Amphiphilic vesicles are ubiquitous in living cells and industrially interesting as drug delivery vehicles. Vesicle self-assembly proceeds rapidly from nanometer to micrometer length scales and is too fast to image experimentally but too slow for molecular dynamics simulations. Here, we use parallel dissipative particle dynamics (DPD) to follow spontaneous vesicle self-assembly for up to 445 mu s with near-molecular resolution. The mean mass and radius of gyration of growing amphiphilic clusters obey power laws with exponents of 0.85 +/- 0.03 and 0.41 +/- 0.02, respectively. We show that DPD provides a computational window onto fluid dynamics on scales unreachable by other explicit-solvent simulations.