# Materium: An Autoregressive Approach for Material Generation

arXiv: https://arxiv.org/abs/2512.07486 · HTML: https://mlsanity.com/paper/2512.07486/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 21 of 21)

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- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
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- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
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- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [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)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [Meshtron: High-Fidelity, Artist-Like 3D Mesh Generation at Scale](https://mlsanity.com/paper/2412.09548/) (2024)
- [Scalable Diffusion for Materials Generation](https://mlsanity.com/paper/2311.09235/) (2023)
- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (2024)
- [Data-driven discovery of novel 2D materials by deep generative models](https://mlsanity.com/paper/2206.12159/) (2022)
- [Foundational Large Language Models for Materials Research](https://mlsanity.com/paper/2412.09560/) (2024)
- [LLamol: A Dynamic Multi-Conditional Generative Transformer for De Novo Molecular Design](https://mlsanity.com/paper/2311.14407/) (2023)

## Abstract (arXiv)

We present Materium: an autoregressive transformer for generating crystal structures that converts 3D material representations into token sequences. These sequences include elements with oxidation states, fractional coordinates and lattice parameters. Unlike diffusion approaches, which refine atomic positions iteratively through many denoising steps, Materium places atoms at precise fractional coordinates, enabling fast, scalable generation. With this design, the model can be trained in a few hours on a single GPU and generate samples much faster on GPUs and CPUs than diffusion-based approaches. The model was trained and evaluated using multiple properties as conditions, including fundamental properties, such as density and space group, as well as more practical targets, such as band gap and magnetic density. In both single and combined conditions, the model performs consistently well, producing candidates that align with the requested inputs.