The master equation formalism is used to analytically calculate the center-of-mass diffusion coefficient for small two-dimensional islands on fcc(100) metal surfaces. We consider the case of Cu on Cu(100) containing up to nine atoms, with energetics obtained from semiempirical interaction potentials. In the case where only single-particle processes are taken into account, the analytic results agree well with previous Monte Carlo simulation data. However, when recently proposed many-particle processes are included, in some cases the diffusion coefficients increase by an order of magnitude at room temperatures. Qualitatively, the oscillatory behavior of diffusion as a function of the island size is not affected by the many-particle processes.