  Recently, the {\it{Fermi}} space telescope has discovered two large
$\gamma$-ray emission regions, the so-called "Fermi bubbles", that extend up to
$\sim 50^\circ$ above and below the Galactic center. The $\gamma$-ray emission
from the bubbles are found to follow a hard spectrum with no significant
spatial variation in intensity and spectral shape. The origin of the emission
is still not clearly understood. Suggested explanations include injection of
cosmic-ray nuclei from the Galactic center by high-speed Galactic winds,
electron acceleration by multiple shocks and stochastic electron acceleration
inside the bubbles. In this letter, it is proposed that the $\gamma$-rays can
be the result of diffusive injection of Galactic cosmic-ray protons during
their propagation through the Galaxy. Considering that the bubbles are slowly
expanding, and cosmic rays undergo much slower diffusion inside the bubbles
than in the averaged Galaxy and at the same time suffer losses due to adiabatic
expansion and inelastic collisions with the bubble plasma, this model can
explain the observed intensity profile, the emission spectrum and the measured
luminosity without invoking any additional particle production processes unlike
other existing models.
