  We investigate the structure of a particular class of massive vacuum Feynman
integrals at two loops. This class enjoys the linear relation $m_1+m_2=m_3$
between its three propagator masses, corresponding to zeros of the associated
K\"all\'en function. Apart from having applications in thermal field theory,
the integrals can be mapped onto one-loop three-point functions with collinear
external momenta, suggesting the term "collinear" masses. We present a
closed-form solution for these integrals, proving that they can always be
factorized into products of one-loop cases, for all integer-valued propagator
powers.
