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To resolve the severe inference bottleneck in generative crystal structure prediction, uFlowCSP implements MeanFlow modeling to learn average rather than instantaneous probability-flow velocities over crystal coordinates and lattices. The architecture pairs a chemistry- and symmetry-aware Transformer with canonical atom ordering and a training-only coarse crystal-system conditioning token that sharpens space-group alignment without requiring extra inference inputs. Operating in just one to five network evaluations, uFlowCSP achieves an 83.64% match rate on MP-20鈥攕urpassing 2,000-step CrystalFlow (78.34%) and ~20,000-step DiffCSP (77.93%) while generating 10,000 candidate structures in under 90 seconds.
Generative crystal structure prediction no longer requires thousands of sequential sampling steps: learning average probability flows yields state-of-the-art structural and space-group fidelity in just 1 to 5 evaluations, generating 10,000 candidates in under a minute.
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.
