Generative crystallographic phasing through invariant relationships
Abstract
Crystal structure determination requires the phases of scattered waves -- yet diffraction measures only their intensities. Direct methods exploit phase invariants but become less reliable as diffraction information diminishes. Learned phase prediction has lowered the resolution barrier, yet remains primarily confined to centrosymmetric crystals with binary phases. We introduce PhiGen, a generative reformulation of traditional direct methods that learns origin-independent phase relationships for binary and continuous phasing. Across 210 space groups, including groups absent from training, it recovered high-quality maps for 99.0% of centrosymmetric structures and invariant-consistent phases for 92.8% of non-centrosymmetric structures. From simulated 3 Å zeolite powder data, the network recovered framework maps for 84.2% of held-out structures, versus 1.0% for Superflip. For experimental ZSM-25 and TNU-9, generated phases seeded high-resolution phase extension. These results suggest a route to structure determination from low-resolution, incomplete, and overlapped diffraction data.
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BibTeX
@misc{li2026generative,
title = {{Generative crystallographic phasing through invariant relationships}},
author = {Qi Li and Rui Jiao and Liming Wu and Chang Chen and Tiannian Zhu and Bintang Wang and Qiuliang Liu and Zhonglong Peng and Munan Hao and YingPeng Yu and Lin Yao and Wei Ding and Mao Su and Lei Bai and Yang Liu and Hongming Weng and Wenbing Huang and Shifeng Jin and Xiaolong Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28987},
eprint = {2609.28987},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28987},
}
RIS
TY - UNPB
TI - Generative crystallographic phasing through invariant relationships
AU - Qi Li
AU - Rui Jiao
AU - Liming Wu
AU - Chang Chen
AU - Tiannian Zhu
AU - Bintang Wang
AU - Qiuliang Liu
AU - Zhonglong Peng
AU - Munan Hao
AU - YingPeng Yu
AU - Lin Yao
AU - Wei Ding
AU - Mao Su
AU - Lei Bai
AU - Yang Liu
AU - Hongming Weng
AU - Wenbing Huang
AU - Shifeng Jin
AU - Xiaolong Chen
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.28987
UR - https://arxiv.org/abs/2609.28987
AB - Crystal structure determination requires the phases of scattered waves -- yet diffraction measures only their intensities. Direct methods exploit phase invariants but become less reliable as diffraction information diminishes. Learned phase prediction has lowered the resolution barrier, yet remains primarily confined to centrosymmetric crystals with binary phases. We introduce PhiGen, a generative reformulation of traditional direct methods that learns origin-independent phase relationships for binary and continuous phasing. Across 210 space groups, including groups absent from training, it recovered high-quality maps for 99.0% of centrosymmetric structures and invariant-consistent phases for 92.8% of non-centrosymmetric structures. From simulated 3 Å zeolite powder data, the network recovered framework maps for 84.2% of held-out structures, versus 1.0% for Superflip. For experimental ZSM-25 and TNU-9, generated phases seeded high-resolution phase extension. These results suggest a route to structure determination from low-resolution, incomplete, and overlapped diffraction data.
ER -