  We consider the Kudla-Millson theta series associated to a quadratic space of
signature $(N,N)$. By combining a `see-saw' argument with the Siegel-Weil
formula, we show that its (regularized) integral along a torus attached to a
totally real field of degree $N$ is the diagonal restriction of an Eisenstein
series. It allows us to express the Fourier coefficients of the diagonal
restriction as intersection numbers, which generalizes a result of
Darmon-Pozzi-Vonk to totally real fields.
