We report about self-diffusion experiments on a compositionally asymmetric poly(ethylene-co-propylene)-block-poly( dimethylsiloxane) diblock copolymer exhibiting the lamellar and the gyroid morphology. The echo attenuation curves were analyzed by fitting a logarithmic normal distribution function. The self-diffusion coefficients were broadly distributed compared to the distribution caused by the polydispersity alone. This is attributed to the onset of anisotropic diffusion in the lamellar morphology and to unavoidable traces of homopolymers. The most probable self-diffusion coefficients and the values calculated for a hypothetical disordered diblock copolymer melt are lower than the self-diffusion coefficients of the constituent homopolymers having the same molar mass. This is explained by entanglements of the majority block which hinder single-chain diffusion parallel to the interfaces formed due to the microphase separation of the different blocks.