  Different frameworks exist to describe the flat-space limit of AdS/CFT,
include momentum space, Mellin space, coordinate space, and partial-wave
expansion. We explain the origin of momentum space as the smearing kernel in
Poincare AdS, while the origin of latter three is the smearing kernel in global
AdS. In Mellin space, we find a Mellin formula that unifies massless and
massive flat-space limit, which can be transformed to coordinate space and
partial-wave expansion. Furthermore, we also manage to transform momentum space
to smearing kernel in global AdS, connecting all existed frameworks. Finally,
we go beyond scalar and verify that $\langle VV\mathcal{O}\rangle$ maps to
photon-photon-massive amplitudes.
