# Score-based denoising for atomic structure identification

arXiv: https://arxiv.org/abs/2212.02421 · HTML: https://mlsanity.com/paper/2212.02421/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 66 references that are in the map.
- First posted on arXiv 5 Dec 2022.

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [Deep Learning for Automated Classification and Characterization of Amorphous Materials](https://mlsanity.com/paper/1909.04648/) (2019)

## Built on by (most cited first, 7 of 7)

- [Score dynamics: scaling molecular dynamics with picoseconds timestep via conditional diffusion model](https://mlsanity.com/paper/2310.01678/) (2023)
- [Molecular relaxation by reverse diffusion with time step prediction](https://mlsanity.com/paper/2404.10935/) (2024)
- [A Generative Diffusion Model for Amorphous Materials](https://mlsanity.com/paper/2507.05024/) (2025)
- [Scaling Kinetic Monte-Carlo Simulations of Grain Growth with Combined Convolutional and Graph Neural Networks](https://mlsanity.com/paper/2511.17848/) (2025)
- [Geometry Denoising with Preferred Normal Vectors](https://mlsanity.com/paper/2511.04848/) (2025)
- [A probabilistic framework for crystal structure denoising, phase classification, and order parameters](https://mlsanity.com/paper/2512.11077/) (2025)
- [Cross-Temperature Defect Identification in Atomistic Simulations via Multi-Level Domain Alignment](https://mlsanity.com/paper/2608.22074/) (2026)

## Abstract (arXiv)

We propose an effective method for removing thermal vibrations that complicate the task of analyzing complex dynamics in atomistic simulation of condensed matter. Our method iteratively subtracts thermal noises or perturbations in atomic positions using a denoising score function trained on synthetically noised but otherwise perfect crystal lattices. The resulting denoised structures clearly reveal underlying crystal order while retaining disorder associated with crystal defects. Purely geometric, agnostic to interatomic potentials, and trained without inputs from explicit simulations, our denoiser can be applied to simulation data generated from vastly different interatomic interactions. The denoiser is shown to improve existing classification methods such as common neighbor analysis and polyhedral template matching, reaching perfect classification accuracy on a recent benchmark dataset of thermally perturbed structures up to the melting point. Demonstrated here in a wide variety of atomistic simulation contexts, the denoiser is general, robust, and readily extendable to delineate order from disorder in structurally and chemically complex materials.