  The disks of Active Galactic Nuclei (AGNs) have emerged as rich environments
for the production and capture of stars and the compact objects that they leave
behind. These stars produce long Gamma-Ray Bursts (LGRBs) at their deaths,
while frequent interactions among compact objects form binary neutron stars and
neutron star-black hole binaries, leading to short GRBs (SGRBs) upon their
merger. Predicting the properties of these transients as they emerge from the
dense environments of AGN disks is key to their proper identification and to
better constrain the star and compact object population in AGN disks. Some of
these transients would appear unusual because they take place in much higher
densities than the interstellar medium. Others, which are the subject of this
paper, would additionally be modified by radiation diffusion since they are
generated within optically thick regions of the accretion disks. Here we
compute the GRB afterglow light curves for diffused GRB sources for a
representative variety of central black-hole masses and disk locations. We find
that the radiation from radio to UV and soft X-rays can be strongly suppressed
by synchrotron self-absorption in the dense medium of the AGN disk. In
addition, photon diffusion can significantly delay the emergence of the
emission peak, turning a beamed, fast transient into a slow, isotropic, and
dimmer one. These would appear as broadband-correlated AGN variability with
dominance at the higher frequencies. Their properties can constrain both the
stellar populations within AGN disks as well as the disk structure.
