  The diffuse Galactic gamma-ray flux between 0.1 and 1 PeV has recently been
measured by the Tibet AS$\gamma$ Collaboration. The flux and spectrum are
consistent with the decay of neutral pions from hadronuclear interactions
between Galactic cosmic rays and the interstellar medium (ISM). We derive the
flux of the Galactic diffuse neutrino emission from the same interaction
process that produces the gamma rays. Our calculation accounts for the effect
of gamma-ray attenuation inside the Milky Way and uncertainties due to the
spectrum and distribution of cosmic rays, gas density, and infrared emission of
the ISM. We find that the contribution from the Galactic plane to the all-sky
neutrino flux is $\lesssim5-10\%$ around 100 TeV. The Galactic and
extragalactic neutrino intensities are comparable in the Galactic plane region.
Our results are consistent with the upper limit reported by the IceCube and
ANTARES Collaborations, and predict that next-generation neutrino experiments
may observe the Galactic component. We also show that the Tibet AS$\gamma$ data
imply either an additional component in the cosmic-ray nucleon spectrum or
contribution from discrete sources, including Pevatrons such as superbubbles
and hypernova remnants, and PeV electron accelerators. Future multi-messenger
observations between 1 TeV and 1 PeV are crucial to decomposing the origin of
sub-PeV gamma rays.
