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.
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