# Ab Initio Structure Solutions from Nanocrystalline Powder Diffraction Data

arXiv: https://arxiv.org/abs/2406.10796 · HTML: https://mlsanity.com/paper/2406.10796/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 74 references that are in the map.
- First posted on arXiv 16 Jun 2024.

## Builds on (most cited first, 20 of 20)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [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)
- [Physics Guided Deep Learning for Generative Design of Crystal Materials with Symmetry Constraints](https://mlsanity.com/paper/2203.14352/) (2022)
- [Towards Symmetry-Aware Generation of Periodic Materials](https://mlsanity.com/paper/2307.02707/) (2023)
- [Diffusion probabilistic models enhance variational autoencoder for crystal structure generative modeling](https://mlsanity.com/paper/2308.02165/) (2023)
- [A probabilistic deep learning approach to automate the interpretation of multi-phase diffraction spectra](https://mlsanity.com/paper/2103.16664/) (2021)
- [End-to-End Crystal Structure Prediction from Powder X-Ray Diffraction](https://mlsanity.com/paper/2401.03862/) (2024)
- [Spectroscopy-Guided Discovery of Three-Dimensional Structures of Disordered Materials with Diffusion Models](https://mlsanity.com/paper/2312.05472/) (2023)
- [Identification of Crystal Symmetry from Noisy Diffraction Patterns by A Shape Analysis and Deep Learning](https://mlsanity.com/paper/2005.12476/) (2020)
- [CrysFormer: Protein Structure Prediction via 3d Patterson Maps and Partial Structure Attention](https://mlsanity.com/paper/2310.03899/) (2023)

## Built on by (most cited first, 12 of 12)

- [deCIFer: Crystal Structure Prediction from Powder Diffraction Data using Autoregressive Language Models](https://mlsanity.com/paper/2502.02189/) (2025)
- [A Generative Diffusion Model for Amorphous Materials](https://mlsanity.com/paper/2507.05024/) (2025)
- [Beyond Structure: Invariant Crystal Property Prediction with Pseudo-Particle Ray Diffraction](https://mlsanity.com/paper/2509.21778/) (2025)
- [Generative Models for Crystalline Materials](https://mlsanity.com/paper/2511.22652/) (2025)
- [XDecomposer: Learning Prior-Free Set Decomposition for Multiphase X-ray Diffraction](https://mlsanity.com/paper/2605.05866/) (2026)
- [Representation of Inorganic Synthesis Reactions and Prediction: Graphical Framework and Datasets](https://mlsanity.com/paper/2512.02947/) (2025)
- [Physically-Constrained Autoencoder-Assisted Bayesian Optimization for Refinement of High-Dimensional Defect-Sensitive Single Crystalline Structure](https://mlsanity.com/paper/2601.00855/) (2025)
- [XRDiff: Crystal Structure Prediction from Powder X-Ray Diffraction Data Using Diffusion Models](https://mlsanity.com/paper/2606.14003/) (2026)
- [Symmetry- and Property-Aware Crystal Generation with Reinforcement Learning for Inverse Materials Design](https://mlsanity.com/paper/2609.13468/) (2026)
- [CbLDM: A Diffusion Model for recovering nanostructure from atomic pair distribution function](https://mlsanity.com/paper/2509.01370/) (2025)
- [XDXD: End-to-end crystal structure determination with low resolution X-ray diffraction](https://mlsanity.com/paper/2510.17936/) (2025)
- [Machine Learning-Driven Crystal System Prediction for Perovskites Using Augmented X-ray Diffraction Data](https://mlsanity.com/paper/2602.04435/) (2026)

## Abstract (arXiv)

A major challenge in materials science is the determination of the structure of nanometer sized objects. Here we present a novel approach that uses a generative machine learning model based on diffusion processes that is trained on 45,229 known structures. The model factors both the measured diffraction pattern as well as relevant statistical priors on the unit cell of atomic cluster structures. Conditioned only on the chemical formula and the information-scarce finite-size broadened powder diffraction pattern, we find that our model, PXRDnet, can successfully solve simulated nanocrystals as small as 10 angstroms across 200 materials of varying symmetry and complexity, including structures from all seven crystal systems. We show that our model can successfully and verifiably determine structural candidates four out of five times, with average error among these candidates being only 7% (as measured by post-Rietveld refinement R-factor). Furthermore, PXRDnet is capable of solving structures from noisy diffraction patterns gathered in real-world experiments. We suggest that data driven approaches, bootstrapped from theoretical simulation, will ultimately provide a path towards determining the structure of previously unsolved nano-materials.