  We introduce a test for the conditional independence of random variables $X$
and $Y$ given a random variable $Z$, specifically by sampling from the joint
distribution $(X,Y,Z)$, binning the support of the distribution of $Z$, and
conducting multiple $p$-Wasserstein two-sample tests. Under a $p$-Wasserstein
Lipschitz assumption on the conditional distributions $\mathcal{L}_{X|Z}$,
$\mathcal{L}_{Y|Z}$, and $\mathcal{L}_{(X,Y)|Z}$, we show that it is possible
to control the Type I and Type II error of this test, and give examples of
explicit finite-sample error bounds in the case where the distribution of $Z$
has compact support.
