The origins of high-energy astrophysical neutrinos measured by the IceCube Neutrino Observatory remain a mystery despite extensive searches for multimessenger correlations. In particular, no point sources have been identified so far. However, a likely source for diffuse neutrino emission are cosmic-ray interactions in the Galactic plane. Due to the excellent pointing of their track-like signature, muon-neutrino-induced muons are an excellent channel for measuring spatial correlations. Two methods were developed to test for a spatially extended flux from the entire Galactic plane. Both methods are maximum likelihood fits, one binned and the other unbinned, and using different background estimation methods. We consider two templates for Galactic neutrino emission based primarily on gamma-ray observations and models that cover a wide range of possibilities. We present constraints from seven years of IceCube Neutrino Observatory muon data on the neutrino flux coming from the Galactic plane.