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Diffuse $\gamma$-ray emission produced by the interaction of cosmic-rayparticles with matter and radiation in the Galaxy can be used to probe thedistribution of cosmic rays and their sources in different regions of theGalaxy. With its large field of view and long observation time, the MilagroGamma Ray Observatory is an ideal instrument for surveying large regions of theNorthern Hemisphere sky and for detecting diffuse $\gamma$-ray emission at veryhigh 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 TeVfor Galactic longitudes between 30$^\circ$ and 110$^\circ$ and between136$^\circ$ and 216$^\circ$ and for Galactic latitudes between -10$^\circ$ and10$^\circ$ are determined. The measured fluxes are consistent with predictionsof the GALPROP model everywhere except for the Cygnus region($l\in[65^\circ,85^\circ]$). For the Cygnus region, the flux is twice thepredicted value. This excess can be explained by the presence of active cosmicray sources accelerating hadrons which interact with the local denseinterstellar medium and produce gamma rays through pion decay.

A Measurement of the Spatial Distribution of Diffuse TeV Gamma Ray Emission from the Galactic Plane with Milagro