  A fermion model with random on-site potential defined on a two-dimensional
square lattice with $\pi$-flux is studied. The continuum limit of the model
near the zero energy yields Dirac fermions with random potentials specified by
four independent coupling constants. The basic symmetry of the model is
time-reversal invariance. Moreover, it turns out that the model has enhanced
(chiral) symmetry on several surfaces in the four-dimensional space of the
coupling constants. It is shown that one of the surfaces with chiral symmetry
has Sp(n)$\times$Sp(n) symmety whereas others have U(2n) symmetry, both of
which are broken to Sp(n), and the fluctuation around a saddle point is
described, respectively, by Sp($n)_2$ WZW model and U(2n)/Sp(n) nonlinear sigma
model. Based on these results, we propose a phase diagram of the model.
