Split-Flows: Measure Transport and Information Loss Across Molecular Resolutions
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.
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@inproceedings{hummerich_2026,
title = {Split-Flows: Measure Transport and Information Loss Across Molecular Resolutions},
author = {Sander Hummerich and Tristan Bereau and Ullrich Köthe},
booktitle = {Proceedings of the 29th International Conference on Artificial Intelligence and Statistics},
volume = {267},
year = {2026},
doi = {10.48550/arXiv.2511.01464},
url = {https://proceedings.mlr.press/v267/}
}