We test a proposed relation between mutual diffusion coefficient and viscosity in suspensions which is essentially identical to a dynamic mode-coupling theory of diffusion in binary fluid mixtures near a critical mixing point. In contrast to conventional treatments of suspension hydrodynamics, this relation is non-perturbative in the sense that it is not necessary to assume that the volume fraction of suspended particles is a small parameter. In order to apply this theory to protein solutions, we measured the mutual diffusion coefficient of several globular proteins in aqueous solutions containing 2% ampholyte and protein up to 40% by weight. The viscosity was also measured in aqueous solutions of up to 30% protein by weight. The mutual diffusion coefficient was then related to the viscosity and osmotic compressibility of the concentrated suspension relative to the infinite dilution limit. We conclude that this non-perturbative relation provides a convenient estimate of protein diffusion coefficients as a function of protein concentration.