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

arXiv: https://arxiv.org/abs/2511.01464 · HTML: https://mlsanity.com/paper/2511.01464/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 37 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Builds on (most cited first, 8 of 8)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [Stochastic interpolants with data-dependent couplings](https://mlsanity.com/paper/2310.03725/) (2023)
- [Generative Coarse-Graining of Molecular Conformations](https://mlsanity.com/paper/2201.12176/) (2022)
- [DiAMoNDBack: Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping of Cα Protein Traces](https://mlsanity.com/paper/2307.12451/) (2023)

## Built on by (most cited first, 3 of 3)

- [Coarse-Grained Boltzmann Generators](https://mlsanity.com/paper/2602.10637/) (2026)
- [Recovering molecules from coarse-grained beads: free-energy-conditioned generative backmapping across chemical space](https://mlsanity.com/paper/2609.04432/) (2026)
- [Coarse-Graining Hidden Representations: Unsupervised Neuron Selection via Mapping Entropy](https://mlsanity.com/paper/2609.05126/) (2026)

## Abstract (arXiv)

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.