  We discuss quantum propagation of dipole excitations in two dimensions. This
problem differs from the conventional Anderson localization due to existence of
long range hops. We found that the critical wavefunctions of the dipoles always
exist which manifest themselves by a scale independent diffusion constant. If
the system is T-invariant the states are critical for all values of the
parameters. Otherwise, there can be a "metal-insulator" transition between this
"ordinary" diffusion and the Levy-flights (the diffusion constant
logarithmically increasing with the scale). These results follow from the
two-loop analysis of the modified non-linear supermatrix $\sigma$-model.
