The diffusion of clusters of atoms or vacancies on single-crystal surfaces can have an important; impact on the evolution of films. We have investigated the role of cluster diffusion in the coarsening of clusters with a detailed lattice gas model of commensurate Xe films on Pt(111). Both atomic and vacancy clusters can diffuse in this system. We show that, while cluster diffusion and coalescence are the dominant coarsening mechanisms for vacancy clusters, the coarsening of atomic clusters is dominated by Ostwald ripening. We have also used our lattice gas model to test several microscopic assumptions that are made in macroscopic theories of cluster coarsening.