We introduce 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). We show the utility of FKC on applications in several domains: classical image generation, multi-conditional molecule design, and sampling from Boltzmann densities.

├── applications
│   ├── molecules
│   │    └── dual_target_sbdd
│   │        - code for generating 3D molecules conditioned on two protein pockets (FKC Product)
│   ├── temperature_annealing
│   │        - code for temperature annealing experiments on 2D GMMs & LJ-13 (FKC Annealing)
│   └── images
│            - coming soon! (FKC CFG)
└── notebooks
        - examples and notebooks for annealing/product on 2D Gaussians

Diffusion (diffusion_edu.ipynb): introduction to diffusion models

Annealing (diffusion_annealed.ipynb): toy example of FKC annealing incl. resampling code (prop 3.2)

Product (diffusion_product.ipynb): toy example of FKC product incl. resampling code (prop 3.3)

Each experiment has a different procedure and requires installing specific dependencies. Please follow the links below to run the code for each experiment:

• FKC CFG | Stable Diffusion (SD) XL: coming soon! (section 5.1)
• FKC Annealing | Temperature Annealing: temperature annealing experiments on 2D GMMs and 13-particle Lennard-Jones potential (section 5.2)
• FKC Product | Multi-Target Structure-Based Drug Design: generate 3D molecule simultaneously conditioned on two protein prockets using FKC product (section 5.3)

@article{skreta2025feynman,
  title={Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts},
  author={Skreta, Marta and Akhound-Sadegh, Tara and Ohanesian, Viktor and Bondesan, Roberto and Aspuru-Guzik, Al{\'a}n and Doucet, Arnaud and Brekelmans, Rob and Tong, Alexander and Neklyudov, Kirill},
  journal={arXiv preprint arXiv:2503.02819},
  year={2025}
}