Feynman-Kac steering

Summary

Feynman-Kac steering is a sequential Monte Carlo-based scheme for guiding diffusion models at inference time. Examples include its use in the Alphafold3 clone Boltz.

It reweights a base model using a reward,

$$p_{\mathrm{FK}}(x_0\mid c)\propto p_{\theta }(x_0\mid c)\exp \left[\lambda r(x_0,c)\right],$$

where $\lambda$ acts like an inverse temperature: large values concentrate particles around high-reward modes, while small values approach the unguided prior (1).

At scheduled intermediate steps, particles are sampled with replacement from a multinomial distribution parameterized by their normalized potential scores, duplicating high-potential trajectories before the next propagation step. The released implementation supports adaptive resampling: at candidate steps it resamples only when the ESS is below $k/2$, otherwise leaving the particle population unchanged (1). Hartman et al. instead resample every $\Delta t$ steps beginning at a chosen $t_{\mathrm{start}}$; resampling less frequently preserves exploration, while delaying guidance until after the high-noise regime improves rewards because early reward estimates are unreliable (2). Useful gains have been reported with only a few particles (1,2).

Figures

Ref (2)

Ref (3)

1.

Singhal R, Horvitz Z, Teehan R, Ren M, Yu Z, McKeown K, et al. A General Framework for Inference-time Scaling and Steering of Diffusion Models. In: Proceedings of the 42nd International Conference on Machine Learning. PMLR; 2025. p. 55810–27. Available from: https://proceedings.mlr.press/v267/singhal25b.html

2.

Hartman E, Wallin J, Malmström J, Olsson J. Controllable protein design with particle-based Feynman-Kac steering. 2025; Available from: https://arxiv.org/abs/2511.09216

3.

Rector-Brooks J, Lambert T, Skreta M, Roth D, Long Y, Li Z-Q, et al. General Multimodal Protein Design Enables DNA-Encoding of Chemistry. 2026; Available from: https://arxiv.org/abs/2604.05181