Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918049396817920 |
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| author | Skreta, Marta Akhound-Sadegh, Tara Ohanesian, Viktor Bondesan, Roberto Aspuru-Guzik, Alán Doucet, Arnaud Brekelmans, Rob Tong, Alexander Neklyudov, Kirill |
| author_facet | Skreta, Marta Akhound-Sadegh, Tara Ohanesian, Viktor Bondesan, Roberto Aspuru-Guzik, Alán Doucet, Arnaud Brekelmans, Rob Tong, Alexander Neklyudov, Kirill |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02819 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts Skreta, Marta Akhound-Sadegh, Tara Ohanesian, Viktor Bondesan, Roberto Aspuru-Guzik, Alán Doucet, Arnaud Brekelmans, Rob Tong, Alexander Neklyudov, Kirill Machine Learning 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. |
| title | Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2503.02819 |