  Soft theorems for the scattering of low energy photons and gravitons and
cosmological consistency conditions on the squeezed-limit correlation functions
are both understood to be consequences of invariance under large gauge
transformations. We apply the same method used in cosmology -- based on the
identification of an infinite set of "adiabatic modes" and the corresponding
conserved currents -- to derive flat space soft theorems for electrodynamics
and gravity. We discuss how the recent derivations based on the asymptotic
symmetry groups (BMS) can be continued to a finite size sphere surrounding the
scattering event, when the soft photon or graviton has a finite momentum. We
give a finite distance derivation of the antipodal matching condition
previously imposed between future and past null infinities, and explain why all
but one radiative degrees of freedom decouple in the soft limit. In contrast to
earlier works on BMS, we work with adiabatic modes which correspond to large
gauge transformations that are $r$-dependent.
