  I discuss the factorization-compatible definitions of
transverse-momentum-dependent (TMD) pion wave functions which are fundamental
theory inputs entering QCD factorization formulae for many hard exclusive
processes. I will first demonstrate that the soft subtraction factor introduced
to remove both rapidity and pinch singularities can be greatly reduced by
making the maximal use of the freedom to construct the Wilson-line paths when
defining the TMD wave functions. I will then turn to show that the newly
proposed TMD definition with non-dipolar Wilson lines is equivalent to the one
with dipolar gauge links and with a complicated soft function, to all orders of
the perturbative expansion in the strong coupling, as far as the infrared
behavior is concerned.
