  We consider stability of differentially rotating non-magnetic proto-neutron
stars. When neutrino transport is efficient, the star can be subject to a
diffusive instability that can occur even in the convectively stable region.
The instability arises on the time-scale comparable to the time-scale of
thermal diffusion. Hydrodynamic motions driven by the instability can lead to
anisotropy in the neutrino flux since the instability is suppressed near the
equator and rotation axis.
