The diffusion processes involved in the accommodation of grain boundary sliding in diffusional deformation are revisited by considering the role of grain boundary curvature and of the associated grain boundary migration. A method is developed for calculating grain boundary profiles, diffusional fluxes, and the dissipation power arising from the coupling of diffusion fluxes and grain boundary migration during the quasi-steady-state stage of deformation. In conditions of dominance of Coble creep, the controlling length scale is the square root of the ratio of grain boundary diffusivity to grain boundary mobility. Zero curvature is the particular solution valid when mobility is infinite. The analysis brings the definition of a lower bound for the grain boundary viscosity parameter to be used in numerical simulations of diffusional deformation. This lower bound is consistent with previous identifications of the parameter in literature.