ICML 2025

Feynman-Kac Correctors in Diffusion:
Annealing, Guidance, and Product of Experts
Marta Skreta * 1 2 Tara Akhound-Sadegh * 3 4 Viktor Ohanesian * 5 Roberto Bondesan 5 Alán Aspuru-Guzik 1 2
Arnaud Doucet 6 Rob Brekelmans 2 Alexander Tong † 7 4 8 Kirill Neklyudov † 7 4 9
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. Exist-
ing classifier-free guidance methods use a sim-
ple heuristic to mix conditional and uncondi-
tional scores to approximately sample from con-
ditional distributions. However, such methods
do not approximate the intermediate distribu-
tions, necessitating additional ‘corrector’ steps.
In this work, we provide an efficient and prin-
cipled method for sampling from a sequence of
annealed, geometric-averaged, or product distri-
butions derived from pretrained score-based mod-
els. 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 sam-
pling quality. We empirically demonstrate the util-
ity of our methods by proposing amortized sam-
pling 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.
*Equal contribution ,†Equal senior-authorship 1University of
Toronto 2Vector Institute 3McGill University 4Mila - Quebec AI In-
stitute 5Imperial College London 6Google DeepMind 7Université
de Montréal 8Current AT affiliation: Duke University 9Institut
Courtois.
Correspondence to:
AT <a...