  We derive CP-violating transport equations for fermions for electroweak
baryogenesis from the CTP-formalism including thermal corrections at the
one-loop level. We consider both the VEV-insertion approximation (VIA) and the
semiclassical (SC) formalism. We show that the VIA-method is based on an {\em
assumption} that leads to an ill-defined source term containing a pinch
singularity, whose regularisation by thermal effects leads to ambiguities
including spurious ultraviolet and infrared divergences. We then carefully
review the derivation of the semiclassical formalism and extend it to include
thermal corrections. We present the semiclassical Boltzmann equations for
thermal WKB-quasiparticles with source terms up to the second order in
gradients that contain both dispersive and finite width corrections. We also
show that the SC-method reproduces the current divergence equations and that a
correct implementation of the Fick's law captures the semiclassical source term
even with conserved total current $\partial_\mu j^\mu = 0$. Our results show
that the VIA-source term is not just ambiguous, but that it does not exist.
Finally, we show that the collisional source terms reported earlier in the
semiclassical literature are also spurious, and vanishes in a consistent
calculation.
