Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps
Abstract
Recent progress in flow-based generative modeling has led to models that output high-quality samples while using only a small number of function evaluations. However, at present, there is a lack of similar advances in estimating the model likelihood. In particular, most existing methods either rely on restrictive architectures that enable exact calculations, or use stochastic approximations such as Hutchinson's trace estimator that introduce substantial variance. In this work, we introduce SCAlable LikeLihood distillation of flOw maPs (SCALLOP). SCALLOP builds on the recently proposed F2D2, a likelihood flow map model that can generate samples and their densities in a small number of function evaluations. While F2D2 uses Hutchinson's estimator during training, we introduce an alternative and more scalable likelihood distillation objective that is Hutchinson-free and admits a vectorized formulation. Empirically, we demonstrate the effectiveness of SCALLOP as a Boltzmann generator in molecular science, and further validate its benefit on image datasets. SCALLOP significantly reduces both training variance and training time while consistently improving performance compared to F2D2, and is competitive with the state-of-the-art while achieving up to 10x inference speedup over the fastest baseline.
Related
- Bridging Stochastic Flow Maps and Boltzmann Generators with Normalizing Flows
- Mode Coverage in Normalizing Flow Boltzmann Generators via Log-Ratio Variation
- Boltzmann generators for amorphous particle systems
- Bayesian Graphical Models under Positivity Constraints: A Scalable Generalized Likelihood Approach
- Scalable, Likelihood-Free Calibration of Ice-Sheet Models with Deep Diffusion Emulators and Feature Matching
BibTeX
@misc{ouyang2026fewstep,
title = {{Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps}},
author = {RuiKang OuYang and Hanlin Yu and Xinyue Ai and Yutong He and Nicholas M. Boffi and Pradeep Ravikumar and Jose Miguel Hernandez-Lobato and Max Simchowitz and Benjamin Kurt Miller and Omar Chehab},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.29110},
eprint = {2606.29110},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.29110},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps
AU - RuiKang OuYang
AU - Hanlin Yu
AU - Xinyue Ai
AU - Yutong He
AU - Nicholas M. Boffi
AU - Pradeep Ravikumar
AU - Jose Miguel Hernandez-Lobato
AU - Max Simchowitz
AU - Benjamin Kurt Miller
AU - Omar Chehab
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2606.29110
UR - https://arxiv.org/abs/2606.29110
AB - Recent progress in flow-based generative modeling has led to models that output high-quality samples while using only a small number of function evaluations. However, at present, there is a lack of similar advances in estimating the model likelihood. In particular, most existing methods either rely on restrictive architectures that enable exact calculations, or use stochastic approximations such as Hutchinson's trace estimator that introduce substantial variance. In this work, we introduce SCAlable LikeLihood distillation of flOw maPs (SCALLOP). SCALLOP builds on the recently proposed F2D2, a likelihood flow map model that can generate samples and their densities in a small number of function evaluations. While F2D2 uses Hutchinson's estimator during training, we introduce an alternative and more scalable likelihood distillation objective that is Hutchinson-free and admits a vectorized formulation. Empirically, we demonstrate the effectiveness of SCALLOP as a Boltzmann generator in molecular science, and further validate its benefit on image datasets. SCALLOP significantly reduces both training variance and training time while consistently improving performance compared to F2D2, and is competitive with the state-of-the-art while achieving up to 10x inference speedup over the fastest baseline.
ER -