PXRD-Bench: How Close Are We to Determining Crystal Structures from Powder Diffraction?

Dongyeop Woo; Nofit Segal; Nayoung Kim; Minkyu Kim; Rafael Gomez-Bombarelli; Sungsoo Ahn

cs.AIOct 12, 2026

PXRD-Bench: How Close Are We to Determining Crystal Structures from Powder Diffraction?

Authors: Dongyeop Woo, Nofit Segal, Nayoung Kim, Minkyu Kim, Rafael Gomez-Bombarelli, Sungsoo Ahn

Organizations: Korea Advanced Institute of Science & Technology (kaist.edu) · Massachusetts Institute of Technology (mit.edu)

Abstract

Determining crystal structures from powder X-ray diffraction (PXRD) would enable routine characterization of newly synthesized materials, including those absent from reference databases. Generative models offer a promising approach, but existing evaluations remain fragmented and largely assume single-phase samples with known composition. To fill this gap, we introduce PXRD-Bench, a unified benchmark that extends evaluation to unknown per-element atom counts and recovery of both structures in two-phase mixtures. It provides approximately 4.1 million training structures with simulated PXRD, tests generalization to unseen compositions and structural prototypes, and evaluates recovery from experimental PXRD after excluding structurally matching training entries. To provide a strong reference baseline, we also introduce Bragglite, a PXRD-to-structure model developed through a systematic study of PXRD modeling choices. It achieves a 44.2% Top-1 match rate on experimental RRUFF patterns with known composition, 24.6% above the strongest prior baseline. Further analysis yields several key findings: some models fail to benefit from experimental PXRD, while generalization to unseen structural prototypes and recovery from two-phase mixtures remain challenging. Together, our benchmark, systematic studies, and Bragglite clarify the capabilities and limitations of current PXRD-to-structure models.

Figures & tables

Figure 1: Overview of benchmark tasks and evaluation settings. Three tasks recover crystal structures from PXRD under known composition, element set, and two-phase conditions. Models trained on simulated PXRD are evaluated on experimental RRUFF and opXRD patterns. Generalization splits test unseen composition–prototype pairs, new compositions, and new structural prototypes.

Panel of Figure 2 — Figure 2: Coverage of PXRD-Bench’s simulated structure/PXRD corpus. (a) Structures containing each element (%); (b) element-pair frequencies normalized by total pair occurrences; (c) deduplicated source shares; (d) crystal systems; and (e) primitive-cell atom counts.

Figure 3: Schematic illustration of PXRD profile augmentations. Bragg reflections derived from a crystal structure are perturbed by weak-peak removal, position jitter, peak-wise intensity scaling, a common angular shift, pseudo-Voigt broadening, background addition, and Gaussian noise. Blue denotes perturbed signals and gray denotes reference signals.

		Simulated PXRD		RRUFF		opXRD
Dataset	Model	Top-1	Top-20	Top-1	Top-20	Top-1	Top-20
MP-20	Chemical input: exact stoichiometry
	PXRDGen	54.75	77.99	30.80 $\pm$ 3.27 0	57.00 $\pm$ 1.41 0	30.00 $\pm$ 1.96 0	36.43 $\pm$ 0.98 0
	RealPXRD-Solver	56.35	80.61	27.80 $\pm$ 4.76 0	51.20 $\pm$ 1.10 0	27.14 $\pm$ 0.80 0	36.07 $\pm$ 0.80 0
	XRDiff	55.10	78.11	17.80 $\pm$ 0.84 0	39.80 $\pm$ 0.84 0	21.07 $\pm$ 3.87 0	31.43 $\pm$ 2.04 0
	Crystalyze	29.32	48.03	0 5.00 $\pm$ 1.58 0	14.80 $\pm$ 1.48 0	11.07 $\pm$ 1.49 0	17.86 $\pm$ 1.79 0

Table 1: Main benchmark results. Top-

K

match rates (%) on simulated and experimental PXRD datasets. Results on experimental datasets are reported as mean

\pm

standard deviation over five sampling seeds. Bold and underlined values indicate the best and second-best means, respectively, within each dataset and chemical-input setting.

Chemical input: exact stoichiometry
	Pair OOD		Prototype OOD		Composition OOD
Model	Top-1	Top-20	Top-1	Top-20	Top-1	Top-20
PXRDGen	62.40	89.98	7.55	33.97	63.80	89.61
RealPXRD-Solver	58.94	88.88	3.31	17.52	62.90	90.66
XRDiff	47.48	83.87	2.36	18.51	50.13	84.16
Crystalyze	16.06	39.53	0.58	3.19	14.00	36.91

Table 2: Out-of-distribution generalization. Top-

K

match rates (%) on the OOD simulated PXRD splits of PXRD-Bench, grouped by chemical input. Bold indicates the best result within each setting.

Figure 4: Data scaling. Performance vs. training data fraction.

Figure 5: Analysis of PXRD augmentation and simulation-to-experiment transfer. (a) Additive ablation of the PXRD augmentation components. (b) Relationship between simulated MP-20 and experimental validation performance on RRUFF and opXRD. Filled markers denote the final training checkpoint; solid lines connect results across training checkpoints.

Table 8

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Source	Snapshot	Selection criteria	Record counts
			Candidates	Final corpus
Materials Project	2026-04-13	$0\leq E_{\mathrm{hull}}\leq 0.10$	100,384	77,493
OQMD	v1.5 (2021-10)	Signed stability $\leq 0.10$ ; negative values retained	219,945	166,102
Alexandria	PBE 3D, 2025-07-02	$0\leq E_{\mathrm{hull}}\leq 0.10$	2,331,796	2,139,337
AFLOW	AFLUX, 2026-08-16	No energy filter	2,981,679	1,879,759
Total			5,633,804	4,262,691

Appendix

Table 5: Frozen source snapshots, selection criteria, and record counts before and after dataset curation. Candidate counts are measured after structural validation and before composition-bucket filtering, cross-source deduplication, and the 52-atom restriction. Final counts are measured after the 52-atom restriction, chemical curation, OOD-consistency filtering, and benchmark-overlap exclusion, totaling 4,262,691 structures, including 4,107,627 training structures. Each retained structure is attributed to the source of its representative record, selected during deduplication using the fixed priority MP, OQMD, Alexandria, then AFLOW. The final counts therefore reflect representative provenance rather than independent source contributions or source quality.

E_{\mathrm{hull}}

denotes energy above hull; OQMD uses its signed stability field, including negative values. All energy values are in eV/atom.

Peak-position representation
Input feature	MP-20	RRUFF	opXRD
$2\theta,I$	60.94	36.67 $\pm$ 1.86 0	36.67 $\pm$ 6.18 0
$d,I$	59.96	39.17 $\pm$ 2.28 0	35.83 $\pm$ 2.28 0
$q,I$	64.84	41.25 $\pm$ 1.74 0	37.50 $\pm$ 2.95 0
Additional peak features
$+$ prominence, width	66.21	43.33 $\pm$ 2.28 0	41.67 $\pm$ 4.17 0

Appendix

Table 6: Top-1 validation match rates (%) for ablations of the PXRD input representation and peak-position encoding. The first three rows compare peak-position representations using intensity only. Subsequent rows cumulatively augment the

q,I

representation with peak prominence and width, followed by Fourier embeddings of the peak position.

	Top-1	Top-20	$\Delta$ Top-1 (pp)
Bragglite	78.86 $\pm$ 0.40 0	90.62 $\pm$ 0.40 0	–
$-$ In-context fusion	78.64 $\pm$ 0.34 0	90.33 $\pm$ 0.28 0	$-0.22$
$-$ GEM	76.35 $\pm$ 0.59 0	89.90 $\pm$ 0.05 0	$-2.51$

Appendix

Table 7: Architecture component study on the MP-20 validation set. Top-

K

match rates (%) are reported as mean

\pm

sample standard deviation over three training seeds. All models are evaluated at the final 300K-step EMA checkpoint.

PXRD encoder	Top-1	Top-20
Transformer encoder	75.37	89.04
MLP encoder	72.70	87.96

Appendix

Table 8: PXRD encoder study on the MP-20 validation set. Values are Top-

K

match rates (%).

Figure 8: Overlap of Top-1 successes between Bragglite and prior baselines on the RRUFF and opXRD test sets. Each bar partitions the test samples into cases where both models succeed, only the baseline succeeds, only Bragglite succeeds, or neither succeeds. Retained denotes the fraction of baseline successes that are also recovered by Bragglite.

		Dominant		Minor		All-phase
Dataset	Model	Top-1	Top-20	Top-1	Top-20	Top-1	Top-20
MP-20	MatterGen	14.28	55.69	15.48	55.41	2.13	30.67
	XRDiff	25.28	38.28	23.14	36.48	6.76	14.64
	Bragglite	33.99	48.78	30.59	45.02	13.26	25.34
GALAXI	MatterGen	0.00	76.19	4.76	71.43	0.00	42.86
	XRDiff	28.57	38.10	9.52	14.29	0.00	9.52

Appendix

Table 9: Detailed two-phase recovery results. Dominant-phase, minor-phase, and all-phase Top-

K

match rates (%) on the MP-20 and GALAXI two-phase benchmarks. All-phase recovery requires both constituent phases to be recovered within their respective candidate sets.

MP-20- polymorph- split	Chemical input: exact stoichiometry
		Simulated PXRD		RRUFF		opXRD
Dataset	Model	Top-1	Top-20	Top-1	Top-20	Top-1	Top-20
	PXRDGen	55.43	78.92	30.00 $\pm$ 3.08 0	59.00 $\pm$ 1.41 0	24.29 $\pm$ 1.60 0	36.79 $\pm$ 2.04 0
	RealPXRD-Solver	57.42	79.54	26.60 $\pm$ 2.61 0	47.80 $\pm$ 2.68 0	24.64 $\pm$ 1.49 0	33.21 $\pm$ 1.60 0
	XRDiff	60.26	77.54	23.00 $\pm$ 2.35 0	45.60 $\pm$ 1.52 0	18.93 $\pm$ 2.71 0	29.29 $\pm$ 1.60 0
	Crystalyze	31.07	49.46	0 2.00 $\pm$ 1.41 0	11.00 $\pm$ 1.22 0	11.79 $\pm$ 0.98 0	17.50 $\pm$ 0.80 0

Appendix

Table 10: Top-

K

match rates (%) for models trained on MP-20-polymorph-split, following the MP-20 configuration in Table 1 .

Backbone
Component	Known composition	Element set $+N$
Hidden dimension	512
Transformer layers	14
Attention heads	16
FFN expansion ratio	4
FFN activation	GELU

Appendix

Table 11: Bragglite model configurations. All configurations are shared between the known-composition and element-set models unless specified otherwise. Parameter counts include the PXRD encoder and conditioning modules.

	Known composition	Element set $+N$
Loss weights $(\lambda_{H},\lambda_{F},\lambda_{L})$	$(0,50,5)$	$(64,150,5)$
EDM $(P_{\mathrm{mean}},P_{\mathrm{std}})$	$(-1.2,1.2)$	$(-1.2,1.5)$
EDM $(\sigma_{\min},\sigma_{\max})$	$(0.002,80)$	$(0.001,40)$

Appendix

Table 12: Diffusion-objective settings. Loss weights and EDM noise-distribution parameters for the two chemical-input settings.

	Known composition	Element set $+N$
Learning rate	$2\times 10^{-4}$	$1\times 10^{-4}$
LR schedule	Constant	Cosine decay
Warmup steps	1,000	500

Appendix

Table 13: Conditioning-specific optimization settings.

	MP-20	PXRD-Bench
Maximum atom count $N_{\max}$	20	52
Training steps	800K	4M
Approx. epochs	$\sim$ 15K	$\sim$ 250
Batch size	512	256
GPUs / gradient accumulation	1 / 1	1 / 1
Training seed	123	123

Appendix

Table 14: Corpus-specific training settings.

Setting	Value
Training steps	200K ( $\sim$ 3,846 epochs)
Checkpoint	Final 200K-step EMA checkpoint
Training seed (representation)	$123$
Training seeds (augmentation)	$\{123,124,125\}$
Sampling seeds	$\{777,778,779,780,781\}$ per training run

Appendix

Table 15: Ablation training settings. Settings that differ from the main training protocol.

Setting	Known composition	Element set $+N$
Solver / steps	Heun / 150
Noise schedule	Karras, $\rho=7$
$S_{\mathrm{churn}}$	60
Churn range $[S_{\min},S_{\max}]$	$[0,999]$
$S_{\mathrm{noise}}$	1.003
$\sigma_{\mathrm{data}}$	0.3

Appendix

Table 16: Sampling configurations. Settings are shared across MP-20 and PXRD-Bench and follow the Crystalite sampling configuration.

Training data / input	Batch size	Steps	Time (h)	Peak memory (GiB)
PXRD-Bench / Known composition	256	4M	200.18	7.97
PXRD-Bench / Element set	256	4M	201.29	7.98
MP-20 / Known composition	512	800K	37.10	7.15
MP-20 / Element set	512	800K	37.89	7.16

Appendix

Table 17: Training cost. Wall-clock training time and peak GPU memory usage for the main Bragglite configurations. All models are trained on a single NVIDIA GeForce RTX 3090 GPU.

Figure 9: Qualitative comparison of structures generated by PXRDGen, XRDiff, and Bragglite on experimental PXRD patterns, using Skutterudite and Stolzite examples from the RRUFF test split. For each method, the generated crystal structure and its simulated PXRD pattern are shown alongside the reference structure and experimental pattern. The reported $r$ denotes the correlation between the simulated and experimental PXRD profiles.

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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.

Abstract

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