Materium: An autoregressive approach for material generation

We present Materium: an autoregressive transformer for crystal-structure 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 multi-condition settings, the model shows controllable trends toward the requested inputs, although exact target matching remains challenging for high-variance properties.