The self-diffusivity of an asymmetric poly(ethylenepropylene)-poly(dimethylsiloxane) diblock copolymer (PEP-PDMS) was investigated using pulsed field gradient NMR both in the ordered and the disordered state. In a temperature range below the order-to-disorder transition temperature, the diblock copolymer forms micelles which order in a simple cubic structure, and at lower temperatures, a noncubic structure is formed. We have found a broad distribution of self-diffusivities. The distribution width increases with decreasing temperature. The self-diffusivity as well as its distribution width changes only slightly at the order-to-disorder transition. In contrast to self-diffusion in symmetric diblock copolymers where single chains diffuse independently, our results are interpreted as a collective diffusion of chains confined to micelles which further cluster to larger aggregates. This behavior cannot be described by existing models of chain dynamics in the melt. The disordered state is characterized by a large temperature range above the order-to-disorder transition where concentration fluctuations dominate. This is revealed in the temperature dependence of the self-diffusivity and its distribution width, in the viscosity and in the inverse intensity of the first-order Bragg reflection in small angle neutron scattering (SANS).