title: Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of
    Experts
summary: 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.
paper_authors._id: 67d0b23d33256c62f20dbc1f
paper_authors.name: Marta Skreta
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-03-12T08:41:41.189Z
paper_authors._id: 65a49ef27ec6af0f956a5c61
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/65a49ef27ec6af0f956a5c61/OGJ1OVezooF7dUn1SiEKG.jpeg
paper_authors.fullname: Marta Skreta
paper_authors.type: user
paper_authors.user: mskrt
paper_authors._id: 67d0b23d33256c62f20dbc20
paper_authors.name: Tara Akhound-Sadegh
paper_authors._id: 67d0b23d33256c62f20dbc21
paper_authors.name: Viktor Ohanesian
paper_authors._id: 67d0b23d33256c62f20dbc22
paper_authors.name: Roberto Bondesan
paper_authors._id: 67d0b23d33256c62f20dbc23
paper_authors.name: Alán Aspuru-Guzik
paper_authors._id: 67d0b23d33256c62f20dbc24
paper_authors.name: Arnaud Doucet
paper_authors._id: 67d0b23d33256c62f20dbc25
paper_authors.name: Rob Brekelmans
paper_authors._id: 67d0b23d33256c62f20dbc26
paper_authors.name: Alexander Tong
paper_authors._id: 67d0b23d33256c62f20dbc27
paper_authors.name: Kirill Neklyudov
paper_title: Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of
    Experts
paper_summary: 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.
paper_ai_keywords: score-based generative models inference-time behavior pretrained models classifier-free guidance conditional scores unconditional scores conditional distributions intermediate distributions corrected steps annealed distributions geometric-averaged distributions product distributions Feynman-Kac Correctors (FKCs) Feynman-Kac formula partial differential equations (PDEs) Sequential Monte Carlo (SMC) resampling algorithms inference-time scaling amortized sampling inference-time temperature annealing multi-objective molecule generation text-to-image generation