  Extreme Mass Ratio Inspirals (EMRIs) can be classified as dry EMRIs and wet
EMRIs based on their formation mechanisms. Dry (or the "loss-cone") EMRIs,
previsouly considered as the main EMRI sources for the Laser Interferometer
Space Antenna, are primarily produced by multi-body scattering in the nuclear
star cluster and gravitational capture. In this Letter, we highlight an
alternative EMRI formation channel: (wet) EMRI formation assisted by the
accretion flow around accreting galactic-center massive black holes (MBHs). In
this channel, the accretion disk captures stellar-mass black holes that are
intially moving on inclined orbits, and subsequently drives them to migrate
towards the MBH - this process boosts the formation rate of EMRIs in such
galaxies by orders of magnitude. Taking into account the fraction ($\mathcal
O(10^{-2}-10^{-1})$) of active galactic nuclei where the MBHs are expected to
be rapidly accreting, we forecast that wet EMRIs will contribute an important
fraction of all EMRIs observed by spaceborne gravitational wave detectors and
likely dominate for MBH hosts heavier than a few $10^5 M_\odot$.
