Fission gas diffusion from a microstructure with a distribution of grain sizes undergoing grain growth is analyzed. Hillert's theory is used to describe the evolution in grain morphology, during which some grains enlarge while others shrink and may even disappear. Limiting cases of Booth release (when only diffusion occurs) and Malen release (when grain-boundary sweeping is dominant) are derived for a body with a distribution of grain sizes. The moving boundary diffusion equation that couples the diffusion and sweeping mechanisms is derived. The grain-size distribution is divided into 25 groups for which the diffusion equations are solved numerically for the average intragranular gas concentration. The results are compared to existing single-grain-size models which, in all cases, overpredict the fractional release. Depletion of intragranular fission gas provides a source for migration via grain boundaries to the free surface.