A probabilistic foundation model for crystal structure denoising, phase classification, and order parameters

Atomistic simulations generate large volumes of noisy structural data, but extracting phase labels, order parameters (OPs), and defect information in a way that is universal, robust, and interpretable remains challenging. Existing tools such as PTM and CNA are restricted to a small set of hand-crafted lattices (e.g.\ FCC/BCC/HCP), degrade under strong thermal disorder or defects, and produce hard, template-based labels without per-atom probability or confidence scores. Here we introduce a log-probability foundation model that unifies denoising, phase classification, and OP extraction within a single probabilistic framework. We reuse the MACE-MP foundation interatomic potential on crystal structures mapped to AFLOW prototypes, training it to predict per-atom, per-phase logits $l$ and to aggregate them into a global log-density $\log \hat{P}_θ(\boldsymbol{r})$ whose gradient defines a conservative score field. Denoising corresponds to gradient ascent on this learned log-density, phase labels follow from $\arg\max_c l_{ac}$, and the $l$ values act as continuous, defect-sensitive and interpretable OPs quantifying the Euclidean distance to ideal phases. We demonstrate universality across hundreds of prototypes, robustness under strong thermal and defect-induced disorder, and accurate treatment of complex systems such as ice polymorphs, ice--water interfaces, and shock-compressed Ti.

Grand canonical generative diffusion model for crystalline phases and grain boundaries

The diffusion model has emerged as a powerful tool for generating atomic structures for materials science. This work calls attention to the deficiency of current particle-based diffusion models, which represent atoms as a point cloud, in generating even the simplest ordered crystalline structures. The problem is attributed to particles being trapped in local minima during the score-driven simulated annealing of the diffusion process, similar to the physical process of force-driven simulated annealing. We develop a solution, the grand canonical diffusion model, which adopts an alternative voxel-based representation with continuous rather than fixed number of particles. The method is applied towards generation of several common crystalline phases as well as the technologically important and challenging problem of grain boundary structures.

Spectroscopy-Guided Discovery of Three-Dimensional Structures of Disordered Materials with Diffusion Models

The ability to rapidly develop materials with desired properties has a transformative impact on a broad range of emerging technologies. In this work, we introduce a new framework based on the diffusion model, a recent generative machine learning method to predict 3D structures of disordered materials from a target property. For demonstration, we apply the model to identify the atomic structures of amorphous carbons ($a$-C) as a representative material system from the target X-ray absorption near edge structure (XANES) spectra--a common experimental technique to probe atomic structures of materials. We show that conditional generation guided by XANES spectra reproduces key features of the target structures. Furthermore, we show that our model can steer the generative process to tailor atomic arrangements for a specific XANES spectrum. Finally, our generative model exhibits a remarkable scale-agnostic property, thereby enabling generation of realistic, large-scale structures through learning from a small-scale dataset (i.e., with small unit cells). Our work represents a significant stride in bridging the gap between materials characterization and atomic structure determination; in addition, it can be leveraged for materials discovery in exploring various material properties as targeted.