We'll discuss an extension of the work of Kudla-Millson on the modularity of special cycles on a non-compact Shimura variety associated to U(n,1) over a split CM field. The volume of their intersections with a diagonally embedded Shimura subvariety is related to Fourier coefficients of a Hilbert modular form coming from the restriction of an Eisenstein series on U(n,n). The main new idea is an application of the regularized Siegel-Weil formula of Gan-Qiu-Takeda.