扩散中的费曼-卡克校正器：退火、引导与专家乘积

摘要

儘管基於分數的生成模型在多個領域中成為首選模型，但在控制推理時行為方面，尤其是在以原則性方式組合多個預訓練模型時，可用的工具卻相對有限。現有的無分類器指導方法採用了一種簡單的啟發式方法，通過混合條件與非條件分數來近似採樣條件分佈。然而，此類方法並未近似中間分佈，因此需要額外的“校正”步驟。在本研究中，我們提供了一種高效且基於原則的方法，用於從一系列退火、幾何平均或由預訓練分數模型導出的乘積分佈中進行採樣。我們基於著名的費曼-卡茨公式，通過仔細考慮適當偏微分方程（PDEs）中的項，推導出了一種加權模擬方案，稱之為費曼-卡茨校正器（FKCs）。為了模擬這些PDEs，我們提出了順序蒙特卡羅（SMC）重採樣算法，該算法利用推理時的縮放來提高採樣質量。我們通過提出基於推理時溫度退火的攤銷採樣、利用預訓練模型改進多目標分子生成，以及改進文本到圖像生成的無分類器指導，實證展示了我們方法的實用性。我們的代碼可在https://github.com/martaskrt/fkc-diffusion獲取。

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-卡克校正器：退火、引导与专家乘积

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

摘要

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