  We present the detection and morphological characterization of hot molecular
gas outflows in nearby ultra-luminous infrared galaxies, using the near-IR
integral-field spectrograph SINFONI on the VLT. We detect outflows observed in
the 2.12 micron H$_{2}$ 1-0 S(1) line for three out of four ULIRGs analyzed;
IRAS 12112+0305, 14348-1447, and 22491-1808. The outflows are mapped on scales
of 0.7-1.6 kpc, show typical outflow velocities of 300-500 km/s, and appear to
originate from the nuclear region. The outflows comprise hot molecular gas
masses of ~6-8x10$^3$ M(sun). Assuming a hot-to-cold molecular gas mass ratio
of 6x10$^{-5}$, as found in nearby luminous IR galaxies, the total (hot+cold)
molecular gas mass in these outflows is expected to be ~1x10$^{8}$ M(sun). This
translates into molecular mass outflow rates of ~30-85 M(sun)/yr, which is a
factor of a few lower than the star formation rate in these ULIRGs. In
addition, most of the outflowing molecular gas does not reach the escape
velocity of these merger systems, which implies that the bulk of the outflowing
molecular gas is re-distributed within the system and thus remains available
for future star formation. The fastest H$_{2}$ outflow is seen in the
Compton-thick AGN of IRAS 14348-1447, reaching a maximum outflow velocity of
~900 km/s. Another ULIRG, IRAS 17208-0014, shows asymmetric H$_{2}$ line
profiles different from the outflows seen in the other three ULIRGs. We discuss
several alternative explanations for its line asymmetries, including a very
gentle galactic wind, internal gas dynamics, low-velocity gas outside the disk,
or two superposed gas disks. We do not detect the hot molecular counterpart to
the outflow previously detected in CO(2-1) in IRAS 17208-0014, but we note that
our SINFONI data are not sensitive enough to detect this outflow if it has a
small hot-to-cold molecular gas mass ratio of < 9x10$^{-6}$.
