提出慢速退火Langevin采样，实现无需训练的可控生成
Slowly Annealed Langevin Dynamics: Theory and Applications to Training-Free Guided Generation
- 通过渐进退火设计采样路径，利用时间减速提升对目标分布的追踪能力
- 理论证明退火速度越慢，生成结果与目标分布的差异越小
- 适用于预训练扩散模型的无训练引导生成，适合需要快速部署的场景
我们研究了慢速退火Langevin动力学（SALD），这是一种用于追踪移动目标分布并随时间减速逼近终端目标的采样方法。通过引入KL微分不等式，建立了非渐近收敛保证，表明减速可增强中间目标的收缩性及路径复杂度的控制。为实现基于预训练得分模型的无训练引导生成，我们进一步提出速度感知的SALD（VA-SALD），显式融入预训练模型的边际分布，并利用减速校正引导带来的额外偏差。该方法为基于扩散及其他生成模型家族提供了原理严谨的无训练引导生成框架，同时明确了中间函数不等式与引导偏置的作用。代码已开源：https://github.com/anitan0925/sald。
原文摘要 · Abstract (English)
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.
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