The motion of Brownian particles in the vicinity of a fluid interface is studied by considering the spatial modification of the hydrodynamic mobility due to the direct hydrodynamic interactions between the particles and the interface. The analysis determines, for a simple model system, the conditions under which the simple Fickian form of the diffusion equation can be obtained in the presence of an interface. In addition, the theory shows that the diffusivity tensor can be evaluated from a knowledge of the mobility tensor for steady motion of a particle in Stokes flow.