We describe a series of experiments and numerical simulations that were designed to determine the rate of stress-driven diffusion along interfaces in a damascene copper interconnect structure. Wafer curvature experiments were used to measure the rate of stress relaxation in an array of parallel damascene copper lines, which were encapsulated in a dielectric, and passivated with an overlayer of silicon nitride or silicon carbide. The stress relaxation was found to depend strongly on the choice of passivation. Three-dimensional finite element simulations were used to model the experiments, and showed that this behavior is caused by changes in the diffusivity of the interface between the copper lines and the passivation. By fitting the predicted stress relaxation rates to experimental measurements, we have identified the interfaces that contribute to stress relaxation in the structure, and have estimated values for their diffusion coefficients.