According to Empedocles the wandering through all of the elements is atonement for a blood guild incurred in the divine world; the goal is return to the gods, apotheosis.
Burkert outlines the Pythagorean-Orphic doctrine in which metempsychosis is an expiatory cosmic journey through all elements and life-forms, culminating in reunion with the divine.
, Greek Religion: Archaic and Classical, 1977thesis