  The Schr\"{o}dinger equation admits smooth and finite solutions that
spontaneously evolve into a singularity, even for a free particle. This blowup
is generally ascribed to the intrinsic dispersive character of the associated
time evolution. We resort to the notion of quantum trajectories to reinterpret
this singular behavior. We show that the blowup can be directly related to
local phase variations, which generate an underlying velocity field responsible
for driving the quantum flux toward the singular region.
