# Feynman-Kac-Flow: Inference Steering of Conditional Flow Matching to an Energy-Tilted Posterior

arXiv: https://arxiv.org/abs/2509.01543 · HTML: https://mlsanity.com/paper/2509.01543/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 14 of its 24 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 14 of 14)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding](https://mlsanity.com/paper/2408.08252/) (2024)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [Swallowing the Bitter Pill: Simplified Scalable Conformer Generation](https://mlsanity.com/paper/2311.17932/) (2023)
- [ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generation](https://mlsanity.com/paper/2410.22388/) (2024)
- [Message Passing Networks for Molecules with Tetrahedral Chirality](https://mlsanity.com/paper/2012.00094/) (2020)
- [Accelerating 3D Molecule Generation via Jointly Geometric Optimal Transport](https://mlsanity.com/paper/2405.15252/) (2024)

## Built on by (most cited first, 7 of 7)

- [Diamond Maps: Efficient Reward Alignment via Stochastic Flow Maps](https://mlsanity.com/paper/2602.05993/) (2026)
- [GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Models](https://mlsanity.com/paper/2509.25170/) (2025)
- [MolCrystalFlow: Molecular Crystal Structure Prediction via Flow Matching](https://mlsanity.com/paper/2602.16020/) (2026)
- [LatentFlow: A General Framework for Conditioning Stochastic Processes](https://mlsanity.com/paper/2607.12922/) (2026)
- [Potential-Guided Particle Steering for Negation-Constrained Dexterous Grasping](https://mlsanity.com/paper/2609.00555/) (2026)
- [Ensemble-Conditioned Molecular Design](https://mlsanity.com/paper/2609.15077/) (2026)
- [Traversing the Satisfaction-Diversity Frontier in Text-to-Image Diffusion](https://mlsanity.com/paper/2610.02372/) (2026)

## Abstract (arXiv)

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.