  We show that tree-level and one-loop Mellin space correlators in anti-de
Sitter space obey certain difference equations, which are the direct analog to
the differential equations for Feynman loop integrals in the flat space.
Finite-difference relations, which we refer to as ``summation-by-parts
relations'', in parallel with the integration-by-parts relations for Feynman
loop integrals, are derived to reduce the integrals to a basis. We illustrate
the general methodology by explicitly deriving the difference equations and
summation-by-parts relations for various tree-level and one-loop Witten
diagrams up to the four-point bubble level.
