  Observations of the Galactic Center (GC) region in very-high-energy (VHE,
>100 GeV) gamma rays, conducted with the High Energy Stereoscopic System
(H.E.S.S.), led to the detection of an extended region of diffuse gamma-ray
emission in 2006. To date, the exact origin of this emission has remained
unclear, although a tight spatial correlation between the density distribution
of the molecular material of the Central Molecular Zone (CMZ) and the
morphology of the observed gamma-ray excess points towards a hadronic
production scenario. In this proceeding, we present a numerical study of the
propagation of high-energy cosmic rays (CRs) through a turbulent environment
such as the GC region. In our analysis, we derive an energy-dependent
parametrization for the diffusion coefficient which we use for our simulation
of the diffuse gamma-ray emission at the GC. Assuming that hadronic CRs have
been released by a single impulsive event at the center of our Galaxy, we probe
the question whether or not the interaction processes of the diffusing hadrons
with ambient matter can explain the observed diffuse gamma-ray excess. Our
results disfavor this scenario, as our analysis indicates that the diffusion
process is, on timescales compared to the typical proton lifetime at the GC
region, too slow to explain the extension of the observed emission.
