  In this paper, we use Borcherds lifting and the big CM value formula of
Bruinier, Kudla, and Yang to give an explicit factorization formula for the
norm of $\Psi(\frac{d_1+\sqrt{d_1}}2) -\Psi(\frac{d_2+\sqrt{d_2}}2)$, where
$\Psi$ is the $j$-invariant or the Weber invariant $\omega_2$. The
$j$-invariant case gives another proof of the well-known Gross-Zagier
factorization formula of singular moduli, while the Weber invariant case gives
a proof of the Yui-Zagier conjecture for $\omega_2$. The method used here could
be extended to deal with other modular functions on a genus zero modular curve.
