  The diffusion of hard-core particles subject to a global bias is described by
a nonlinear, anisotropic generalization of the diffusion equation with
conserved, local noise. Using renormalization group techniques, we analyze the
effect of an additional noise term, with spatially long-ranged correlations, on
the long-time, long-wavelength behavior of this model. Above an upper critical
dimension $d_{LR}$, the long-ranged noise is always relevant. In contrast, for
$d<d_{LR}$, we find a ``weak noise'' regime dominated by short-range noise. As
the range of the noise correlations increases, an intricate sequence of
stability exchanges between different fixed points of the renormalization group
occurs. Both smooth and discontinuous crossovers between the associated
universality classes are observed, reflected in the scaling exponents. We
discuss the necessary techniques in some detail since they are applicable to a
much wider range of problems.
