  We extend a CDGA $V$ with a perfect pairing of degree $n$ on cohomology to a
CDGA $\hat V$ with a pairing of degree $n$ on chain level such that $\hat V$
admits a Hodge decomposition and retracts onto $V$ preserving the pairing on
cohomology; here we suppose that $V$ is either 1-connected, or that $V$ is
connected, of finite type, and $n$ is odd. We show that a Hodge decomposition
of $\hat V$ induces a differential Poincar\'e duality model of $V$ in a natural
way. Assuming that $H(V)$ is 1-connected, we apply our extension to a Sullivan
model of $V$ in the proof of the existence and "uniqueness" of a 1-connected
differential Poincar\'e duality model of $V$ by Lambrechts & Stanley; we
eliminate their extra assumptions in the uniqueness statement, including
$H^2(V)=0$ if $n$ is odd.
