  A lingering mystery in core-collapse supernova theory is how collective
neutrino oscillations affect the dynamics. All previously identified flavor
instabilities, some of which might make the effects considerable, are
essentially collisionless phenomena. Here it is shown that collisional
instabilities exist as well. They are associated with asymmetries between the
neutrino and antineutrino interaction rates, are possibly prevalent deep inside
supernovae, and pose an unusual instance of decoherent interactions with a
thermal environment causing the sustained growth of quantum coherence.
