# Structural Constraint Integration in Generative Model for Discovery of Quantum Material Candidates

arXiv: https://arxiv.org/abs/2407.04557 · HTML: https://mlsanity.com/paper/2407.04557/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 8 of its 45 references that are in the map.
- First posted on arXiv 5 Jul 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

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

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [MatterGen: a generative model for inorganic materials design](https://mlsanity.com/paper/2312.03687/) (2023)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [Scalable Diffusion for Materials Generation](https://mlsanity.com/paper/2311.09235/) (2023)
- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (2024)

## Abstract (arXiv)

Billions of organic molecules are known, but only a tiny fraction of the functional inorganic materials have been discovered, a particularly relevant problem to the community searching for new quantum materials. Recent advancements in machine-learning-based generative models, particularly diffusion models, show great promise for generating new, stable materials. However, integrating geometric patterns into materials generation remains a challenge. Here, we introduce Structural Constraint Integration in the GENerative model (SCIGEN). Our approach can modify any trained generative diffusion model by strategic masking of the denoised structure with a diffused constrained structure prior to each diffusion step to steer the generation toward constrained outputs. Furthermore, we mathematically prove that SCIGEN effectively performs conditional sampling from the original distribution, which is crucial for generating stable constrained materials. We generate eight million compounds using Archimedean lattices as prototype constraints, with over 10% surviving a multi-staged stability pre-screening. High-throughput density functional theory (DFT) on 26,000 survived compounds shows that over 50% passed structural optimization at the DFT level. Since the properties of quantum materials are closely related to geometric patterns, our results indicate that SCIGEN provides a general framework for generating quantum materials candidates.