We study the diffusive behavior of two-dimensional charged colloidal suspensions subjected to a sinusoidal substrate by means of Brownian dynamics simulations. We mainly focus on the dependence of the mean-square displacement on the substrate strength. Our findings show a variation in the particle diffusion due to a substrate-induced distortion of the dynamic cage of nearest-neighbor colloids. This mechanism leads to a transition from normal diffusion at short times to subdiffusion on intermediate time scales. However, at long times normal diffusion is recovered. We also show that the variation in the long-time self-diffusion coefficient may be associated with the freezing and re-entrant melting transitions.