uFlowCSP: Crystal Structure Prediction using Mean flow generative models
Abstract
Crystal structure prediction (CSP) is fundamental to computational materials discovery. Generative models including CDVAE, DiffCSP, FlowMM, and CrystalFlow learn stable-crystal distributions directly, but diffusion and flow-matching inference requires tens to thousands of sequential network evaluations per candidate. We introduce uFlowCSP, a MeanFlow-based CSP model that learns the average, rather than instantaneous, probability-flow velocity. It generates a complete structure in one to five evaluations, delivering 5x-58x faster inference with equal or better performance. A chemistry- and symmetry-aware Transformer uses canonical atom ordering, global composition, and per-token chemistry embeddings. A coarse crystal-system token is used only during training; it provides additive gains, particularly improving space-group agreement despite being absent at inference, which remains formula-only. On MP-20 with 20 candidates per target, one step matches CrystalFlow (78.38% vs. 78.34%) with 100x fewer evaluations and about 10x lower wall-clock time. Five steps reach 83.64%, exceeding CrystalFlow (78.34% at 2,000 evaluations) and DiffCSP (77.93% at about 20,000), while using 20x fewer evaluations. uFlowCSP generates 10,000 structures in 0.39-1.31 minutes, versus 6.5 for CrystalFlow and 76.1 for DiffCSP. Under CSPBench's energy-ranked top-five structure-and-space-group criterion, five-step uFlowCSP reaches 72%/72%/65% structure, space-group, and consensus match rates. CrystalFlow reaches 78%/73%/68% at 100 steps but falls to 49%/32%/31% at five. Thus, uFlowCSP improves accuracy per network evaluation, not merely peak accuracy.
Related
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BibTeX
@misc{dey2026uflowcsp,
title = {{uFlowCSP: Crystal Structure Prediction using Mean flow generative models}},
author = {Sourin Dey and Dipannoy Das Gupta and Lai Wei and Sadman Sadeed Omee and Jianjun Hu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09799},
eprint = {2609.09799},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09799},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - uFlowCSP: Crystal Structure Prediction using Mean flow generative models
AU - Sourin Dey
AU - Dipannoy Das Gupta
AU - Lai Wei
AU - Sadman Sadeed Omee
AU - Jianjun Hu
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09799
UR - https://arxiv.org/abs/2609.09799
AB - Crystal structure prediction (CSP) is fundamental to computational materials discovery. Generative models including CDVAE, DiffCSP, FlowMM, and CrystalFlow learn stable-crystal distributions directly, but diffusion and flow-matching inference requires tens to thousands of sequential network evaluations per candidate. We introduce uFlowCSP, a MeanFlow-based CSP model that learns the average, rather than instantaneous, probability-flow velocity. It generates a complete structure in one to five evaluations, delivering 5x-58x faster inference with equal or better performance. A chemistry- and symmetry-aware Transformer uses canonical atom ordering, global composition, and per-token chemistry embeddings. A coarse crystal-system token is used only during training; it provides additive gains, particularly improving space-group agreement despite being absent at inference, which remains formula-only. On MP-20 with 20 candidates per target, one step matches CrystalFlow (78.38% vs. 78.34%) with 100x fewer evaluations and about 10x lower wall-clock time. Five steps reach 83.64%, exceeding CrystalFlow (78.34% at 2,000 evaluations) and DiffCSP (77.93% at about 20,000), while using 20x fewer evaluations. uFlowCSP generates 10,000 structures in 0.39-1.31 minutes, versus 6.5 for CrystalFlow and 76.1 for DiffCSP. Under CSPBench's energy-ranked top-five structure-and-space-group criterion, five-step uFlowCSP reaches 72%/72%/65% structure, space-group, and consensus match rates. CrystalFlow reaches 78%/73%/68% at 100 steps but falls to 49%/32%/31% at five. Thus, uFlowCSP improves accuracy per network evaluation, not merely peak accuracy.
ER -