The Collaborative International Dictionary of English v.0.48:

Diverge \Di*verge"\, v. i. [imp. & p. p. Diverged; p. pr. &
   vb. n. Diverging.] [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.
      [1913 Webster]

   2. To differ from a typical form; to vary from a normal
      condition; to dissent from a creed or position generally
      held or taken.
      [1913 Webster]

WordNet (r) 3.0 (2006):

diverge
    v 1: move or draw apart; "The two paths diverge here" [ant:
         converge]
    2: have no limits as a mathematical series [ant: converge,
       meet]
    3: extend in a different direction; "The lines start to diverge
       here"; "Their interests diverged" [ant: converge, meet]
    4: be at variance with; be out of line with [syn: deviate,
       vary, diverge, depart] [ant: conform]

Moby Thesaurus II by Grady Ward, 1.0:

151 Moby Thesaurus words for "diverge":
   aberrate, agree to disagree, alter, ameliorate, angle, angle off,
   be changed, be converted into, be distinct, be distinguished,
   be renewed, bear off, bend, bestrew, bias, bottom out, branch off,
   branch out, break, break up, break with, broadcast, change,
   change the bearing, checker, chop, chop and change, circumfuse,
   clash with, come about, come around, come round, conflict with,
   contrast with, crook, curve, deal out, deflect, degenerate, depart,
   depart from, deploy, deteriorate, detour, deviate, deviate from,
   differ, differentiate, diffract, diffuse, digress, disaccord with,
   disagree, disagree with, disband, dispel, dispense, disperse,
   dispread, disseminate, dissent, distort, distribute, disunify,
   divagate, divaricate, divaricate from, diverge from, diversify,
   divert, divide, dogleg, drift, excurse, fall out, fan out, flop,
   fork, go away, go off, go separate ways, hairpin, haul around,
   have a falling-out, heel, improve, issue, jar with, jibe,
   meliorate, mitigate, modulate, mutate, not accord with,
   not square with, oblique, outspread, overscatter, oversow,
   overspread, part, part company, propagate, publish, pull, radiate,
   ramble, ramify, refract, relieve, retail, revive, scatter,
   separate, sheer, shift, skew, slue, sow, sow broadcast, splay,
   split, split up, spread, spread out, stand apart,
   stand over against, stray, strew, subdivide, sway, swerve, tack,
   take a turn, trend, turn, turn aside, turn away, turn into,
   turn the corner, twist, undergo a change, utter, variate,
   variegate, vary, veer, wander, warp, worsen, zigzag



The Free On-line Dictionary of Computing (30 December 2018):

diverge

   If a series of approximations to some value get progressively
   further from it then the series is said to diverge.

   The reduction of some term under some evaluation strategy
   diverges if it does not reach a normal form after a finite
   number of reductions.

   (1994-12-08)