The diffusion of multiparticle systems with long-range dipolar repulsion and long-range dipolar repulsion perturbed by randomly distributed dipolar impurities is studied by means of computer simulations. Our investigation is motivated by experimental studies of the diffusion of alkali atoms on clean and contaminated (e.g. by oxygen atoms) single crystal metal and semiconductor surfaces. Concentration profiles of the diffusion fronts are in qualitative agreement with the experimental findings. Comparing to the behavior of non-interacting particles, it is found that dipolar repulsion considerably enhance the chemical diffusion coefficient, particularly at lower coverages where a sharp peak is observed close to theta approximate to 0.09. In contrast, the chemical diffusion coefficient of non-interacting particles exhibits a smooth maximum close to theta similar or equal to 0.5. The presence of random dipolar impurities causes a delay of the diffusion process and the low coverage peak of the diffusion coefficient becomes shifted to theta approximate to 0.16. The number of distinct sites visited by the diffusing particles, which is relevant for the evaluation of the rate constant for diffusion-limited reactions, is also studied and the results are compared with those of non-interacting particles.