  We use Stein's method to bound the Wasserstein distance of order $2$ between
a measure $\nu$ and the Gaussian measure using a stochastic process $(X_t)_{t
\geq 0}$ such that $X_t$ is drawn from $\nu$ for any $t > 0$. If the stochastic
process $(X_t)_{t \geq 0}$ satisfies an additional exchangeability assumption,
we show it can also be used to obtain bounds on Wasserstein distances of any
order $p \geq 1$. Using our results, we provide optimal convergence rates for
the multi-dimensional Central Limit Theorem in terms of Wasserstein distances
of any order $p \geq 2$ under simple moment assumptions.
