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 $pgamma$ 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.
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