The low-energy density of states (DOS) of disordered 2D d-wave superconduct
ors is extremely sensitive to details of both the disorder model and the el
ectronic band structure. Using diagrammatic methods and numerical solutions
of the Bogoliubov-de Gennes equations, we show that the physical origin of
this sensitivity is the existence of a novel diffusive mode with momentum
close to (pi, pi) which is gapless only in systems with a global nesting sy
mmetry. We find that in generic situations the DOS vanishes at the Fermi le
vel. However, proximity to the highly symmetric case may nevertheless lead
to observable nonmonotonic behavior of the DOS in the cuprates.