  The accretion disks that fuel active galactic nuclei (AGN) may house numerous
stars and compact objects, formed in situ or captured from nearby star
clusters. Embedded neutron stars and black holes may form binaries and
eventually merge, emitting gravitational waves detectable by LIGO/VIRGO. AGN
disks are a particularly promising environment for the production of high-mass
gravitational wave events involving black holes in the pair instability mass
gap, and may facilitate electromagnetic counterparts to black hole binary
mergers. However, many orders of magnitude separate the typical length scales
of binary formation and those on which gravitational waves can drive binary
inspirals, making binary mergers inside the disk uncertain. Previous
hydrodynamical simulations of binaries have either been restricted to two
dimensions entirely, or focused on binaries aligned with the midplane of the
disk. Herein we present the first three-dimensional, high-resolution, local
shearing-box hydrodynamical simulations of disk-embedded binaries over a range
of orbital inclinations. We find that retrograde binaries can shrink up to four
times as quickly as prograde binaries, and that all binaries not perfectly
aligned (or anti-aligned) with the AGN disk are driven into alignment. An
important consequence of this is that initially retrograde binaries will
traverse the inclinations where von Zeipel-Lidov-Kozai oscillations can drive
binary eccentricities to large values, potentially facilitating mergers. We
also find that interactions with the AGN disk may excite eccentricities in
retrograde binaries and cause the orbits of embedded binaries to precess.
