Generative models show ample promise for materials design, but face severe limitations in the amorphous materials space due to their complex structures. Traditional approaches struggle to capture the intricate, non-periodic arrangements that characterize disordered materials, creating a significant gap in computational materials science.

To address this challenge, we developed DM², a denoising diffusion framework that generates reliable atomistic structures across diverse amorphous systems and processing conditions. Our approach outperforms classical simulations by up to 1000 times, representing a leap in computational efficiency while maintaining structural accuracy.

With DM², we enable a range of applications in amorphous materials research, including performing fracture simulations with large, slow-cooled structures, generating mesoporous structures, and augmenting experimental datasets with synthetic data. These capabilities open new avenues for understanding and modeling complex disordered materials.

This work provides a comprehensive roadmap on how to use, validate, and develop generative models for amorphous materials. Our framework represents bridges the gap between computational efficiency and structural fidelity in materials science, paving the way for accelerated discovery and design of disordered materials with tailored properties.

DM² employs a denoiser model trained to predict the displacement added to amorphous structures during the diffusion process. During training, displacements ε are sampled from Gaussian distributions and systematically added to the training structures, enabling the model to learn the underlying structural patterns of disordered materials. Structure-level labels such as cooling rates are embedded into the training set using a Gaussian basis set, allowing the model to generate structures conditioned on given processing parameters. To generate new structures, the model is provided with a random input structure and a target cooling rate. The structure is then denoised over multiple time steps following a carefully designed noise schedule similar to the denoising diffusion probabilistic model (DDPM) framework, progressively refining the atomic positions to produce physically realistic amorphous structures.

DM² Framework Overview: Our denoising diffusion approach for generating amorphous structures, showing the training process with Gaussian noise addition and the iterative denoising procedure for structure generation.