The diffuse gamma radiation arising from the interaction of cosmic ray particles with matter and radiation in the Galaxy is one of the few probes available to study the origin of the cosmic rays. Milagro is a water Cherenkov detector that continuously views the entire overhead sky. The large field-of-view combined with the long observation time makes Milagro the most sensitive instrument available for the study of large, low surface brightness sources such as the diffuse gamma radiation arising from interactions of cosmic radiation with interstellar matter. In this paper we report our results on diffuse emission from the galactic plane and in particular the Cygnus region. Our observations show at least one new TeV source MGRO J2020+37 as well as correlations with the matter density in the region as would be expected from cosmic-ray proton interactions. However, the TeV gamma-ray flux from the Cygnus region (after excluding MGRO J2020+37) is roughly 5 times that expected from a conventional model of cosmic ray production and propagation.