  We explore the use of the differential representation of AdS amplitudes to
compute Witten diagrams. The differential representation expresses AdS
amplitudes in terms of conformal generators acting on contact Witten diagrams,
which allows us to construct differential equations for Witten diagrams. These
differential equations can then be transformed into difference equations in
Mellin space, which can be solved recursively. Using this method, we
efficiently re-computed scalar four-point amplitudes and obtained new results
for scalar six-point amplitudes mediated by gluons and scalars, as well as two
examples of scalar eight-point amplitudes from gluon exchange.
