  We study the analytic structure of loop Witten diagrams in Euclidean AdS
represented by their conformal partial wave expansions. We show that, as in
flat space, amplitude's singularities are associated with non-trivial cuts of
the diagram and factorize into products of the coefficient functions for the
subdiagrams resulting from these cuts. We consider an example of a one-loop
four-point diagram in detail and then briefly discuss how the procedure can be
extended to more general diagrams. Finally, we show that this analysis
reproduces simple relations that follow from the large-N considerations on the
boundary.
