# Diffusion annealed Langevin dynamics: a theoretical study

arXiv: https://arxiv.org/abs/2511.10406 · HTML: https://mlsanity.com/paper/2511.10406/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2025.

## Built on by (most cited first, 4 of 4)

- [Diffusion Path Samplers via Sequential Monte Carlo](https://mlsanity.com/paper/2601.21951/) (2026)
- [Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamics](https://mlsanity.com/paper/2602.01449/) (2026)
- [Slowly Annealed Langevin Dynamics: Theory and Applications to Training-Free Guided Generation](https://mlsanity.com/paper/2605.07950/) (2026)
- [Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures](https://mlsanity.com/paper/2605.16473/) (2026)

## Abstract (arXiv)

In this work we study the diffusion annealed Langevin dynamics, a score-based diffusion process recently introduced in the theory of generative models and which is an alternative to the classical overdamped Langevin diffusion. Our goal is to provide a rigorous construction and to study the theoretical efficiency of these models for general base distribution as well as target distribution. As a matter of fact these diffusion processes are a particular case of Nelson processes i.e. diffusion processes with a given flow of time marginals. Providing existence and uniqueness of the solution to the annealed Langevin diffusion leads to proving a Poincar'e inequality for the conditional distribution of X knowing X+Z=y uniformly in y, as recently observed by one of us and her coauthors. Part of this work is thus devoted to the study of such Poincar'e inequalities. Additionally we show that strengthening the Poincar'e inequality into a logarithmic Sobolev inequality improves the efficiency of the model.