Forced Rayleigh scattering was used to investigate the diffusion of a photoreactive dye molecule in two homogeneous poly(styrene-b-isoprene) (SI) diblock copolymers with overall molecular weights of approximately 2000. Although diffusion rates were intermediate to TTI transport in homopolymer polystyrene (PS) and polyisoprene (PI), system dynamics appear to be largely dictated in each case by the PI block. The size of the polymer jumping unit, on the other hand, is evaluated from a free-volume analysis of the data, and is found to be governed predominantly by the PS component of the copolymer. The mechanism for tracer diffusion in low-molecular-weight block copolymers appears analogous to transport in a high molecular weight SI diblock copolymer (M-n = 13,600) that has been solvated sufficiently in toluene to be microstructurally disordered.