Split-Flows: Measure Transport and Information Loss Across Molecular Resolutions

Sander Hummerich, Ullrich Koethe, Tristan Bereau
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1747-1755, 2026.

Abstract

By reducing resolution, coarse-grained models greatly accelerate molecular simulations, unlocking access to long-timescale phenomena, though at the expense of microscopic information. Recovering this fine-grained detail is essential for tasks that depend on atomistic accuracy, making backmapping a central challenge in molecular modeling. We introduce split-flows, a novel flow-based approach that reinterprets backmapping as a continuous-time measure transport across resolutions. Unlike existing generative strategies, split-flows establish a direct probabilistic link between resolutions, enabling expressive conditional sampling of atomistic structures and—for the first time—a tractable route to computing mapping entropies, an information-theoretic measure of the irreducible detail lost in coarse-graining. We demonstrate these capabilities on diverse molecular systems, including Chignolin, a lipid bilayer, and alanine dipeptide, highlighting split-flows as a principled framework for accurate backmapping and systematic evaluation of coarse-grained models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-hummerich26a, title = { Split-Flows: Measure Transport and Information Loss Across Molecular Resolutions }, author = {Hummerich, Sander and Koethe, Ullrich and Bereau, Tristan}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1747--1755}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/hummerich26a/hummerich26a.pdf}, url = {https://proceedings.mlr.press/v300/hummerich26a.html}, abstract = { By reducing resolution, coarse-grained models greatly accelerate molecular simulations, unlocking access to long-timescale phenomena, though at the expense of microscopic information. Recovering this fine-grained detail is essential for tasks that depend on atomistic accuracy, making backmapping a central challenge in molecular modeling. We introduce split-flows, a novel flow-based approach that reinterprets backmapping as a continuous-time measure transport across resolutions. Unlike existing generative strategies, split-flows establish a direct probabilistic link between resolutions, enabling expressive conditional sampling of atomistic structures and—for the first time—a tractable route to computing mapping entropies, an information-theoretic measure of the irreducible detail lost in coarse-graining. We demonstrate these capabilities on diverse molecular systems, including Chignolin, a lipid bilayer, and alanine dipeptide, highlighting split-flows as a principled framework for accurate backmapping and systematic evaluation of coarse-grained models. } }
Endnote
%0 Conference Paper %T Split-Flows: Measure Transport and Information Loss Across Molecular Resolutions %A Sander Hummerich %A Ullrich Koethe %A Tristan Bereau %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-hummerich26a %I PMLR %P 1747--1755 %U https://proceedings.mlr.press/v300/hummerich26a.html %V 300 %X By reducing resolution, coarse-grained models greatly accelerate molecular simulations, unlocking access to long-timescale phenomena, though at the expense of microscopic information. Recovering this fine-grained detail is essential for tasks that depend on atomistic accuracy, making backmapping a central challenge in molecular modeling. We introduce split-flows, a novel flow-based approach that reinterprets backmapping as a continuous-time measure transport across resolutions. Unlike existing generative strategies, split-flows establish a direct probabilistic link between resolutions, enabling expressive conditional sampling of atomistic structures and—for the first time—a tractable route to computing mapping entropies, an information-theoretic measure of the irreducible detail lost in coarse-graining. We demonstrate these capabilities on diverse molecular systems, including Chignolin, a lipid bilayer, and alanine dipeptide, highlighting split-flows as a principled framework for accurate backmapping and systematic evaluation of coarse-grained models.
APA
Hummerich, S., Koethe, U. & Bereau, T.. (2026). Split-Flows: Measure Transport and Information Loss Across Molecular Resolutions . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1747-1755 Available from https://proceedings.mlr.press/v300/hummerich26a.html.

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