Can galactic magnetic fields diffuse into the voids?

Cosmic voids are magnetized at the level of at least $10^{-17}$ G on Mpc scales, as implied by blazar observations. We show that an electrically conducting plasma is present in the voids, and that, because of the plasma, \emph{diffusion} into the voids of galactic fields generated by a mean-field dynamo is far too slow to explain the present-day void magnetization. Indeed, we show that even in the presence of turbulence in the voids, dynamo-generated galactic fields diffuse out to a galactocentric radius of only 200-400 kpc. Therefore, it is challenging to meet the required volume filling-factor of the void magnetic field. We conclude that a primordial origin remains the most natural explanation to the space-filling weak fields in voids.