The Collaborative International Dictionary of English v.0.48:

Unrestraint \Un`re*straint"\, n.
   Freedom from restraint; freedom; liberty; license.
   [1913 Webster]

WordNet (r) 3.0 (2006):

unrestraint
    n 1: the quality of lacking restraint [ant: control,
         restraint]

Moby Thesaurus II by Grady Ward, 1.0:

115 Moby Thesaurus words for "unrestraint":
   abandon, abandonment, accessibility, approachability, artlessness,
   bluffness, bluntness, broadness, brusqueness, candidness, candor,
   carelessness, communicativeness, conversableness, crapulence,
   crapulency, crapulousness, directness, disobedience, drunkenness,
   ease, easiness, easygoingness, excess, excessiveness, extravagance,
   extroversion, forthrightness, frankness, freedom, freeness,
   genuineness, gluttony, immoderacy, immoderateness, immoderation,
   impotence, imprecision, impulsiveness, incontinence, indifference,
   indiscipline, indulgence, ingenuousness, inordinacy,
   inordinateness, insubordination, intemperance, intemperateness,
   interregnum, irrepressibility, irresponsibility, lawlessness,
   laxity, laxness, leniency, license, licentiousness, looseness,
   loosening, mutiny, naturalness, negligence, noncoercion,
   nonintimidation, openheartedness, openness, outgoingness,
   outspokenness, overdoing, overindulgence, overpermissiveness,
   permissiveness, plain dealing, plain speaking, plainness,
   plainspokenness, power vacuum, prodigality, rampant will,
   relaxation, relaxedness, remissness, riotousness, roundness,
   self-indulgence, sincerity, slackness, sloppiness, sociability,
   softness, straightforwardness, swinishness, talkativeness,
   too much, too-muchness, unaccountability, unconstraint,
   uncontinence, uncontrol, uninhibitedness, unrepression, unreserve,
   unreservedness, unrestriction, unreticence, unruliness,
   unsecretiveness, unstrictness, unsuppression, untaciturnity,
   wantonness, weakness, wildness, willfulness