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 diffusion 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- as well as high-dimensional settings.
BibTeX
@inproceedings{
habring2026forwardkl,
title={Forward-{KL} Convergence of Time-Inhomogeneous Langevin Diffusions},
author={Andreas Habring and Martin Zach},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
url={https://openreview.net/forum?id=QJYHWz4x7H}
}