将能量势能引入条件流匹配，实现生成样本精准导向。
Feynman-Kac-Flow: Inference Steering of Conditional Flow Matching to an Energy-Tilted Posterior
- 用能量势能对输出分布进行倾斜，实现生成引导。
- 首次在条件流匹配中构建费曼-卡茨引导框架，支持高维分布生成。
- 成功解决化学反应过渡态的立体手性生成难题，适合分子模拟研究者。
条件流匹配（CFM）是一种快速且高质量的生成建模方法，但在许多应用中需要将生成样本精确引导至特定要求。尽管梯度引导、序贯蒙特卡洛引导或费曼-卡茨引导等方法已在扩散模型中成熟应用，但尚未扩展至流匹配方法。本文首次将此需求形式化为通过能量势能对输出进行倾斜，并推导出适用于CFM的费曼-卡茨引导框架。我们在一系列合成任务上评估该方法，包括高维空间中倾斜分布的生成，这对引导方法极具挑战性。进一步展示该方法在解决化学反应过渡态生成这一长期未解难题中的有效性，确保产物具有正确的手性——即反应路径需满足几何约束。相关代码已开源：https://github.com/heid-lab/fkflow。
原文摘要 · Abstract (English)
Conditional Flow Matching(CFM) represents a fast and high-quality approach to generative modelling, but in many applications it is of interest to steer the generated samples towards precise requirements. While steering approaches like gradient-based guidance, sequential Monte Carlo steering or Feynman-Kac steering are well established for diffusion models, they have not been extended to flow matching approaches yet. In this work, we formulate this requirement as tilting the output with an energy potential. We derive, for the first time, Feynman-Kac steering for CFM. We evaluate our approach on a set of synthetic tasks, including the generation of tilted distributions in a high-dimensional space, which is a particularly challenging case for steering approaches. We then demonstrate the impact of Feynman-Kac steered CFM on the previously unsolved challenge of generated transition states of chemical reactions with the correct chirality, where the reactants or products can have a different handedness, leading to geometric constraints of the viable reaction pathways connecting reactants and products. Code to reproduce this study is avaiable open-source at https://github.com/heid-lab/fkflow.
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