  Very recently, diffuse gamma rays with $0.1\,{\rm PeV}<E_\gamma <1\,$PeV have
been discovered from the Galactic disk by the Tibet air shower array and muon
detector array (Tibet AS+MD array). While the measured sub-PeV flux may be
compatible with the hadronic origin in the conventional Galactic cosmic ray
propagation model, we find that it is in possible tension with the
non-detection of Galactic neutrino emissions by the IceCube neutrino telescope.
We further find that the presence of an extra cosmic ray component of
relatively hard spectrum, which is probably related to the Cygnus Cocoon region
and other PeV cosmic-ray sources in the Galactic disk, would alleviate the
tension. This scenario may imply the existence of an extreme accelerator of
cosmic rays beyond PeV in the Cygnus region, which might lead to a hardening of
the gamma-ray spectrum of Cygnus Cocoon beyond $\sim 30-100\,$TeV extending
probably up to 1\,PeV.
