The dynamic structure factor S(q,t) of seven diblock copolymers in a common solvent was measured by photon correlation spectroscopy as a function of concentration (0) in the disordered state near the disordered-to-order transition (ODT). Both symmetric and asymmetric diblock copolymers of styrene-b-isoprene (SI) with molecular masses ranging from 0.95 to 3.6 million g/mol and their hydrogenated styrene-b-(ethylene-alt-propylene) (SEP) counterparts have been considered. The maximum of the static structure factor S(q*) and the characteristic spacing 1/q* do not conform to theoretical predictions over the whole phi range up to phi(ODT). The S(q,t) is determined mainly by the relative contribution of two relaxation processes one of which is diffusive (q(2)-dependent rate). When composition fluctuation corrections become important for S(q*) at phi(chi) < phi(ODT), S(q,t) exhibits a dynamic crossover from a dominant pure relaxational (q-independent rate) to a dominant diffusive character. This new dynamic behavior in the shape of S(q,t) of narrowly distributed diblock copolymer solutions is captured theoretically. Above about phi(chi) the self-diffusion coefficient D-s(phi) obtained from the S(q,t) at low q/q* values becomes thermodynamically retarded. The real phase morphology of diblock copolymers is well complemented by their dynamic structure.