Diverge, v. i. [imp. & p. p. Diverged; p. pr. & vb. n. Diverging.]
Etymology: [L. di- = dis- + vergere to bend, incline. See Verge.]
1. To extend from a common point in different directions; to tend from one point and recede from each other; to tend to spread apart; to turn aside or deviate (as from a given direction); -- opposed to converge; as, rays of light diverge as they proceed from the sun.
2. To differ from a typical form; to vary from a normal condition; to dissent from a creed or position generally held or taken.
Shades of meaning
Fernald has no entry of its own for diverge; he lists it under bend, wander.
Where he writes about it:
Deflect, deviate, and diverge are said of any turning away; deviate commonly of a slight and gradual movement, diverge of a more sharp and decided one. — from bend
To wander (AS. windan, wind) is to move in an indefinite or indeterminate way which may or may not be a departure from a prescribed way; to deviate (L. de, from, and via, a way) is to turn from a prescribed or right way, physically, mentally, or morally, usually in an unfavorable sense; to diverge (L. di, apart, and vergo, incline, tend) is to turn from a course previously followed or that something else follows, and has no unfavorable implication; to digress (L. di, apart, aside, and gradior, step) is used only with reference to speaking or writing; to err is used of intellectual or moral action, and of the moral with primary reference to the intellectual, an error being viewed as in some degree due to ignorance. — from wander