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We study collective diffusion of adsorbed particles on stepped surfaces using analytic and numerical techniques. We employ the Langmuir lattice gas model where the distribution of adatoms on the surface is solely determined by the difference in adsorption energy of atoms on terraces and along step edges. For the system in equilibrium, we consider the master equation approach for collective diffusion across the steps within the dynamic mean field approximation. We demonstrate that results obtained for the collective diffusion coefficient D c (Θ) are sensitive to the choice of relevant slow variables for inhomogeneous systems such as stepped surfaces. Next, we consider diffusion across steps in situations where the system is not in equilibrium such as during spreading or ordering. To this end, we consider a phenomenological theory using balance between particle fluxes across a stepped surface within the linear response theory. This allows us to derive expressions for effective diffusion coefficients in the limit of large and small coverages, where the results agree well with D c (Θ) in the corresponding limits.