  Diffuse $\gamma$-ray emission produced by the interaction of cosmic-ray
particles with matter and radiation in the Galaxy can be used to probe the
distribution of cosmic rays and their sources in different regions of the
Galaxy. With its large field of view and long observation time, the Milagro
Gamma Ray Observatory is an ideal instrument for surveying large regions of the
Northern Hemisphere sky and for detecting diffuse $\gamma$-ray emission at very
high energies. Here, the spatial distribution and the flux of the diffuse
$\gamma$-ray emission in the TeV energy range with a median energy of 15 TeV
for Galactic longitudes between 30$^\circ$ and 110$^\circ$ and between
136$^\circ$ and 216$^\circ$ and for Galactic latitudes between -10$^\circ$ and
10$^\circ$ are determined. The measured fluxes are consistent with predictions
of the GALPROP model everywhere except for the Cygnus region
($l\in[65^\circ,85^\circ]$). For the Cygnus region, the flux is twice the
predicted value. This excess can be explained by the presence of active cosmic
ray sources accelerating hadrons which interact with the local dense
interstellar medium and produce gamma rays through pion decay.
