  We numerically study the spatial spreading of quantized vortex lines in low
temperature liquid helium. The vortex lines, initially concentrated in a small
region, diffuse into the surrounding vortex-free helium, a situation which is
typical of many experiments. We find that this spreading, which occurs in the
absence of viscosity, emerges from the interactions between the vortex lines,
and can be interpreted as a diffusion process with effective coefficient equal
to approximately 0.5$\kappa$ where $\kappa$ is the quantum of circulation.
