The temporal transformations of the radial distribution of a liquid in a presoaked porous cylindrical catalyst support pellet detected by H-1 NMR microimaging technique in the course of the pellet drying are analyzed quantitatively in terms of the diffusion equation. The approach is shown to be adequate for evaluating the diffusivity and its dependence on the degree of pellet saturation with a liquid, provided that the NMR microimaging data are properly corrected for the relaxation weighting effects. It is demonstrated that for liquids characterized by a low surface tension, such as acetone, benzene and cyclohexane, transformations of the concentration profiles can be adequately modeled assuming a liquid content-independent diffusivity. In contrast, the diffusivity of water in titania and alumina pellets substantially decreases with the decrease of water content. For alumina pellets with a pronounced "bimodality" in the pore size distribution the water concentration dependence of diffusivity is shown to be non-monotonic. It is argued that for liquids with high surface tension, the shape of the concentration profiles and the behavior of diffusivity as a function of liquid content are both related to the shape of the cummulative pore size distribution of the porous solid under study due to the existence of efficient capillary flows induced by capillary suction.