  In many analyses in Higgs, top and electroweak physics, the kinematic
reconstruction of the final state is improved by constrained fits. This is a
particularly powerful tool at $e^{+}e^{-}$ colliders, where the initial state
four-momentum is known and can be employed to constrain the final state. A
crucial ingredient to kinematic fitting is an accurate estimate of the
measurement uncertainties, in particular for composed objects like jets. This
contribution will show how the particle flow concept, which is a design-driver
for most detectors proposed for future Higgs factories, can -- in addition to
an excellent jet energy measurement -- provide detailed estimates of the
covariance matrices for each individual particle-flow object (PFO) and each
individual jet. Combined with information about leptons and secondary vertices
in the jets, the kinematic fit enables to correct $b$- and $c$-jets for missing
momentum from neutrinos from semi-leptonic heavy quark decays. The impact on
the reconstruction of invariant di-jet masses and the resulting improvement in
$ZH$ vs $ZZ$ separation will be presented, using the full simulation of the ILD
detector, as an example of highly-granular ParticleFlow optimized detector
concept.
