Packora: Systematic Design for Generative Molecular Crystal Structure Prediction

Nayoung Kim; Kiyoung Seong; Sungsoo Ahn

cs.LGAug 27, 2026

Packora: Systematic Design for Generative Molecular Crystal Structure Prediction

Authors: Nayoung Kim, Kiyoung Seong, Sungsoo Ahn

Organizations: Korea Advanced Institute of Science and Technology (KAIST)

Abstract

Molecular crystal structure prediction (CSP) is important in pharmaceuticals, agrochemicals, and organic electronics, where subtle differences in molecular conformation and packing can strongly affect material properties. We present Packora, a flow-based generative model for molecular CSP that jointly predicts atomic coordinates and the lattice from molecular graphs. Packora supports multi-component and organometallic crystals and can condition on any subset of molecular conformers, stereochemical labels, and space-group information within a single model. Inspired by the CCDC CSP blind test, we evaluate generation and ranking separately, using generation to isolate generator quality and ranking to measure end-to-end performance under a common relaxation and ranking pipeline. We also systematically study architecture, training, conditioning, inference, and scaling, identifying an effective design based on cacheable pairwise reasoning, training objective and numerical solver choices, conditioning dropout, and balanced scaling of pairwise and single representations. Packora outperforms the baselines on both structure generation and ranking benchmarks, achieving the best matched-budget coverage across all six generation benchmarks, as well as higher experimental-form recovery, lower experimental-form ranks, and faster convergence in ranking.

Figures & tables

Figure 1: Crystal coverage with 30 candidates per target. We report the crystal-level solve rate

\mathrm{Sol}_{C}

at a generation budget of 30 candidates per target. Numbers in parentheses indicate the number of targets in each benchmark. For OXtal, we report the published results obtained from 30 generated candidates per target. For CLARI and Packora , we generate 1,000 candidates per target and report the mean over 5,000 bootstrap resamples of 30 candidates; error bars show one standard deviation across resamples. Packora achieves the highest solve rate on all six benchmarks.

Figure 2: Crystal structures predicted by Packora . Each example is a collision-free prediction from Packora -L that matches all 15 molecules of the experimental reference with $\mathrm{RMSD}_{15}<2\,\text{\AA}$ . These 18 examples illustrate Packora ’s ability to generate diverse crystal structures across molecular sizes, compositions, packing motifs, and unit-cell geometries. Panel labels indicate the corresponding CSD refcodes.

	Generation	Chemical/data scope		Conditioning inputs
Method	Explicit H output	Multi- component	Organo- metallics	Local 3D input	Stereo labels	Space group
OXtal ( Jin et al., 2025 )	✗	✓	✓	$\blacktriangle$	✗	✗
PackFlow ( Subramanian et al., 2026 )	✗	✗	✗	✗	✗	✗
MolCrystalFlow ( Zeng et al., 2026 )	✓	✗	✗	$\blacktriangle$	✗	✗
CLARI ( Lo et al., 2026 )	✓	✓	✓	✗	✗	✗
Packora	✓	✓	✓	✓	✓	✓

Table 1: Capabilities and scope of generative molecular CSP models. We compare explicit hydrogen generation, chemical scope, and conditioning inputs. ✓ and ✗ denote supported and unsupported capabilities. For local 3D input,

\blacktriangle

, ✓ , and ✗ denote required, optional, and unsupported conditioning, respectively.

Panel of Figure 3 — Figure 3: Model architecture of Packora . The condition $\mathcal{C}$ is embedded into single and pair representations, with the pair representation refined by four Pairmixer blocks ( Ouyang-Zhang et al., 2025 ) . Because this computation depends only on $\mathcal{C}$ , it can be cached across denoising steps. Noisy coordinate $\mathbf{X}_{t}$ and lattice $\bm{\ell}_{t}$ embeddings are then added to the single representation and processed by a DiT trunk, with the refined pair representation providing attention biases throughout. Separate heads predict the coordinate and lattice endpoints $\widehat{\mathbf{X}}_{1}$ and $\widehat{\bm{\ell}}_{1}$ .

Figure 4: Crystal coverage with 1,000 candidates per target. We report the crystal-level solve rate

\mathrm{Sol}_{C}

at a generation budget of 1,000 candidates per target. Numbers in parentheses indicate the number of targets in each benchmark. Packora achieves the highest solve rate on all six benchmarks.

Figure 5: Crystal coverage with 30 candidates per target under the strict criterion. We report the crystal-level solve rate

\mathrm{Sol}_{C}^{15/15}

at a generation budget of 30 candidates per target.

\mathrm{Sol}_{C}^{15/15}

requires all 15 molecules to match using COMPACK ( Bardwell et al., 2011 ) . Numbers in parentheses indicate the number of targets in each benchmark. We generate 1,000 candidates per target and report the mean over 5,000 bootstrap resamples of 30 candidates; error bars show one standard deviation across resamples. Packora achieves the highest solve rate on all six benchmarks.

Figure 6: Crystal coverage with 1,000 candidates per target under the strict criterion. We report the crystal-level solve rate

\mathrm{Sol}_{C}^{15/15}

at a generation budget of 1,000 candidates per target.

\mathrm{Sol}_{C}^{15/15}

requires all 15 molecules to match under COMPACK ( Bardwell et al., 2011 ) . Numbers in parentheses indicate the number of targets in each benchmark. Packora achieves the highest solve rate on all six benchmarks.

Figure 7: FastCSP single-polymorph benchmark. We generate 1,000 candidates for each of the 26 targets, relax them with UMA-S-1.2 ( Wood et al., 2025 ) , and rank them by increasing energy. (a) Best energy rank of the experimental target form for CLARI-H, Packora -M, and Packora -L; lower is better, with rank 1 denoting the predicted minimum-energy structure. Packora -L and Packora -M recover 19 and 17 targets within the top 20, respectively, compared with 15 for CLARI-H. (b) Fraction of targets recovered by energy-rank cutoff

k

; Packora achieves higher recovery across cutoffs. (c) Cumulative fraction of the generated candidates converged by BFGS step; Packora candidates converge faster throughout relaxation. Relaxing all candidates on eight NVIDIA H200 GPUs takes 16.8, 11.4, and 10.2 h for CLARI-H, Packora -M, and Packora -L, respectively.

Method	Recovered $\uparrow$	Top-1 $\uparrow$	Top-5 $\uparrow$	Top-20 $\uparrow$	Mean rank $\downarrow$
CLARI-H	16/26	9/26	13/26	15/26	4.25
Packora -M	17/26	10/26	17/26	17/26	2.00
Packora -L	19/26	13/26	16/26	19/26	2.05

Table 2: Experimental-form recovery on FastCSP single-polymorph benchmark. We generate 1,000 candidates for each of the 26 targets, relax them with UMA-S-1.2 ( Wood et al., 2025 ) , and rank the relaxed structures by increasing energy. Recovered denotes the fraction of targets with an experimental-form match at any rank, while Top-

k

denotes the fraction whose best match appears within the top

k

ranks. Mean rank is computed over recovered targets only, with lower values indicating better ranking. Bold marks the best result. Packora achieves both higher recovery across rank cutoffs and lower experimental-form ranks.

Figure 8: FastCSP multi-polymorph benchmark. We generate 1,000 candidates for each of the 29 target structures across eight systems, relax them with UMA-S-1.2 ( Wood et al., 2025 ) , and rank them by increasing energy within each system. (a) Best energy rank of each of the 29 polymorphs for CLARI-H, Packora -M, and Packora -L; lower is better, with rank 1 denoting the predicted minimum-energy structure. Marker color identifies the polymorph across systems. Packora -L and Packora -M recover 21 and 19 polymorphs, respectively, compared with 18 for CLARI-H. (b) Fraction of polymorphs recovered by energy-rank cutoff

k

; Packora achieves higher recovery across cutoffs. (c) Cumulative fraction of the generated candidates converged by BFGS step; Packora candidates converge faster throughout relaxation. Relaxing all candidates on eight NVIDIA H200 GPUs takes 16.8, 10.6, and 8.9 h for CLARI-H, Packora -M, and Packora -L, respectively.

Method	Recovered $\uparrow$	Top-1 $\uparrow$	Top-5 $\uparrow$	Top-20 $\uparrow$	Mean rank $\downarrow$
CLARI-H	18/29	5/29	9/29	13/29	102.17
Packora -M	19/29	6/29	11/29	15/29	47.11
Packora -L	21/29	5/29	13/29	17/29	54.62

Table 3: Experimental-form recovery on FastCSP multiple-polymorph benchmark. We generate 1,000 candidates for each of the 29 targets, relax them with UMA-S-1.2 ( Wood et al., 2025 ) , and rank the relaxed structures by increasing energy. Recovered denotes the fraction of targets with an experimental-form match at any rank, while Top-

k

denotes the fraction whose best match appears within the top

k

Panel of Figure 9 — Figure 9: Model variants for architecture ablations. (a) In the pre-entry variant, noisy coordinate and lattice embeddings and optional geometric enhancement module (GEM) features are injected before Pairmixer . (b) In the post-entry variant, the condition-only Input Embedder and Pairmixer are evaluated before noisy-state injection, allowing their outputs to be cached across denoising steps. Modules with dotted outlines denote optional components. Both variants produce single and pair representations $\mathbf{S}$ and $\mathbf{P}$ , which are passed to the same DiT trunk.

Figure 10: Architecture selection, extensions, and caching. Panels (a)–(d) report validation

\mathrm{Sol}_{C}

on the

\leq

300-atom subset with a generation budget of 30 candidates under EDM Heun 200. Pairmixer gives the dominant gain; post-entry Config. (F) remains close to Config. (C), while single updates and GEM do not improve final coverage. Panel (e) reports runtime for synthetic

[64,300]

EDM Heun inputs, including cache construction, and panel (f) reports peak memory. Caching post-entry condition-only pair states removes the per-step Pairmixer cost at a fixed memory increase.

Figure 11: Training recipe selection. All panels report validation

\mathrm{Sol}_{C}

under EDM Heun 200 with a generation budget of 30 candidates. (a) The Beta–uniform mixture gives the strongest completed score. (b) With L1 regression, crystal translation improves the best score from

0.466

0.486

; under translation, L1 outperforms L2 (

0.486

vs.

0.407

). (c) A

10{:}1

coordinate-to-lattice ratio is optimal. (d) At

\lambda{=}5

, smooth-LDDT improves the best score by only

0.004

while increasing training cost from 436 to 599 GPU-hours. (e) Muon outperforms AdamW. (f) EMA decay

0.9999

outperforms raw weights and decay

0.999

Figure 12: Moderate template dropout is most robust across conditioning settings. Validation

\mathrm{Sol}_{C}

at epoch 300 using EDM–Heun with 200 steps and 30 candidates per target. S, T, and SG denote stereochemistry, template coordinates, and space-group conditioning, respectively. Among models trained with

p_{\mathrm{tpl}}\in\{0,0.5,1\}

p_{\mathrm{tpl}}{=}0.5

achieves the highest average performance across the five inference-time conditioning settings and is therefore selected. Template-conditioned results for

p_{\mathrm{tpl}}{=}1

fall below the plotted range and are shown as downward triangles.

Figure 13: Inference ablations. (a) Validation

\mathrm{Sol}_{C}

versus NFE budget for flow ODE, flow SDE, and EDM–Heun. (b) EDM–Heun with 400 NFEs across discretization exponents

\rho

; the failed

\rho=1

result is shown at the lower boundary, and the star marks the selected

\rho=7

. (c) Validation trajectories with no template augmentation, rotation only, and rotation plus translation at inference. (d) Autoguidance using degraded checkpoints from epochs 50, 100, and 150 across guidance weights

\omega

Figure 14: Balanced width scaling reaches the sampling-budget Pareto frontier. (a) Single-sample solve rate

\mathrm{Sol}_{S}

(

k{=}1

) versus crystal-level solve rate

\mathrm{Sol}_{C}

k{=}30

at epoch 300. Marker shape and color indicate the width-scaling family. Scaling either the single or pair width alone does not consistently improve the trade-off between per-sample success and target coverage, whereas jointly scaling both widths reaches the Pareto frontier. Adding weight decay of

10^{-2}

further shifts the balanced model toward higher

k{=}30

coverage. W0 is selected as Packora -M, and W4 with weight decay (W4 + WD) as Packora -L. (b) Epoch sweeps for single-width scaling (W0, W3, W5), pair-width scaling (W0, W1, W2), and balanced scaling (W0, W4). Top and bottom rows report

\mathrm{Sol}_{S}

and

\mathrm{Sol}_{C}

, respectively. All metrics use the shared validation protocol with 30 candidates per target and 200-step EDM–Heun sampling.

ID	$d_{s}$	$d_{p}$	Heads	Params (M)	GFLOPs	$\mathrm{Sol}_{S}\uparrow$	$\mathrm{Sol}_{C}\uparrow$
W0	512	128	8	87.56	379.6	0.088	0.486
W1	512	192	8	89.65	762.6	0.084	0.490
W2	512	256	8	92.54	1287.2	0.087	0.480
W3	768	128	12	184.79	421.0	0.100	0.462
W4	768	192	12	186.91	804.7	0.100	0.487
W5	1024	128	16	330.79	483.8	0.111	0.454

Table 4: Width-scaling ablation. All rows keep depth, Pairmixer placement, conditioning, validation split, and sampler fixed while varying the single width

d_{s}

and pair width

d_{p}

\mathrm{Sol}_{S}

and

\mathrm{Sol}_{C}

are evaluated at epoch 300 with 30 candidates per target and 200-step EDM–Heun sampling (400 NFE). GFLOPs denote analytical denoiser-forward costs at

N{=}300

. Teal rows mark the selected width configurations: W0 defines Packora -M, while W4 defines the width of Packora -L before applying weight decay as selected in Figure 14 .

Appendix figures & tables19 assets

Supplementary material from the paper’s appendix.

Appendix

	Unfiltered				$\leq 512$ atoms
Property	Min	Mean	Median	Max	Min	Mean	Median	Max
Training
Atoms / unit cell	5	203.65	180	3,558	5	201.71	180	512
Molecules / unit cell	1	5.42	4	246	1	5.35	4	160
Atoms / molecule	1.06	48.96	42.00	682.00	1.06	48.89	42.00	512.00
Formula-unit count $Z$	1	3.34	4	40	1	3.33	4	40

Appendix

Table 5: Size statistics for the CLARI training and validation splits. Statistics are reported before and after applying the 512-atom unit-cell limit following hydrogen completion.

	Training		Validation
Property	Unfiltered	$\leq 512$ atoms	Unfiltered	$\leq 512$ atoms
Composition
Organic	491,219	490,475	573	573
Organometallic	425,795	422,332	475	474
Molecular flexibility
Rigid	194,017	193,620	226	226

Appendix

Table 6: Composition, flexibility, and conditioning availability in the CLARI splits. Entries report the number of structures before and after applying the 512-atom unit-cell limit.

Capacity
Parameter	Packora -M	Packora -L
Parameters	88M	187M
Single width	512	768
Pair width	128	192
Attention heads	8	12
Backbone

Appendix

Table 7: Architecture hyperparameters. Model capacity and backbone configuration for Packora -M and Packora -L.

Parameter	Value
Flow matching
Priors	Centered Gaussian fpr $\mathbf{X}$ ; standard Gaussian for $\bm{\ell}$
Interpolant	Linear ( $x_{t}=(1-t)x_{0}+tx_{1}$ )
Time distribution	$0.98\,\operatorname{Beta}(1.9,1.0)+0.02\,\operatorname{Uniform}(0,1)$
Objective	$L^{1}$ coordinate–lattice loss
Loss weights	Coordinates 10; lattice 1

Appendix

Table 8: Training hyperparameters. Flow-matching, optimization, conditioning, and model-selection settings. All settings are shared between Packora -M and Packora -L unless noted.

Parameter	Value
Stage 1
Maximum atoms	300
Bucket caps	32, 64, 96, 128, 160, 192, 224, 256, 288, 300
Per-GPU batch	16 for every bucket
Global batch	128
Stage 2

Appendix

Table 9: Two-stage training curriculum and batching. Atom-count buckets and batch sizes used for fixed-shape training across eight GPUs.

Parameter	Value
Numerical solver
Solver	EDM–Heun with stochastic churn
Noise schedule	Karras
Sampling steps	200
Sigma range	$\sigma_{\min}=0.002$ , $\sigma_{\max}=80$
Schedule exponent	$\rho=7$

Appendix

Table 10: Sampling hyperparameters. Sampling and conditioning configuration used for benchmark generation.

$\mathrm{Sol}_{C}$ at 30-candidate budget
Method	Rigid (50)	Flexible (50)	CSP5 (6)	CSP6 (5)	CSP7 (8)	Teaching (773)
A-Transformer	0.060	0.000	0.000	0.000	0.000	–
AssembleFlow	0.000	0.000	0.000	0.000	0.000	–
OXtal	0.300	0.220	0.167	0.200	0.125	–
CLARI-M	$0.692\pm 0.038$	$0.283\pm 0.044$	$0.410\pm 0.136$	$0.286\pm 0.119$	$0.154\pm 0.102$	$0.506\pm 0.010$
CLARI-L	$0.728\pm 0.039$	$0.336\pm 0.043$	$0.541\pm 0.160$	$0.332\pm 0.138$	$0.138\pm 0.105$	$0.549\pm 0.010$

Appendix

Table 11: Tabular results for structure generation benchmark. We report standard

\mathrm{Sol}_{C}

and strict

\mathrm{Sol}_{C}^{15/15}

at 30 and 1,000 candidates per target. At 30 candidates, CLARI and Packora results are mean

\pm

standard deviation over 5,000 resamples from 1,000-candidate pools; other baselines are reported as provided in Jin et al. [2025] . Results at 1,000 candidates use the full pool. Bold and underline denote the best and second-best generative results, respectively.

Dataset	Method	$\mathrm{Col}_{S}\downarrow$	$\mathrm{Pac}_{S}\uparrow$	$\mathrm{Pac}_{C}\uparrow$	$\mathrm{Rec}_{S}\uparrow$	$\mathrm{Rec}_{C}\uparrow$	$\mathrm{Sol}_{C}\uparrow$
Rigid	A-Transformer	0.731	0.015	0.060	0.033	0.120	0.060
	AssembleFlow	0.524	0.001	0.040	0.211	0.760	0.000
	OXtal	0.011	0.873	1.000	0.737	0.960	0.300
	Packora -M	0.036	0.433	0.876	0.860	0.978	0.807
	Packora -L	0.028	0.405	0.872	0.847	0.979	0.795
Flexible	A-Transformer	0.900	0.001	0.020	0.000	0.000	0.000

Appendix

Table 12: Full metrics at a 30-candidate budget. We report per-sample collision, packing, and recovery rates (

\mathrm{Col}_{S}

\mathrm{Pac}_{S}

\mathrm{Rec}_{S}

) and crystal-level packing, recovery, and solve rates (

\mathrm{Pac}_{C}

\mathrm{Rec}_{C}

\mathrm{Sol}_{C}

), following the definitions in Jin et al. [2025] . Other baselines use their exact 30-candidate pools, while Packora -M and Packora -L report means over 5,000 seeded draws of 30 candidates from their 1,000-candidate pools. CLARI is omitted because only

\mathrm{Sol}_{C}

is available.

Figure 15: Crystal coverage with empirical unit-cell

Z

sampling at 30 candidates per target. The solid bars reproduce Figure 1 ; diagonally hatched bars represent results with

Z

sampled from an empirical prior. Bars report mean

\mathrm{Sol}_{C}

, and error bars show one standard deviation across 5,000 resamples with replacement from each 1,000-candidate pool.

Figure 16: Crystal coverage with empirical unit-cell

Z

sampling at 1,000 candidates per target. The solid bars reproduce Figure 4 ; diagonally hatched bars represent results with

Z

sampled from an empirical prior. Bars report exact

\mathrm{Sol}_{C}

over the full 1,000-candidate pools.

Figure 17: Strict crystal coverage with empirical unit-cell

Z

sampling at 30 candidates per target. The solid bars reproduce Figure 5 ; diagonally hatched bars represent results with

Z

sampled from an empirical prior. Bars report mean

\mathrm{Sol}_{C}^{15/15}

, and error bars show one standard deviation across 5,000 resamples with replacement from each 1,000-candidate pool.

Figure 18: Strict crystal coverage with empirical unit-cell

Z

sampling at 1,000 candidates per target. The solid bars reproduce Figure 6 ; diagonally hatched bars represent results with

Z

sampled from an empirical prior. Bars report exact

\mathrm{Sol}_{C}^{15/15}

over the full 1,000-candidate pools.

Figure 19: Effect of empirical unit-cell

Z

sampling across candidate budgets. Curves show mean

\mathrm{Sol}_{C}

for Packora -M and Packora -L on the Rigid and Flexible benchmarks over 5,000 resamples, and shaded bands show the 2.5th–97.5th percentiles. The gray solid lines denote supplied

Z

, and the teal dotted lines denote empirical

Z

. The two settings remain close across candidate budgets.

Figure 20: Structure overlays for Packora -L predictions. Experimental structures are shown in gray and Packora -L predictions in green. Labels report the CSD refcode and corresponding $\mathrm{RMSD}_{15}$ .

Figure 21: Structure overlays for Packora -L predictions. Experimental structures are shown in gray and Packora -L predictions in green. Labels report the CSD refcode and corresponding $\mathrm{RMSD}_{15}$ .

Target	Subset	Rank	$\mathrm{RMSD}_{30}$	Rank	$\mathrm{RMSD}_{30}$	Rank	$\mathrm{RMSD}_{30}$
		CLARI-H		Packora -M		Packora -L
Target II	Semi-rigid	5	0.55	NR	–	6	0.58
Target IV	Semi-rigid	1	0.16	1	0.14	1	0.18
Target V	Semi-rigid	8	0.33	5	0.18	7	0.12
Target VIII	Semi-rigid	NR	–	NR	–	1	0.22
Target XII	Semi-rigid	1	0.25	1	0.25	1	0.28

Appendix

Table 13: Complete FastCSP single-polymorph results. Each method reports the energy rank and

\mathrm{RMSD}_{30}

(Å) of the best candidate matching the experimental form. NR denotes no recovery, with the corresponding

\mathrm{RMSD}_{30}

unavailable.

System	Refcode	Form	Rank	$\mathrm{RMSD}_{30}$	Rank	$\mathrm{RMSD}_{30}$	Rank	$\mathrm{RMSD}_{30}$
			CLARI-H		Packora -M		Packora -L
Target I	XULDUD01	Monoclinic	NR	–	1	0.297	1	0.267
Target I	XULDUD	Orthorhombic	18	0.308	NR	–	18	0.270
CILJIQ	CILJIQ	Form I	1	0.200	1	0.252	1	0.256
CILJIQ	CILJIQ01	Form II	13	0.165	11	0.118	11	0.117
Glycine	GLYCIN16	gamma	6	0.191	5	0.183	5	0.187

Appendix

Table 14: Complete FastCSP multi-polymorph results. Each method reports the energy rank and

\mathrm{RMSD}_{30}

(Å) of the best candidate matching each experimental form. NR denotes no recovery, with the corresponding

\mathrm{RMSD}_{30}

unavailable.

Stage	# Structures
Raw CSD entries	1,451,367
Filtering and structure preprocessing	833,033
Benchmark-family exclusion	831,018
Benchmark-component exclusion	798,459
Deduplication	766,391
Training split	751,023

Appendix

Table 15: Ablation dataset preprocessing counts. We report the number of structures remaining after each stage.

Config.	Entry	TriMul	TriAtt	SU	GEM	$\mathrm{Sol}_{C}\uparrow$	Params (M)	GFLOPs
(A)	–	–	–	–	–	0.421	85.98	41.2
(B)	–	–	–	–	✓	0.432	86.01	45.7
(C)	pre	✓	–	–	–	0.479	87.56	379.6
(D)	pre	✓	–	✓	–	0.469	105.40	391.8
(E)	pre	✓	–	–	✓	0.476	87.59	384.2
(F)	post	✓	–	–	–	0.474	87.56	379.6

Appendix

Table 16: Architecture ablation with model size and compute. We report parameter count and GFLOPs for each architecture variant, together with its best validation

\mathrm{Sol}_{C}

under the shared

\leq 300

-atom, 30-candidate protocol with 200-step EDM–Heun sampling. Config. (F) is the selected cacheable post-entry design.

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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.

Sourin Dey, Dipannoy Das Gupta, Lai Wei +2

Department of Computer Science and Engineering University of South Carolina Columbia, SC 29201 · Department of Computer Science and Cybersecurity University of North Georgia Columbia, SC 29201

Crystal Structure Prediction One-Step Generative Modeling Crystal Structure Generation Flow-Based Generative Modeling Conditional Generative Modeling Computational Materials Science

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Abstract

Crystal Structure Prediction

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