  Extra-galactic sources of photons have been used to constrain space-time
quantum fluctuations in the Universe. In these proposals, the fundamental
"fuzziness" of distance caused by space-time quantum fluctuations has been
directly identified with fluctuations in optical paths. Phase-front
corrugations deduced from these optical-path fluctuations are then applied to
light from extra-galactic point sources, and used to constrain various models
of quantum gravity. However, when a photon propagates in three spatial
dimensions, it does not follow a specific ray, but rather samples a finite,
three-dimensional region around that ray --- thereby averaging over space-time
quantum fluctuations all through that region. We use a simple, random-walk type
model to demonstrate that, once the appropriate wave optics is applied, the
averaging of neighboring space-time fluctuations will cause much less
distortion to the phase front. In our model, the extra suppression factor due
to diffraction is the wave length in units of the Planck length, which is at
least $10^{29}$ for astronomical observations.
