Soft graviton theorems receive one-loop contributions that are logarithmic in
the energy of the soft graviton, and which are closely related to tails of
gravitational waveforms. We demonstrate that these logarithmic corrections are
encoded in the Ward identity of superrotation symmetries, i.e. they follow from
conservation of superrotation charge across spatial infinity $i^0$. Our proof
relies on a careful analysis of the radiative phase space admitting such
gravitational tails, and the determination of the fluxes through null infinity
$\mathscr I$ that act as canonical generators of superrotations on both
gravitational and matter fields. All logarithmic terms are derived from the
fluxes through correlations of the supertranslation Goldstone mode, provided
care is taken in manipulating gravitationally interacting (i.e. dressed) rather
than free fields. In cases where massive particles take part in the scattering
process, logarithmic corrections also partly arise from the superrotation
charge generator at timelike infinity $i^\pm$.
