An efficient numerical method for the calculation of the collective diffusion coefficient is developed. The method is based on the Bortz-Kalos-Lebowitz algorithm, with local updating of the particle lists for each process, coupled to the memory expansion for the calculation of the center-of-mass diffusion coefficient. The method is applied to the diffusion in a two-dimensional lattice gas model of square symmetry with repulsive lateral interactions. The numerical results are compared to two popular approximations, the Darken equation and the dynamical mean-field theory, whose respective merits are discussed. Finally, the decay of the dynamic structure factor with time is investigated.