Economical bioconversion of lignocellulosic substrates requires processing fiber suspensions with high-solids content. Mixing and reaction in such suspensions becomes challenging due to their high viscosity and yield stress. An efficient way of mixing highly viscous materials is by repeated stretching and folding. When the separation between layers having different concentrations becomes sufficiently small, diffusion becomes the dominant homogenizing mechanism. In this context, the amount of energy necessary to economically mix the material to a specified degree of homogeneity is a function of diffusion rates. Measurement of effective diffusivities is, therefore, of importance in assessing mass transport mechanisms in operations that involve mixing and chemical reactions of solutes in suspensions of cellulosic fibers. We used magnetic resonance imaging to measure spatially resolved concentration profiles of solutes diffusing in stagnant beds of cellulosic fibers. The time evolution of the experimental concentration profiles is compared with predictions made using a numerical model of one-dimensional diffusion. The measured effective diffusion coefficients are interpreted using a model that accounts for the porosity, tortuosity and adsorption equilibrium constant.