Collective surface diffusion of adsorbed particles on correlated heterogeneous surfaces is studied by Monte Carlo simulation, in the framework of the Kubo-Green theory. The energetic disordered surface is described through the dual site-bond model (DSBM) introduced by Mayagoitia [Surf. Sci. 221, 394 (1989)]. The influence of the energetic correlation on the jump (D-J) and collective (D) diffusion coefficients is analyzed by simulating the coverage fluctuations in the grand canonical ensemble and the mean-square displacements of particles in the canonical ensemble. The topography is shown to strongly affect the coverage dependence of the transport coefficient. The effects of nearest-neighbor lateral interactions is also discussed.