickian and non-Fickian theoretical concentration and torque profiles as well as real experimental data.