  The differential representation is a novel formalism for studying boundary
correlators in $(d+1)$-dimensional anti-de Sitter space. In this letter, we
generalize the differential representation beyond tree level using the notion
of operator-valued integrals. We use the differential representation to compute
three-point bubble and triangle Witten diagrams with external states of
conformal dimension $\Delta=d$. We compare the former to a position space
computation.
