Forced Rayleigh scattering (FRS) and pulsed-field-gradient NMR have been used to measure the self-diffusion coefficient, D, of a poly(ethylene oxide)-poly(ethylethylene) diblock copolymer in the molten state. The copolymer contains 42% PEO by volume and has a total molecular weight of 4100 g/mol. Upon heating from room temperature the sample transforms from crystalline lamellae to hexagonal cylinders, and then to a bicontinuous cubic "gyroid" phase (with Ia3d space group symmetry), before finally disordering at 175 °C. FRS measurements were performed in the gyroid and cylinder phases, and NMR measurements in the gyroid and disordered states. Cylinder samples both with and without shear alignment were employed. A hysteresis loop permitted measurements of D in both cylinder and gyroid phases at the same temperature (60 °C). FRS decays from cylindrical samples were described by a sum of two exponentials. For the aligned samples, values of the diffusivity along (Dpar) and across (Dperp) the cylinders were extracted; the mobility along the cylinders was approximately 2 orders of magnitude larger. This is consistent with the estimated enthalpic penalty for withdrawing the minor block from the cylindrical microdomain. FRS decays from the gyroid phase were consistently single exponential and gave a diffusivity consistent with Dpar in the cylinders, reduced by the tortuosity of the gyroid network. The FRS and NMR results agreed very well, and the mobility varied smoothly with temperature through the order-disorder transition. However, the magnitude of the copolymer mobility was significantly lower than that of either constituent homopolymer or of two other disordered PEO-PEE diblocks, even after accounting for differences in molecular weight. This is tentatively attributed to the onset of entanglement effects.