扩散中的费曼-卡茨校正器：退火、引导与专家乘积

摘要

尽管基于分数的生成模型在多个领域中成为首选，但在推理阶段以原则性方式控制行为（例如组合多个预训练模型）的工具却相对有限。现有的无分类器引导方法采用一种简单的启发式策略，通过混合条件与无条件分数来近似从条件分布中采样。然而，这类方法未能近似中间分布，因而需要额外的“校正”步骤。在本研究中，我们提出了一种高效且原则性的方法，用于从一系列基于预训练分数模型的退火、几何平均或乘积分布中采样。我们基于著名的费曼-卡茨公式，通过精确考虑相应偏微分方程（PDEs）中的项，推导出一种称为费曼-卡茨校正器（FKCs）的加权模拟方案。为了模拟这些PDEs，我们提出了序贯蒙特卡洛（SMC）重采样算法，该算法利用推理时的缩放来提升采样质量。我们通过提出基于推理时温度退火的摊销采样、利用预训练模型改进多目标分子生成，以及增强文本到图像生成的无分类器引导，实证展示了我们方法的实用性。我们的代码可在https://github.com/martaskrt/fkc-diffusion获取。

English

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

扩散中的费曼-卡茨校正器：退火、引导与专家乘积

Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts

摘要

Summary

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