  We consider the mean-field limit of systems of particles with singular
interactions of the type $-\log|x|$ or $|x|^{-s}$, with $0< s<d-2$, and with an
additive noise in dimensions $d \geq 3$. We use a modulated-energy approach to
prove a quantitative convergence rate to the solution of the corresponding
limiting PDE. When $s>0$, the convergence is global in time, and it is the
first such result valid for both conservative and gradient flows in a singular
setting on $\mathbb{R}^d$. The proof relies on an adaptation of an argument of
Carlen-Loss to show a decay rate of the solution to the limiting equation, and
on an improvement of the modulated-energy method developed in arXiv:1508.03377,
arXiv:1803.08345, arXiv:2107.02592 making it so that all prefactors in the time
derivative of the modulated energy are controlled by a decaying bound on the
limiting solution.
