# Slowly Annealed Langevin Dynamics: Theory and Applications to Training-Free Guided Generation

arXiv: https://arxiv.org/abs/2605.07950 · HTML: https://mlsanity.com/paper/2605.07950/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 35 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 18 of 18)

- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [Dynamic Search for Inference-Time Alignment in Diffusion Models](https://mlsanity.com/paper/2503.02039/) (2025)
- [Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Models](https://mlsanity.com/paper/2502.11420/) (2025)
- [Simulated Tempering Langevin Monte Carlo II: An Improved Proof using Soft Markov Chain Decomposition](https://mlsanity.com/paper/1812.00793/) (2018)
- [Non-asymptotic Analysis of Diffusion Annealed Langevin Monte Carlo for Generative Modelling](https://mlsanity.com/paper/2502.09306/) (2025)
- [Training-Free Adaptation of Diffusion Models via Doob's h-Transform](https://mlsanity.com/paper/2602.16198/) (2026)
- [Towards a unified framework for guided diffusion models](https://mlsanity.com/paper/2512.04985/) (2025)
- [Evolvable Conditional Diffusion](https://mlsanity.com/paper/2506.13834/) (2025)
- [Inference-Time Alignment for Diffusion Models via Variationally Stable Doob's Matching](https://mlsanity.com/paper/2601.06514/) (2026)
- [Covariance-Adaptive Sequential Black-box Optimization for Diffusion Targeted Generation](https://mlsanity.com/paper/2406.00812/) (2024)
- [Diffusion annealed Langevin dynamics: a theoretical study](https://mlsanity.com/paper/2511.10406/) (2025)
- [Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamics](https://mlsanity.com/paper/2602.01449/) (2026)
- [Black-box Optimizer with Implicit Natural Gradient](https://mlsanity.com/paper/1910.04301/) (2019)

## Built on by (most cited first, 1 of 1)

- [Steepest Guidance: A Practical and Principled Approach to Inference-Time Alignment of Flow and Diffusion-based Models](https://mlsanity.com/paper/2609.39091/) (2026)

## Abstract (arXiv)

We study Slowly Annealed Langevin Dynamics (SALD), a sampler for tracking a path of moving target distributions and approximating the terminal target through time slowdown. We establish non-asymptotic convergence guarantees via a KL differential inequality, showing that slowdown improves tracking through contraction of intermediate targets and the complexity of the path. Motivated by training-free guided generation with pretrained score-based generative models, we further introduce Velocity-Aware SALD (VA-SALD), which explicitly incorporates the underlying marginal distributions of the pretrained model and uses slowdown to correct the additional deviation induced by guidance. This yields a principled framework for training-free guided generation for diffusion-based and related generative model families, together with convergence guarantees that clarify the roles of intermediate functional inequalities and guidance bias. Code is available at https://github.com/anitan0925/sald.