  Both long-duration gamma-ray bursts (LGRBs) from core collapse of massive
stars and short-duration GRBs (SGRBs) from mergers of binary neutron star (BNS)
or neutron star--black hole (NSBH) are expected to occur in the accretion disk
of active galactic nuclei (AGNs). We show that GRB jets embedded in the
migration traps of AGN disks are promised to be choked by the dense disk
material. Efficient shock acceleration of cosmic rays at the reverse shock is
expected, and high-energy neutrinos would be produced. We find that these
sources can effectively produce detectable TeV--PeV neutrinos through $p\gamma$
interactions. From a choked LGRB jet with isotropic equivalent energy of
$10^{53}\,{\rm erg}$ at $100\,{\rm Mpc}$, one expects $\sim2\,(7)$ neutrino
events detectable by IceCube (IceCube-Gen2). The contribution from choked LGRBs
to the observed diffuse neutrino background depends on the unknown local event
rate density of these GRBs in AGN disks. For example, if the local event rate
density of choked LGRBs in AGN disk is $\sim5\%$ that of low-luminosity GRBs
$(\sim10\,{\rm Gpc}^{-3}\,{\rm yr}^{-1})$, the neutrinos from these events
would contribute to $\sim10\%$ of the observed diffuse neutrino background.
Choked SGRBs in AGN disks are potential sources for future joint
electromagnetic, neutrino, and gravitational wave multi-messenger observations.
