  We study heat kernel measures on sub-Riemannian infinite-dimensional
Heisenberg-like Lie groups. In particular, we show that Cameron-Martin type
quasi-invariance results hold in this subelliptic setting and give
$L^p$-estimates for the Radon-Nikodym derivatives. The main ingredient in our
proof is a generalized curvature-dimension estimate which holds on
approximating finite-dimensional projection groups. Such estimates were first
introduced by Baudoin and Garofalo in \cite{BaudoinGarofalo2011}.
