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

2026-05-08

AI Summary

This work addresses the challenge of achieving efficient and stable guided generation using pretrained score-based generative models without additional training. To this end, the authors propose Slow Annealing Langevin Dynamics (SALD), which employs a time-rescaling strategy to accurately track a dynamic target distribution path. They further introduce a velocity-aware variant, VA-SALD, that explicitly incorporates the marginal distribution of the pretrained model to correct guidance-induced bias. This study presents the first integration of time-rescaling mechanisms with Langevin dynamics for training-free guided generation and establishes a non-asymptotic convergence theory, elucidating the roles of intermediate functional inequalities and guidance bias. The proposed approach significantly enhances path-tracking stability and convergence efficiency while preserving high generation quality.

Abstract

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.

Problem

• training-free guided generation
• score-based generative models
• Langevin dynamics
• guidance bias
• convergence guarantees

Innovation

• Slowly Annealed Langevin Dynamics
• training-free guided generation
• score-based generative models
• non-asymptotic convergence
• Velocity-Aware SALD