  We study the duality between color and kinematics for the Sudakov form
factors of ${\rm tr}(F^2)$ in non-supersymmetric pure Yang-Mills theory. We
construct the integrands that manifest the color-kinematics duality up to two
loops. The resulting numerators are given in terms of Lorentz products of
momenta and polarization vectors, which have the same powers of loop momenta as
that from the Feynman rules. The integrands are checked by $d$-dimensional
unitarity cuts and are valid in any dimension. We find that massless-bubble and
tadpole topologies are needed at two loops to realize the color-kinematics
duality. Interestingly, the two-loop solution contains a large number of free
parameters suggesting the duality may hold at higher loop orders.
