The well-known bivariate trap model with random topography is used to investigate the effects of surface heterogeneities on surface diffusion. Monte Carlo simulations are performed in order to characterize how the tracer,jump, and chemical diffusion coefficients depend on temperature and concentration of deep traps, Theta. The chemical diffusion coefficient is calculated by applying the fluctuation and the Kubo-Green methods. Both methods are in good agreement at low values of Theta only. The discrepancies are discussed and explained. At low surface coverages and low temperatures the effects of heterogeneities are largely pronounced since most of the adatoms are trapped by the deep traps. At high coverages the mobility of adatoms adsorbed on shallow traps dominates the diffusion behavior.