# GLASS: Global Latent Aggregation with Slot-based Set Decoding for Scalable All-Atom Crystal Generation

arXiv: https://arxiv.org/abs/2609.37158 · HTML: https://mlsanity.com/paper/2609.37158/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 65 of its 95 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 30 of 65)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [On the Limitations of Representing Functions on Sets](https://mlsanity.com/paper/1901.09006/) (2019)
- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [SetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Data](https://mlsanity.com/paper/2103.15619/) (2021)
- [All-atom Diffusion Transformers: Unified generative modelling of molecules and materials](https://mlsanity.com/paper/2503.03965/) (2025)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [Deep Set Prediction Networks](https://mlsanity.com/paper/1906.06565/) (2019)
- [Universal Approximation of Functions on Sets](https://mlsanity.com/paper/2107.01959/) (2021)
- [FSPool: Learning Set Representations with Featurewise Sort Pooling](https://mlsanity.com/paper/1906.02795/) (2019)
- [Equivariant Frames and the Impossibility of Continuous Canonicalization](https://mlsanity.com/paper/2402.16077/) (2024)
- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (2024)
- [SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matching](https://mlsanity.com/paper/2406.07266/) (2024)

## Abstract (arXiv)

Generative models for crystals enable the discovery of novel structures, but scaling all-atom generation to larger systems such as metal--organic frameworks remains challenging. We connect this difficulty to the correspondence problem of particle-space generation. Even on a single fixed target set, index-free permutation-equivariant particle flows require substantially more training for reliable generation as set size and density increase, under both independent and optimal-transport couplings. To resolve this challenge, we introduce GLASS---Global Latent Aggregation with Slot-based Set Decoding, which encodes structures in a permutation-invariant global latent space and learns their distribution via flow matching. A learned-slot decoder constructs all atoms in parallel, removing atom-wise correspondence from generative transport. On MP20, GLASS is competitive with particle-space models, and flow training can reach the validity of the training data at every structure size. On a QMOF subset, GLASS generates MOFs with up to 150 atoms per unit cell without conditioning on building blocks, topology, or composition, and approaches the structural validity of the training data. On both datasets, flow training exposes a validity--novelty tradeoff, and MOF novelty remains limited by autoencoder generalization on the available data. These results show that separating correspondence assignment from generative transport provides a simple route toward high-validity generation of larger atomistic systems.