This is a continuation of [Wang1], where it was shown that $K$-equivalent complex projective manifolds have the same Betti numbers by using the theory of $p$-adic integrals and Deligne's solution to the Weil conjecture. The aim of this note is to show that with a little more book-keeping work, namely by applying Faltings' $p$-adic Hodge Theory, our $p$-adic method also leads to the equivalence of Hodge numbers --- a result which was previously known via motivic integration.