Fig. 1: Training and validating a generative diffusion model for amorphous materials.

a Forward diffusion and reverse denoising process for amorphous materials. The structure and partial pair distribution functions (PDF) for SiO₂ are provided as an example. In the forward process, noise is progressively added to atomic positions until the structure becomes random. In the reverse (generative) direction, the model gradually denoises the positions of randomly sampled positions and creates physically meaningful amorphous structures. b The denoiser model is trained to predict the displacement added to the amorphous structures. Displacements ϵ are sampled from Gaussian distributions, and added at train time to the training structures. Structure-level labels, such as cooling rates are embedded to the training set with a Gaussian basis set. c To generate new structures, the model is provided with a random input structure and a target cooling rate. The structure is denoised over multiple time steps following a noise schedule similar to the denoising diffusion probabilistic model (DDPM) framework³. d Figures of merit used to validate generated amorphous structures include short range order, medium range order, network connectivity, mechanical properties, and information entropy. e In this work, the generative models for amorphous materials were used across multiple applications, including generating glassy structures conditioned to very slow cooling rate, large scales, pores, or reproducing the phase space of simulated and experimental metallic glasses.