Equivariant generative diffusion learns and generalizes the structural ensemble of amorphous oxides
Abstract
Amorphous materials are statistical ensembles rather than definitive structures, and conventional density-functional (DFT) and machine-learned-potential simulations sample only a small part of that ensemble. We present an SE(3)-equivariant denoising-diffusion model that learns the configurational distribution of amorphous oxides, so the model itself is the structure database. The learning is data efficient. A model trained on 1,781 DFT configurations suffices to reproduce partial radial distribution functions, coordination statistics and bond-angle distributions, and to generate models of over 3×105 atoms at a cost comparable to that of the cheapest classical pair potentials. The trained model can propose amorphous atomic structures for first-principles relaxation to explore the configuration space. For example, it locates an amorphous Zr-Ta-O structure $36$ meV/atom below the previously known minimum. Generation can also extend beyond trained conditions to non-stoichiometric compositions, other mass densities, interfaces, and doping. First-principles verification confirms that generation can be steered to a requested energy, and shows that the denoising training loss does not rank generative quality, because the two measure different things.
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BibTeX
@misc{jiang2026equivariant,
title = {{Equivariant generative diffusion learns and generalizes the structural ensemble of amorphous oxides}},
author = {Jun Jiang and Ian Berry and James N. Fry and Hai-Ping Cheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03973},
eprint = {2610.03973},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03973},
}
RIS
TY - UNPB
TI - Equivariant generative diffusion learns and generalizes the structural ensemble of amorphous oxides
AU - Jun Jiang
AU - Ian Berry
AU - James N. Fry
AU - Hai-Ping Cheng
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03973
UR - https://arxiv.org/abs/2610.03973
AB - Amorphous materials are statistical ensembles rather than definitive structures, and conventional density-functional (DFT) and machine-learned-potential simulations sample only a small part of that ensemble. We present an SE(3)-equivariant denoising-diffusion model that learns the configurational distribution of amorphous oxides, so the model itself is the structure database. The learning is data efficient. A model trained on 1,781 DFT configurations suffices to reproduce partial radial distribution functions, coordination statistics and bond-angle distributions, and to generate models of over 3×10^5 atoms at a cost comparable to that of the cheapest classical pair potentials. The trained model can propose amorphous atomic structures for first-principles relaxation to explore the configuration space. For example, it locates an amorphous Zr-Ta-O structure $36$ meV/atom below the previously known minimum. Generation can also extend beyond trained conditions to non-stoichiometric compositions, other mass densities, interfaces, and doping. First-principles verification confirms that generation can be steered to a requested energy, and shows that the denoising training loss does not rank generative quality, because the two measure different things.
ER -