  We study the soft limits of cosmological correlators from a holographic
perspective, showing how the inflationary consistency relations arise from the
diffeomorphism invariance of the dual quantum field theory. Starting from the
corresponding Ward identity, by taking moments we derive the leading and
subleading behaviour of the stress tensor 3-point function in the limit as one
momentum vanishes. These results are non-perturbative and valid in quantum
field theories of a very general nature. Exploiting the known mapping of
correlators in the dual quantum field theory to those of the cosmology, we then
obtain the leading and subleading soft behaviour of all cosmological 3-point
correlators of curvature perturbations and gravitons. Our results thus provide
a holographic derivation of all leading and subleading consistency relations
for cosmological 3-point functions, and our method is easily generalised. We
verify our results explicitly for slow-roll inflation and for strongly coupled
holographic cosmologies with a perturbative dual description.
