We present differential double-copy relations between gluon and graviton three-point functions in AdSd+1. We introduce a set of differential operators in anti-de Sitter (AdS) that naturally generalize on shell kinematics of scattering amplitudes in flat space. This provides a way to construct AdS correlators by replacing the kinematic variables of amplitudes with the corresponding differential operators and suitably ordering them. By construction, the resulting correlators are manifestly conformally invariant, with the correct flat-space limit and exhibit a differential double-copy structure
