  We present a completely gauge-invariant operator definition of
transverse-momentum-dependent parton densities (TMD), supplied with
longitudinal lightlike gauge links as well as transverse gauge links at
lightcone infinity. Within this framework, we consider the consistent treatment
of specific divergences, emerging in the "unsubtracted" TMD beyond the tree
approximation, and construct the soft factors to cancel unphysical
singularities. We confront this approach with factorization schemes, which make
use of covariant gauges with off-the-lightcone gauge links, and discuss their
mutual connection.
