  We form a generating series of regularized volumes of intersections of
special cycles on a non-compact unitary Shimura variety with a fixed base
change cycle. We show that it is a Hilbert modular form by identifying it with
a theta integral, which we show converges even though the parameters lie
outside the classical convergence range of Weil. By applying the regularized
Siegel-Weil formulas of Ichino and Gan-Qiu-Takeda, we show the modular form is
the restriction of a hermitian modular form of degree n related to Siegel
Eisenstein series on U(n,n). An essential fact used is a computation showing
the Kudla-Millson Schwartz function vanishes under the Ikeda map.
