1660s, "move or lie in different directions from a common point" (the opposite of converge), from Modern Latin divergere "go in different directions," from assimilated form of dis- "apart" (see dis-) + vergere "to bend, turn, tend toward" (from PIE root *wer- (2) "to turn, bend").
Originally a term in optics. The general or figurative senses of "become or be separated from another; differ from a typical form" emerged by mid-19c. Related: Diverged; diverging.