Constrained Diffusion for Accelerated Structure Relaxation of Inorganic Solids with Point Defects

Jingyi Cui; Jacob K. Christopher; Ankita Biswas; Prasanna V. Balachandran; Ferdinando Fioretto

cond-mat.mtrl-sciFeb 22, 2026

Constrained Diffusion for Accelerated Structure Relaxation of Inorganic Solids with Point Defects

Authors: Jingyi Cui, Jacob K. Christopher, Ankita Biswas, Prasanna V. Balachandran, Ferdinando Fioretto

Organizations: University of Virginia

Abstract

Point defects affect material properties by altering electronic states and modifying local bonding environments. However, high-throughput first-principles simulations of point defects are costly due to large simulation cells and complex energy landscapes. To this end, we propose a generative framework for simulating point defects, overcoming the limits of costly first-principles simulators. By leveraging a primal-dual algorithm, we introduce a constraint-aware diffusion model which outperforms existing constrained diffusion approaches in this domain. Across six defect configuration settings for Bi2Te3, the proposed approach provides state-of-the-art performance generating physically grounded structures.

Figures & tables

Figure 1: (a) A 2 $\times$ 2 $\times$ 2 supercell of $\text{Bi}{\vphantom{\text{X}}}_{\smash[t]{\text{2}}}\text{Te}{\vphantom{\text{X}}}_{\smash[t]{\text{3}}}$ for DFT simulations. (b) Another supercell representation, highlighting quintuple layer, structure Te(1)–Bi–Te(2)–Bi–Te(1) with vacancy defect.

Method	Config	RMSD $\downarrow$	RDF $\downarrow$	Force (eV/Å) $\downarrow$
Conditional DM	16Bi + 21Te	$1.86\pm 0.33$	$65.85\pm 19.75$	$1.85\times 10^{9}$
Conditional DM	16Bi + 22Te	$1.93\pm 0.36$	$82.11\pm 29.54$	$3.49\times 10^{9}$
Projected DM	16Bi + 21Te	$2.54\pm 0.55$	$1.11\pm 0.77$	$8.35\times 10^{2}$
Projected DM	16Bi + 22Te	$1.41\pm 0.83$	$0.78\pm 0.55$	$7.20\times 10^{1}$
Post-proc DM	16Bi + 21Te	$2.30\pm 0.40$	$27.25\pm 28.30$	$8.45\times 10^{6}$
Post-proc DM	16Bi + 22Te	$1.14\pm 0.65$	$21.82\pm 28.09$	$9.29\times 10^{6}$

Table 1: Empirical comparison across stoichiometric configurations. Extended table in Appendix C .

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Method	Config	RMSD $\downarrow$	RDF $\downarrow$	Force (eV/Å) $\downarrow$
Conditional DM	16Bi + 21Te	$1.86\pm 0.33$	$65.85\pm 19.75$	$1.85\times 10^{9}$
	16Bi + 22Te	$1.93\pm 0.36$	$82.11\pm 29.54$	$3.49\times 10^{9}$
	18Bi + 22Te	$2.10\pm 0.38$	$87.90\pm 39.29$	$1.64\times 10^{9}$
	14Bi + 26Te	$1.22\pm 0.60$	$40.63\pm 41.77$	$1.28\times 10^{9}$
	14Bi + 24Te	$0.75\pm 0.81$	$27.41\pm 44.46$	$5.52\times 10^{8}$
	13Bi + 24Te	$0.95\pm 0.51$	$22.17\pm 33.53$	$3.90\times 10^{8}$

Appendix

Table 2: Complete experimental results across all six stoichiometric configurations in four defect categories: Te vacancies (16Bi + 22Te, 16Bi + 21Te), Bi vacancies (14Bi + 24Te, 13Bi + 24Te), Bi in Te antisites (18Bi + 22Te), and Te in Bi antisites (14Bi + 26Te).

Computational Materials Science

Computational materials science uses computation and data-driven models to predict, explain, and design materials and their properties.

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Diffusion Model Guidance Crystal Structure Generation Computational Materials Science

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Generative diffusion models have emerged as powerful tools for the discovery of inorganic crystal structures, yet steering their sampling process toward user-defined physical and chemical objectives remains challenging. We present a computational framework that integrates adaptive constraint guidance into a pre-trained crystal diffusion model, enabling the generation of candidate structures that satisfy targeted structural and chemical requirements without model retraining. The approach incorporates differentiable constraint functions directly during sampling, providing an interpretable mechanism for expert-driven exploration of the crystal structure space. To assess the reliability of generated candidates, we introduce a multi-stage validation workflow combining descriptor-based analysis, duplicate removal, comparison with reference crystal databases, graph neural network energy prediction, and thermodynamic stability evaluation through convex-hull analysis. The framework is applied to several classes of inorganic compounds and to constraints involving atomic volume, local coordination environments, and near-neighbor structural motifs. Results demonstrate that adaptive guidance effectively redirects the sampling distribution toward structures exhibiting the desired characteristics while preserving chemical plausibility. Subsequent validation reveals which generated candidates remain viable after energetic and thermodynamic screening. The proposed methodology provides a practical and transparent strategy for incorporating expert knowledge into crystal generative models and establishes a general computational framework for constrained materials discovery.

Abstract

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