PXtal: Learning to Align Powder X-Ray Diffraction and Crystal Structures under Information Asymmetry across Modalities

Determining the crystal structure of a material from its powder X-ray diffraction (PXRD) pattern is a central challenge in materials science. PXRD is an accessible and widely used characterization technique, yet recovering the atomic structure from diffraction data requires solving an underdetermined inverse problem due to the loss of phase information. Generative modeling can provide a prior over atomic structure and learn the mapping from PXRD patterns to crystal structures via simulated structure-spectrum pairs. We present XRDiff, a diffusion model that recovers crystal structures from PXRD given either the stoichiometry or, in a more challenging setting, the elemental constituents and total number of atoms in the unit cell. We evaluate on datasets where each stoichiometry has multiple polymorphs and all polymorphs of a given composition are held out together, ensuring that high performance reflects genuine use of the diffraction signal. XRDiff achieves strong structure recovery rates on simulated benchmarks, indicating that the model learns a spectrum-to-structure mapping precise enough to differentiate between polymorphs. To address generalization to experimental data, we compare a full-spectrum encoding against an encoding based on peak descriptors. The peak-based encoding generalizes substantially better, outperforming even a model trained on full spectra with augmentations fitted to the experimental noise distribution. These results demonstrate that representations robust to the noise and artifacts present in real-world PXRD offer a practical and scalable path toward closing the simulation-to-experiment gap, enabling zero-shot crystal structure solution from experimental PXRD with full or partial chemical composition input.

Fully characterizing a crystalline material requires integrating heterogeneous data sources -- atomic structures, diffraction patterns, electronic density of states, and natural language -- each of which captures a different facet of the same physical object. In practice, however, these modalities are stored and analyzed in isolation, making it difficult to relate or query materials across representational boundaries. We present MatBind, a contrastive learning framework that aligns four materials modalities -- crystal structure, powder X-ray diffraction (pXRD) simulated from structures, density of states (DOS), and text -- into a unified embedding space using crystal structure as the central physical anchor. The framework induces alignment between modalities never explicitly paired during training, enabling emergent zero-shot cross-modal retrieval as a direct consequence of the shared representation. The learned embedding space organizes materials according to physically meaningful properties without explicit supervision, and retrieval performance improves systematically when modalities are combined at query time. These results demonstrate that treating heterogeneous materials data as complementary projections of a single physical reality, rather than as isolated data sources, is not a practical choice but is consistent with the underlying physics.

Miller-index identification from powder XRD patterns requires capabilities untested by existing multimodal benchmarks: the model must read a narrow peak location from a rendered scientific curve and then connect that observation to multi-step crystallographic reasoning. We introduce CrystalXRD-Bench, a 250-sample benchmark built from 10 public crystallographic databases for a single task: recover the full set of HKLs contributing to the highest-intensity peak in an XRD pattern. Each sample pairs the rendered XRD image with the source CIF text and chemical formula, so visual extraction errors and reasoning errors can be examined side by side. We evaluate seven vision-language models. The best Jaccard score is 0.5888 (GPT-5.4) with an exact-match rate of 37.6%, yet six of seven models remain below Jaccard 0.50; the task is far from solved. Error patterns vary systematically: double-peak cases are especially brittle, recall-heavy models gain coverage by over-predicting HKLs, and access to CIF text does not close the gap in crystallographic calculation. Alongside model rankings, the benchmark identifies the conditions under which current VLMs fail on quantitative scientific figures. All data and evaluation code will be publicly available.