ICML 2026

FUSE: FK-Steered Multi-Modal Flow Matching for Efficient Simulation-Based Posterior Estimation

Weichen Qin1, Yufan Xie1, Peihao Wang2, Chia-Jui Chou1, Minghui Du3,4, Peng Xu3,4, Ziren Luo3,4, Yi Yang1, Jingyi Yu1, Bo Liang3,4, and Jiakai Zhang1,5

1ShanghaiTech University, Shanghai, China   2The University of Texas at Austin, Austin, TX, USA   3Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China   4Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), University of Chinese Academy of Sciences (UCAS), Beijing 100049, China   5Cellverse, Co., Ltd

Paper arXiv OpenReview Code Hugging Face coming soon Data coming soon

Paper: Author camera-ready version

TL;DR: FUSE combines multi-modal flow matching with Feynman-Kac-steered sampling for efficient simulation-based posterior estimation, with strong results on SBIBM benchmarks and real-world beta Pictoris b orbital characterization.

Method Overview

FUSE method pipeline for multi-modal flow matching and FK-steered inference.
FUSE keeps parameter and observation representations in distinct token streams while allowing structured interaction. The main SBIBM comparison evaluates FUSE without FK-steering to isolate architectural gains, while FK-steering is a separate test-time likelihood-informed correction for observation-specific refinement.

Abstract

Simulation-Based Inference is critical for scientific discovery, and generative models offer a promising path toward efficient posterior estimation. Existing methods often struggle with effective multimodal modeling and rely on fusion strategies that ignore structural differences between parameters and observations.

FUSE introduces a dual-track architecture that preserves distinct multimodal features while enabling dynamic interaction, together with an FK-steered sampling strategy that uses intermediate observation likelihoods to guide generative trajectories. The method improves posterior fidelity on standard SBI benchmarks and resolves complex degeneracies in beta Pictoris b orbital estimation.

Results

SBIBM Benchmark

SBIBM C2ST benchmark comparison across simulation budgets and tasks.
The 10-task SBIBM benchmark reports FUSE without FK-steering, so the result isolates the MM-DiT architecture from test-time guidance. FUSE is most effective in data-rich regimes and on harder posterior structures such as LV, SLCP, and SLCP-D.

beta Pictoris b

beta Pictoris b posterior reconstruction and normalized Sinkhorn comparison.
In the real-world 8-dimensional beta Pictoris b orbital-characterization task, FUSE follows the long-run PTMCMC reference more closely than NPE and FMPE, especially around sharp orientation-parameter degeneracies.
Appendix comparison between FUSE FK-steering and Naive Best-of-N selection.
Appendix Figure 5 compares sequential FK-steering with Naive Best-of-N final-step selection. The FK-steered trajectories better preserve high-density posterior structure for beta Pictoris b.

Release Status

Code is available on GitHub. Model artifacts and data resources are being prepared for external release and will be linked here as soon as they are available.

The arXiv preprint and OpenReview page are linked above. The PMLR link will be added once public. The current Paper link provides the author camera-ready version.

QR code for the FUSE project page.
Stable project-page QR code for https://qinwch.github.io/FUSE/.

BibTeX

@inproceedings{qin2026fuse,
  title     = {FUSE: FK-Steered Multi-Modal Flow Matching for Efficient Simulation-Based Posterior Estimation},
  author    = {Qin, Weichen and Xie, Yufan and Wang, Peihao and Chou, Chia-Jui and Du, Minghui and Xu, Peng and Luo, Ziren and Yang, Yi and Yu, Jingyi and Liang, Bo and Zhang, Jiakai},
  booktitle = {Proceedings of the International Conference on Machine Learning},
  year      = {2026}
}