# ChargeFlow: Flow-Matching Refinement of Charge-Conditioned Electron Densities

arXiv: https://arxiv.org/abs/2603.23943 · HTML: https://mlsanity.com/paper/2603.23943/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## 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)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids](https://mlsanity.com/paper/2112.00652/) (2021)
- [Higher-Order Equivariant Neural Networks for Charge Density Prediction in Materials](https://mlsanity.com/paper/2312.05388/) (2023)
- [Image Super-resolution Inspired Electron Density Prediction](https://mlsanity.com/paper/2402.12335/) (2024)

## Abstract (arXiv)

Accurate charge densities are central to electronic-structure theory, but computing charge-state-dependent densities with density functional theory remains too expensive for large-scale screening and defect workflows. We present ChargeFlow, a flow-matching refinement model that transforms a charge-conditioned superposition of atomic densities into the corresponding DFT electron density on the native periodic real-space grid using a 3D U-Net velocity field. Trained on 9,502 charged Materials Project-derived calculations and evaluated on an external 1,671-structure benchmark spanning perovskites, charged defects, diamond defects, metal-organic frameworks, and organic crystals, ChargeFlow is not uniformly best on every in-distribution class but is strongest on problems dominated by nonlocal charge redistribution and charge-state extrapolation, improving deformation-density error from 3.62% to 3.21% and charge- response cosine similarity from 0.571 to 0.655 relative to a ResNet baseline. The predicted densities remain chemically useful under downstream analysis, yielding successful Bader partitioning on all 1,671 benchmark structures and high-fidelity electrostatic potentials, which positions flow matching as a practical density-refinement strategy for charged materials.