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

Marta Skreta, Tara Akhound-Sadegh, Viktor Ohanesian, Roberto Bondesan, Alan Aspuru-Guzik, Arnaud Doucet, Rob Brekelmans, Alexander Tong, Kirill Neklyudov

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

Abstract: 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.

Lay Summary: Diffusion models are powerful tools for generating data like images, molecules, or text, but it is generally difficult to control their generation process. This paper introduces a method called Feynman-Kac Correctors (FKC), which allows for precise control over what a diffusion model generates without retraining it. FKC works by adjusting the way samples are drawn from the model, based on the Sequential Monte Carlo framework and, in particular, the Feynman-Kac formula. This enables a principled approach to sampling from combined target distributions, like mixtures or products of multiple pretrained models, or temperature-annealed target distributions. We show that FKC improves sampling in three settings: 1. classifier-free guidance, which is widely used in text-to-image generation, 2. generating molecules that satisfy multiple objectives (binding to two proteins simultaneously) and 3. sampling from physical systems at different temperatures using a model trained at a single temperature. Unlike traditional methods, FKC allows for flexible and efficient sampling with little added computation. This opens up new possibilities for applications in AI, drug discovery, and scientific simulations.

Link To Code: https://github.com/martaskrt/fkc-diffusion

Primary Area: Deep Learning->Generative Models and Autoencoders

Keywords: diffusion models, Sequential Monte Carlo, classifier-free guidance, product of experts, annealing

Submission Number: 11496