  Given a separable and real Hilbert space $\mathbb{H}$ and a trace-class,
symmetric and non-negative operator
$\mathcal{G}:\mathbb{H}\rightarrow\mathbb{H}$, we examine the equation
\begin{align*}
  dX_t = -X_t\, dt + b(X_t) \, dt + \sqrt{2} \, dW_t, \qquad
X_0=x\in\mathbb{H},
  \end{align*} where $(W_t)$ is a $\mathcal{G}$-Wiener process on $\mathbb{H}$
and $b:\mathbb{H}\rightarrow\mathbb{H}$ is Lipschitz. We assume there is a
splitting of $\mathbb{H}$ into a finite-dimensional space $\mathbb{H}^l$ and
its orthogonal complement $\mathbb{H}^h$ such that $\mathcal{G}$ is strictly
positive definite on $\mathbb{H}^l$ and the non-linearity $b$ admits a
contraction property on $\mathbb{H}^h$. Assuming a geometric drift condition,
we derive a Kantorovich ($L^1$ Wasserstein) contraction with an explicit rate
for the corresponding Markov kernels. The estimates for the rate are based on
the eigenvalues of $\mathcal{G}$ on the space $\mathbb{H}^l$, a Lipschitz bound
on $b$ and a geometric drift condition. The results are derived using coupling
methods.
