Rapid convergence of Langevin AIS for multimodal distributions on $\mathbb{R}^d$

We study annealed importance sampling (AIS) driven by the overdamped Langevin diffusion, targeting a multimodal Gibbs measure $π_\varepsilon \propto e^{-U/\varepsilon}$ on $\mathbb{R}^d$ at low temperature $\varepsilon$. For a potential $U$ with nondegenerate critical points, finitely many wells of