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Forced Rayleigh scattering has been employed to measure tracer and self-diffusion in block copolymer melts, for both entangled and unentangled systems, and in both the ordered and disordered states. It is shown that entanglements are particularly effective in retarding the motion of copolymers parallel to the interface between microdomains. The mechanisms of activated reptation and block retraction are proposed for parallel diffusion. The importance of large amplitude composition fluctuations in the disordered state near the ordering transition is also demonstrated, for both copolymer and homopolymer tracers; the results suggest that copolymer tracers are more affected than homopolymers of comparable molecular weight.