  The High-Energy Stereoscopic System (HESS) has detected diffuse TeV emission
correlated with the distribution of molecular gas along the Ridge at the
Galactic Center. Diffuse, non-thermal emission is also seen by the Fermi large
area telescope (Fermi-LAT) in the GeV range and by radio telescopes in the GHz
range. Additionally, there is a distinct, spherically symmetric excess of gamma
rays seen by Fermi-LAT in the GeV range. A cosmic ray flare, occurring in the
Galactic Center, $10^4$ years ago has been proposed to explain the TeV Ridge.
An alternative, steady-state model explaining all three data sets (TeV, GeV,
and radio) invokes purely leptonic processes. We show that the flare model from
the Galactic Center also provides an acceptable fit to the GeV and radio data,
provided the diffusion coefficient is energy independent. However, if
Kolmogorov-type turbulence is assumed for the diffusion coefficient, we find
that two flares are needed, one for the TeV data (occurring approximately $10^4
$ years ago) and an older one for the GeV data (approximately $10^5$ years
old). We find that the flare models we investigate do not fit the spherically
symmetric GeV excess as well as the usual generalized Navarro-Frenk-White
spatial profile, but are better suited to explaining the Ridge. We also show
that a range of single-zone, steady-state models are able to explain all three
spectral data sets. Large gas densities equal to the volumetric average in the
region can be accommodated by an energy independent diffusion or streaming
based steady-state model. Additionally, we investigate how the flare and
steady-state models may be distinguished with future gamma-ray data looking for
a spatial dependence of the gamma-ray spectral index.
