Equivariant diffusion solution for inorganic crystal structure determination from powder X-ray diffraction data.

Determining the crystal structures of inorganic materials is critical because atomic arrangement governs their physical, chemical, and mechanical properties. Powder X-ray diffraction (PXRD) remains a cornerstone characterization technique, yet solving structures directly from experimental PXRD patterns is challenging and traditionally depends heavily on expert manual interpretation. Even leading databases contain thousands of entries with incomplete or implausible structural models. In this work, we develop an equivariant graph neural network-based diffusion model that directly infers atomic coordinates from PXRD patterns. Starting from random noise, the model iteratively refines coordinates to produce chemically valid structures that match the target pattern. It solves crystal structure in an average of 0.6 second on a single GPU, several orders of magnitude faster than previous methods, and achieves success rates of 82.3% and 81.6% on simulated and experimental datasets, respectively. We use the model to correct 39 energetically unfavorable database entries and to complete high quality structural models for 912 entries lacking atomic positions, including difficult cases with light elements, natural minerals, and chemical disorder. This conditional equivariant generative approach enables robust automated crystal structure solution from diffraction data and supports future developments in closed loop autonomous materials discovery.