Autoregressive Boltzmann Generators

Danyal Rehman, Charlie B. Tan, Yoshua Bengio, Joey Bose, Alexander Tong
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:104219-104250, 2026.

Abstract

Efficient sampling of molecular systems at thermodynamic equilibrium is a hallmark challenge in statistical physics. This challenge has driven the development of Boltzmann Generators (BGs), which allow rapid generation of uncorrelated equilibrium samples by combining a generative model with exact likelihoods and an importance sampling correction. However, modern BGs predominantly rely on Normalizing Flows (NFs), which either suffer from limited expressivity due to strict invertibility constraints (discrete time) or computationally expensive likelihoods (continuous time). In this paper, we propose Autoregressive Boltzmann Generators (ArBG), a novel autoregressive modelling framework that overcomes these limitations by departing from the flow-based BG paradigm. ArBG circumvents the topological constraints of flows and enables sequential inference-time interventions, while offering enhanced scalability by leveraging architectures effective in Large Language Models. We empirically demonstrate that ArBG leads to significant improvements over flow-based models across all benchmarks, but particularly in larger peptide systems such as the 10-residue Chignolin. Furthermore, we introduce Robin, a 132M parameter transferable model trained with the ArBG framework which improves over the previous state-of-the-art, reducing the zero-shot energy error, $\mathcal{E}$-$\mathcal{W}_2$, on 8-residue systems by $\sim 60$%.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-rehman26a, title = {Autoregressive Boltzmann Generators}, author = {Rehman, Danyal and Tan, Charlie B. and Bengio, Yoshua and Bose, Joey and Tong, Alexander}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {104219--104250}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/rehman26a/rehman26a.pdf}, url = {https://proceedings.mlr.press/v306/rehman26a.html}, abstract = {Efficient sampling of molecular systems at thermodynamic equilibrium is a hallmark challenge in statistical physics. This challenge has driven the development of Boltzmann Generators (BGs), which allow rapid generation of uncorrelated equilibrium samples by combining a generative model with exact likelihoods and an importance sampling correction. However, modern BGs predominantly rely on Normalizing Flows (NFs), which either suffer from limited expressivity due to strict invertibility constraints (discrete time) or computationally expensive likelihoods (continuous time). In this paper, we propose Autoregressive Boltzmann Generators (ArBG), a novel autoregressive modelling framework that overcomes these limitations by departing from the flow-based BG paradigm. ArBG circumvents the topological constraints of flows and enables sequential inference-time interventions, while offering enhanced scalability by leveraging architectures effective in Large Language Models. We empirically demonstrate that ArBG leads to significant improvements over flow-based models across all benchmarks, but particularly in larger peptide systems such as the 10-residue Chignolin. Furthermore, we introduce Robin, a 132M parameter transferable model trained with the ArBG framework which improves over the previous state-of-the-art, reducing the zero-shot energy error, $\mathcal{E}$-$\mathcal{W}_2$, on 8-residue systems by $\sim 60$%.} }
Endnote
%0 Conference Paper %T Autoregressive Boltzmann Generators %A Danyal Rehman %A Charlie B. Tan %A Yoshua Bengio %A Joey Bose %A Alexander Tong %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-rehman26a %I PMLR %P 104219--104250 %U https://proceedings.mlr.press/v306/rehman26a.html %V 306 %X Efficient sampling of molecular systems at thermodynamic equilibrium is a hallmark challenge in statistical physics. This challenge has driven the development of Boltzmann Generators (BGs), which allow rapid generation of uncorrelated equilibrium samples by combining a generative model with exact likelihoods and an importance sampling correction. However, modern BGs predominantly rely on Normalizing Flows (NFs), which either suffer from limited expressivity due to strict invertibility constraints (discrete time) or computationally expensive likelihoods (continuous time). In this paper, we propose Autoregressive Boltzmann Generators (ArBG), a novel autoregressive modelling framework that overcomes these limitations by departing from the flow-based BG paradigm. ArBG circumvents the topological constraints of flows and enables sequential inference-time interventions, while offering enhanced scalability by leveraging architectures effective in Large Language Models. We empirically demonstrate that ArBG leads to significant improvements over flow-based models across all benchmarks, but particularly in larger peptide systems such as the 10-residue Chignolin. Furthermore, we introduce Robin, a 132M parameter transferable model trained with the ArBG framework which improves over the previous state-of-the-art, reducing the zero-shot energy error, $\mathcal{E}$-$\mathcal{W}_2$, on 8-residue systems by $\sim 60$%.
APA
Rehman, D., Tan, C.B., Bengio, Y., Bose, J. & Tong, A.. (2026). Autoregressive Boltzmann Generators. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:104219-104250 Available from https://proceedings.mlr.press/v306/rehman26a.html.

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