In this paper, we develop a theory for the calculation of the surface diffusion coefficient for an arbitrarily curved fluid–fluid interface. The theory is valid for systems in hydrodynamic equilibrium, with zero mass-averaged velocities in the bulk and interfacial regions. We restrict our attention to systems with isotropic bulk phases, and an interfacial region that is isotropic in the plane parallel to the dividing surface. The dividing surface is assumed to be a simple interface, without memory effects or yield stresses. We derive an expression for the surface diffusion coefficient in terms of two parameters of the interfacial region: the coefficient for plane-parallel diffusion D(AB)aa(), and the driving force d(B)I||(). This driving force is the parallel component of the driving force for diffusion in the interfacial region. We derive an expression for this driving force using the entropy balance.