  Various supernovae (SN), compact object coalescences, and tidal disruption
events are widely believed to occur embedded in active galactic nuclei (AGN)
accretion disks and generate detectable electromagnetic (EM) signals. We
collectively refer to them as \emph{AGN disk transients}. The inelastic
hadronuclear ($pp$) interactions between shock-accelerated cosmic rays and AGN
disk materials shortly after the ejecta shock breaks out of the disk can
produce high-energy neutrinos. However, the expected efficiency of neutrino
production would decay rapidly by adopting a pure Gaussian density atmosphere
profile applicable for stable gas-dominated disks. On the other hand, AGN
outflows and disk winds are commonly found around AGN accretion disks. In this
paper, we present that the circum-disk medium would further consume the shock
kinetic energy to more efficiently produce high-energy neutrinos, especially
for $\sim$\,TeV$-$PeV neutrinos that IceCube detects. Thanks to the existence
of the circum-disk medium, we find that the neutrino production will be
enhanced significantly and make a much higher contribution to the diffuse
neutrino background. Optimistically, $\sim20\%$ diffuse neutrino background can
be contributed from AGN disk transients.
