# Equivariant Diffusion for Crystal Structure Prediction

arXiv: https://arxiv.org/abs/2512.07289 · HTML: https://mlsanity.com/paper/2512.07289/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 27 of its 65 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## 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, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties](https://mlsanity.com/paper/2005.07609/) (2020)
- [Data-Driven Approach to Encoding and Decoding 3-D Crystal Structures](https://mlsanity.com/paper/1909.00949/) (2019)
- [Towards Symmetry-Aware Generation of Periodic Materials](https://mlsanity.com/paper/2307.02707/) (2023)
- [Crystal structure prediction of materials with high symmetry using differential evolution](https://mlsanity.com/paper/2104.09764/) (2021)

## Built on by (most cited first, 9 of 9)

- [DMFlow: Disordered Materials Generation by Flow Matching](https://mlsanity.com/paper/2602.04734/) (2026)
- [SLayerGen: a Crystal Generative Model for all Space and Layer Groups](https://mlsanity.com/paper/2605.08262/) (2026)
- [CrystalREPA: Transferring Physical Priors from Universal MLIPs to Crystal Generative Models](https://mlsanity.com/paper/2605.08960/) (2026)
- [CrystalFormer-CSP: Thinking Fast and Slow for Crystal Structure Prediction](https://mlsanity.com/paper/2512.18251/) (2025)
- [EquiFusion: Kinematics-Agnostic Human Motion Prediction via Equivariant Latent Diffusion](https://mlsanity.com/paper/2607.10984/) (2026)
- [Quotient-Space Diffusion Models](https://mlsanity.com/paper/2604.21809/) (2026)
- [Deep Generative Crystal Structure Prediction: A Benchmark Study and a Controlled Test of Prototype Dependence](https://mlsanity.com/paper/2609.26502/) (2026)
- [EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations](https://mlsanity.com/paper/2610.01315/) (2026)
- [EDISCO: Equivariant DIScrete Diffusion for Euclidean Combinatorial Optimization](https://mlsanity.com/paper/2610.04953/) (2026)

## Abstract (arXiv)

In addressing the challenge of Crystal Structure Prediction (CSP), symmetry-aware deep learning models, particularly diffusion models, have been extensively studied, which treat CSP as a conditional generation task. However, ensuring permutation, rotation, and periodic translation equivariance during diffusion process remains incompletely addressed. In this work, we propose EquiCSP, a novel equivariant diffusion-based generative model. We not only address the overlooked issue of lattice permutation equivariance in existing models, but also develop a unique noising algorithm that rigorously maintains periodic translation equivariance throughout both training and inference processes. Our experiments indicate that EquiCSP significantly surpasses existing models in terms of generating accurate structures and demonstrates faster convergence during the training process.