  Quantum walks constitute important tools in different applications,
especially in quantum algorithms. To a great extent their usefulness is due to
unusual diffusive features, allowing much faster spreading than their classical
counterparts. Such behavior, although frequently credited to intrinsic quantum
interference, usually is not completely characterized. Using a recently
developed Green's function approach [Phys. Rev. A {\bf 84}, 042343 (2011)],
here it is described -- in a rather general way -- the problem dynamics in
terms of a true sum over paths history a la Feynman. It allows one to explicit
identify interference effects and also to explain the emergence of
superdiffusivity. The present analysis has the potential to help in designing
quantum walks with distinct transport properties.
