  Concerning quantitative isoperimetry for a weighted Riemannian manifold
satisfying $\mathrm{Ric}_{\infty} \ge 1$, we give an $L^1$-estimate exhibiting
that the push-forward of the reference measure by the guiding function (arising
from the needle decomposition) is close to the Gaussian measure. We also show
$L^p$- and $W_2$-estimates in the $1$-dimensional case.
