  We present a highly effective algorithmic approach for generating
$\varepsilon$-differentially private synthetic data in a bounded metric space
with near-optimal utility guarantees under the 1-Wasserstein distance. In
particular, for a dataset $X$ in the hypercube $[0,1]^d$, our algorithm
generates synthetic dataset $Y$ such that the expected 1-Wasserstein distance
between the empirical measure of $X$ and $Y$ is $O((\varepsilon n)^{-1/d})$ for
$d\geq 2$, and is $O(\log^2(\varepsilon n)(\varepsilon n)^{-1})$ for $d=1$. The
accuracy guarantee is optimal up to a constant factor for $d\geq 2$, and up to
a logarithmic factor for $d=1$. Our algorithm has a fast running time of
$O(\varepsilon dn)$ for all $d\geq 1$ and demonstrates improved accuracy
compared to the method in (Boedihardjo et al., 2022) for $d\geq 2$.
