  Conventional interpretation of the observed cosmic microwave background (CMB)
dipole is that all of it is produced by local peculiar motions. Alternative
explanations requiring part of the dipole to be primordial have received
support from measurements of large-scale bulk flows. A test of the two
hypothesis is whether other cosmic dipoles produced by collapsed structures
later than last scattering coincide with the CMB dipole. One background is the
cosmic infrared background (CIB) whose absolute spectrum was measured to ~30%
by the COBE satellite. Over the 100 to 500 {\mu}m wavelength range its spectral
energy distribution can provide a probe of its alignment with CMB. This is
tested with the COBE FIRAS dataset which is available for such a measurement
because of its low noise and frequency resolution important for Galaxy
subtraction. Although the FIRAS instrument noise is in principle low enough to
determine the CIB dipole, the Galactic foreground is sufficiently close
spectrally to keep the CIB dipole hidden. A similar analysis is performed with
DIRBE, which - because of the limited frequency coverage - provides a poorer a
dataset. We discuss strategies for measuring the CIB dipole with future
instruments to probe the tilt and apply it to the Planck, Herschel and the
proposed Pixie missions. We demonstrate that a future FIRAS-like instrument
with instrument noise a factor of ~10 lower than FIRAS would make a
statistically significant measurement of the CIB dipole. We find that the
Planck and Herschel data sets will not allow a robust CIB dipole measurement.
The Pixie instrument promises a determination of the CIB dipole and its
alignment with either the CMB dipole or the dipole galaxy acceleration vector.
