Feynman-Kac Correctors: A New Approach for Controlling Diffusion Models

Score-based generative models have established themselves as leaders in various fields, from image generation to molecular design. Despite their power, precisely controlling the inference process, such as combining multiple pre-trained models, often proves challenging. Existing methods, like the so-called "classifier-free guidance," use heuristics to mix conditional and unconditional scores to approximately sample from conditional distributions. However, these methods do not approximate the intermediate distributions, which requires additional correction steps.

New research now presents an efficient and principled approach to sample from a sequence of tempered, geometrically averaged, or product distributions derived from pre-trained score-based models. The approach is based on the Feynman-Kac formula and introduces so-called Feynman-Kac correctors (FKCs). By carefully considering the terms in the corresponding partial differential equations (PDEs), a weighted simulation scheme is derived.

To simulate these PDEs, the researchers propose Sequential Monte Carlo (SMC) resampling algorithms that leverage scaling at inference time to improve sampling quality. The practical applicability of this method is demonstrated through various examples:

The researchers show how amortized sampling can be achieved by tempering during inference time. This allows for more efficient generation of samples. Furthermore, they demonstrate how multi-target molecule generation can be improved using pre-trained models. Finally, they show how FKCs can optimize "classifier-free guidance" for text-to-image generation. These results highlight the potential of FKCs to expand the control and flexibility of diffusion models.

The Significance for AI-Powered Content Creation

For companies like Mindverse, which specialize in AI-powered content creation, these advancements in diffusion models open up new possibilities. The improved control of the inference process allows for more precise adaptation of the generated content to specific requirements. The combination of multiple pre-trained models, enabled by FKCs, could, for example, lead to higher quality and diversity of generated texts, images, and other media. Furthermore, the more efficient sampling methods could increase generation speed and thus accelerate content creation.

The development of customized AI solutions, such as chatbots, voicebots, AI search engines, and knowledge systems, also benefits from these advances. FKCs could help improve the accuracy and relevance of the responses generated by these systems and make interaction with users more natural and effective.

Outlook

Research on Feynman-Kac correctors is still in its early stages, but holds great potential for the future of generative AI. Further research could explore the application of FKCs to other areas, such as the generation of 3D models or music. The development of more efficient algorithms for simulating the underlying PDEs is also a promising field of research. The combination of FKCs with other techniques, such as reinforcement learning, could also lead to further improvements.

Bibliography: - https://arxiv.org/abs/2503.02819 - https://chatpaper.com/chatpaper/de/paper/117556 - https://www.chatpaper.com/chatpaper/paper/117556 - https://www.alextong.net/publication/ - https://x.com/skoularidou/status/1898364199845208383 - https://huggingface.co/papers - https://iclr.cc/virtual/2025/papers.html - https://www.catalyzex.com/author/Arnaud%20Doucet - https://www.alextong.net/ - https://www.catalyzex.com/s/Text%20To%20Image%20Generation