A microscopic theory of self-diffusion in diblock copolymer melts and solutions has been developed based on polymeric mode-coupling methods formulated at the level of the time and space correlated interchain excluded volume and chi-parameter forces. Equilibrium structural correlations are determined via microscopic liquid state integral equation or coarse-grained field theoretic methods. The specific dynamical consequences of self-assembly are predicted to depend rather sensitively on temperature, degree of polymerization, copolymer composition and concentration, and local block friction coefficients. The dominant physical effect for entangled diblocks is the retardation of the relaxation time of the interchain excluded volume forces due to the thermodynamically-driven segregation of blocks into microdomains, resulting in suppression of translational motion. Analytic analysis in the long chain limit allows the derivation of new scaling laws relating the self-diffusion constant and chain degree of polymerization and solution concentration. Potential limitations for real copolymer materials associated with the structurally and dynamically isotropic description adopted by the theory are discussed.