Activated surface diffusion with interacting adsorbates is analyzed within the Linear ResponseTheory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(001) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed.