We studied the dynamics of vesicle formation in an initially homogeneous dilute solution of amphiphilic diblock copolymers, using the external potential dynamics (EPD) method. The system was quenched into the unstable two-phase region inside the spinodal curve. We discovered a new pathway of spontaneous vesicle formation: First, spinodal decomposition sets in, and the fluid acquires a weakly modulated structure. After an incubation time, the composition fluctuations of this background pattern trigger the nucleation of spherical micelles. In a third step, copolymers from the solution slowly aggregate to the micelles; they grow and become semivesicles (bigger spherical micelles with a solventphilic core). Finally, solvent particles diffuse into the semivesicles, and they become full vesicles. We show that the solventphilic parts of the copolymers play a crucial role for the transition from semivesicles to vesicles. The different contributing mechanisms are discussed, and a simple method to control vesicle formation by using uniform sphere micelles as seeds is proposed.