  We present measurements of the fluctuation superconductivity in an underdoped
thin film of La$_{1.905}$Sr$_{0.095}$CuO$_4$ using time-domain THz
spectroscopy. We compare our results with measurements of diamagnetism in a
similarly doped crystal of La$_{2-x}$Sr$_x$CuO$_4$. We show through a
vortex-plasma model that if the fluctuation diamagnetism solely originates in
vortices, then they must necessarily exhibit an anomalously large vortex
diffusion constant, which is more than two orders of magnitude larger than the
Bardeen-Stephen estimate. This points to either the extremely unusual
properties of vortices in the under-doped d-wave cuprates or a contribution to
the diamagnetic response that is not superconducting in origin.
