# Forward-KL Convergence of Time-Inhomogeneous Langevin Diffusions

arXiv: https://arxiv.org/abs/2601.22349 · HTML: https://mlsanity.com/paper/2601.22349/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2026.

## Built on by (most cited first, 2 of 2)

- [Time-Inhomogeneous Preconditioned Langevin Dynamics](https://mlsanity.com/paper/2605.06091/) (2026)
- [R'enyi Tracking Bounds for Langevin Dynamics with Moving Targets](https://mlsanity.com/paper/2609.17577/) (2026)

## Abstract (arXiv)

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.