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

Slowly Annealed Langevin Dynamics tracks moving targets via time slowdown with non-asymptotic convergence guarantees, and velocity-aware extension enables training-free guided diffusion generation with convergence theory.

Atsushi Nitanda, Dake Bu, Yueming LYU, Tanya Veeravalli

Published 2026Sydney Poster Session 4 · Wed, Dec 9, 5:00 PM–8:00 PM local time · Hall 1-4arXiv ↗OpenReview ↗

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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.