To my knowledge weak localization is a result of constructive interference between scattering processes and their time reversed.
Traveling a given path in a vector potential leads to the phase $q\int d\vec{x}\ \vec{A}(x)$. A particle traveling the time reversed path gets an additional "$-$"sign as the path is inverted.
Somehow the spin flip seems to give an additional sign resulting in constructive interference. How is that? How is the phase of a particle in an vector potential connected to the spin?