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Equivariant generative diffusion learns and generalizes the structural ensemble of amorphous oxides
Materials Science · Submitted 2 Oct 2026
abstract compiled · 2026-10-06 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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 $3\times10^{5}$ 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | background 0.77 | 0.08 | 0.04 | asserted 1.00 |
| s1 | 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. | contribution 0.75 | 0.96 | 0.42 | asserted 1.00 |
| s2 | The learning is data efficient. | result 0.68 | 0.79 | 0.05 | asserted 1.00 |
| s3 | 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 $3\times10^{5}$ atoms at a cost comparable to that of the cheapest classical pair potentials. | result 0.99 | 0.96 | 0.24 | asserted 1.00 |
| s4 | The trained model can propose amorphous atomic structures for first-principles relaxation to explore the configuration space. | contribution 0.60 | 0.89 | 0.11 | asserted 0.71 |
| s5 | For example, it locates an amorphous Zr-Ta-O structure $36$ meV/atom below the previously known minimum. | result 1.00 | 0.94 | 0.08 | asserted 1.00 |
| s6 | Generation can also extend beyond trained conditions to non-stoichiometric compositions, other mass densities, interfaces, and doping. | result 0.70 | 0.87 | 0.11 | asserted 0.59 |
| s7 | 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. | result 0.73 | 0.95 | 0.14 | asserted 1.00 |
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Original 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 $3\times10^{5}$ 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.
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