  We characterize infrared spectral energy distributions of 343 (Ultra)
Luminous Infrared Galaxies from $z=0.3-2.8$. We diagnose the presence of an AGN
by decomposing individual Spitzer mid-IR spectroscopy into emission from
star-formation and an AGN-powered continuum; we classify sources as
star-forming galaxies (SFGs), AGN, or composites. Composites comprise 30% of
our sample and are prevalent at faint and bright $S_{24}$, making them an
important source of IR AGN emission. We combine spectroscopy with
multiwavelength photometry, including Herschel imaging, to create three
libraries of publicly available templates (2-1000 $\mu$m). We fit the far-IR
emission using a two temperature modified blackbody to measure cold and warm
dust temperatures ($T_c$ and $T_w$). We find that $T_c$ does not depend on
mid-IR classification, while $T_w$ shows a notable increase as the AGN grows
more luminous. We measure a quadratic relationship between mid-IR AGN emission
and total AGN contribution to $L_{\rm IR}$. AGN, composites, and SFGs separate
in $S_8/S_{3.6}$ and $S_{250}/S_{24}$, providing a useful diagnostic for
estimating relative amounts of these sources. We estimate that >40% of IR
selected samples host an AGN, even at faint selection thresholds ($S_{24}$>100
$\mu$Jy). Our decomposition technique and color diagnostics are relevant given
upcoming observations with the James Webb Space Telescope.
