  We present a differential representation for holographic four-point
correlators. In this representation, the correlators are given by acting
differential operators on certain seed functions. The number of these functions
is much smaller than what is normally seen in known examples of holographic
correlators, and all of them have simple Mellin amplitudes. This representation
establishes a direct connection between correlators in position space and their
Mellin space counterpart. The existence of this representation also imposes
non-trivial constraints on the structure of holographic correlators. We
illustrate these ideas by correlators in ${\rm AdS}_5 \times {\rm S}^5$ and
${\rm AdS}_5 \times {\rm S}^3$.
