PXRD-Diff: diagnosing the encoder bottleneck in diffusion-based powder-diffraction structure inversion, with classical autoindexing as a drop-in remedy
- 1Purdue University
Abstract
Inverting a one-dimensional powder X-ray diffraction (PXRD) pattern to a three-dimensional crystal structure remains an open problem, and recent generative approaches report results under mutually incompatible protocols with failure modes seldom catalogued. PXRD-Diff, a 3.7 M-parameter conditional diffusion model trained on the CDVAE MP-20 split, is presented, and DiffractGPT, PXRDnet and deCIFer are reproduced through the same pymatgen StructureMatcher harness. The central, statistically robust finding is mechanistic: the learned PXRD encoder reaches a 0.007 normalised auxiliary lattice-regression loss in isolation, yet substituting that head’s own lattice into the sampler recovers only 1.2 % of structures, because its ~1.1 Å length error shifts every Bragg peak by ~15 %. The limiter is the global pooling that discards absolute peak positions, not the denoiser alone. A perturbation study locates a sharp sensitivity knee at ~0.5 Å cell error, and a true-lattice oracle lifts match to 4.5 % at n = 1000 (three seeds; 95 % Wilson confidence interval [3.8, 5.3]), disjoint from the no-true-lattice indexer’s 1.5 % [1.2, 2.0]. Replacing the learned lattice head with a classical Q-space autoindexer raises no-true-lattice match to 1.5 % from a learned head that recovers essentially nothing; a three-seed paired McNemar test confirms the gain is significant (p < 10−4; 27 fixed, none broken), concentrated in the high-symmetry systems below the sensitivity knee. Reproduced on one harness, deCIFer reaches 73.8 % match, DiffractGPT 18.9 % and PXRDnet 30.0 %, leaving PXRD-Diff 12–46 times behind. The contributions are the encoder-bottleneck diagnosis, the classical-indexer drop-in, a four-item failure catalogue and the shared evaluation harness; code, checkpoints and the differentiable Bragg simulator are released.
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BibTeX
@misc{cai2026pxrddiff,
title = {{PXRD-Diff: diagnosing the encoder bottleneck in diffusion-based powder-diffraction structure inversion, with classical autoindexing as a drop-in remedy}},
author = {Frank Cai},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15008282/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008282/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - PXRD-Diff: diagnosing the encoder bottleneck in diffusion-based powder-diffraction structure inversion, with classical autoindexing as a drop-in remedy
AU - Frank Cai
PY - 2026
DA - 2026/09/03
PB - ChemRxiv
DO - 10.26434/chemrxiv.15008282/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008282/v1
AB - Inverting a one-dimensional powder X-ray diffraction (PXRD) pattern to a three-dimensional crystal structure remains an open problem, and recent generative approaches report results under mutually incompatible protocols with failure modes seldom catalogued. PXRD-Diff, a 3.7 M-parameter conditional diffusion model trained on the CDVAE MP-20 split, is presented, and DiffractGPT, PXRDnet and deCIFer are reproduced through the same pymatgen StructureMatcher harness. The central, statistically robust finding is mechanistic: the learned PXRD encoder reaches a 0.007 normalised auxiliary lattice-regression loss in isolation, yet substituting that head’s own lattice into the sampler recovers only 1.2 % of structures, because its ~1.1 Å length error shifts every Bragg peak by ~15 %. The limiter is the global pooling that discards absolute peak positions, not the denoiser alone. A perturbation study locates a sharp sensitivity knee at ~0.5 Å cell error, and a true-lattice oracle lifts match to 4.5 % at n = 1000 (three seeds; 95 % Wilson confidence interval [3.8, 5.3]), disjoint from the no-true-lattice indexer’s 1.5 % [1.2, 2.0]. Replacing the learned lattice head with a classical Q-space autoindexer raises no-true-lattice match to 1.5 % from a learned head that recovers essentially nothing; a three-seed paired McNemar test confirms the gain is significant (p < 10−4; 27 fixed, none broken), concentrated in the high-symmetry systems below the sensitivity knee. Reproduced on one harness, deCIFer reaches 73.8 % match, DiffractGPT 18.9 % and PXRDnet 30.0 %, leaving PXRD-Diff 12–46 times behind. The contributions are the encoder-bottleneck diagnosis, the classical-indexer drop-in, a four-item failure catalogue and the shared evaluation harness; code, checkpoints and the differentiable Bragg simulator are released.
ER -