Forward-KL Convergence of Time-Inhomogeneous Langevin Diffusions
Abstract
Many practical samplers rely on time-dependent drifts -- often induced by annealing or tempering schedules -- to improve exploration and stability. This motivates a unified non-asymptotic analysis of the corresponding Langevin diffusions and their discretizations. We provide a convergence analysis that includes non-asymptotic bounds for the continuous-time diffusion and its Euler--Maruyama discretization in the forward-Kullback--Leibler divergence under a single set of abstract conditions on the time-dependent drift. The results apply to many practically-relevant annealing schemes, including geometric tempering and annealed Langevin sampling. In addition, we provide numerical experiments comparing the annealing schemes covered by our theory in low- and high-dimensional settings.
Keywords
Cite
@article{arxiv.2601.22349,
title = {Forward-KL Convergence of Time-Inhomogeneous Langevin Diffusions},
author = {Andreas Habring and Martin Zach},
journal= {arXiv preprint arXiv:2601.22349},
year = {2026}
}