In this talk, we establish a duality result between the singular theta lift introduced by Borcherds and the Kudla-Millson theta lift. For O(p,2), this gives rise to the construction of Green functions for certain special cycles, while for arbitrary signature, one obtains differential characters in the sense of Cheeger and Simons. We also discuss the extension of these results to unitary groups. This is joint work with Jan Bruinier.