  A direct generalization of the transverse momentum integrated(TMI) light-cone
wave function to define a transverse momentum dependent(TMD) light-cone wave
function will cause light-cone singularities and they spoil TMD factorization.
We motivate a definition in which the light-cone singularities are regularized
with non-light like Wilson lines. The defined TMD light-cone wave function has
some interesting relations to the corresponding TMI one. When the transverse
momentum is very large, the TMD light-cone wave function is determined
perturbatively in term of the TMI one. In the impact $b$-space with a small
$b$, the TMD light-cone wave function can be factorized in terms of the TMI
one. In this letter we study these relations. By-products of our study are the
renormalization evolution of the TMI light-cone wave function and the
Collins-Soper equation of the TMD light-cone wave function, the later will be
useful for resumming Sudakov logarithms.
