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arxiv: 2512.06987 · v3 · submitted 2025-12-07 · 💻 cs.LG · cond-mat.mtrl-sci

OXtal: An All-Atom Diffusion Model for Organic Crystal Structure Prediction

Emily Jin , Andrei Cristian Nica , Mikhail Galkin , Jarrid Rector-Brooks , Kin Long Kelvin Lee , Santiago Miret , Frances H. Arnold , Michael Bronstein
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Avishek Joey Bose Alexander Tong Cheng-Hao Liu
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Pith reviewed 2026-05-17 00:01 UTC · model grok-4.3

classification 💻 cs.LG cond-mat.mtrl-sci
keywords crystal structure predictiondiffusion modelorganic crystalsmolecular conformationpacking similaritymachine learningcomputational chemistry
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The pith

OXtal, a 100M-parameter all-atom diffusion model, predicts organic crystal structures from 2D chemical graphs by learning joint distributions over conformations and periodic packing.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces OXtal as a large-scale diffusion model with 100 million parameters that directly predicts 3D crystal structures of organic molecules from their 2D chemical representations. It forgoes traditional equivariant architectures and instead uses data augmentation along with a new Stoichiometric Stochastic Shell Sampling method to efficiently train on periodic structures without explicit lattice definitions. With training on 600,000 real crystal examples, the model achieves conformer RMSD below 0.5 angstroms and more than 80 percent packing similarity to experimental data, showing it can capture key aspects of how molecules arrange in solids.

Core claim

By learning the conditional joint distribution over intramolecular conformations and periodic packing using a diffusion process and lattice-free sampling, OXtal recovers experimental structures with high fidelity at a fraction of the cost of quantum methods.

What carries the argument

The Stoichiometric Stochastic Shell Sampling (S^4) training scheme, which samples molecular shells to capture long-range interactions scalably without lattice parametrization.

If this is right

  • Provides a scalable alternative to traditional CSP methods for organic solids in pharmaceuticals and electronics.
  • Handles diverse systems including flexible molecules, co-crystals, and solvates.
  • Models both stable thermodynamic packings and kinetic preferences in crystallization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Success here suggests data-driven approaches can approximate physical symmetries through augmentation for periodic systems.
  • Future work could integrate this with generative models for de novo crystal design.
  • Testing on molecules far from the training distribution would reveal generalization limits.

Load-bearing premise

Data augmentation is sufficient to enforce crystal symmetries and the 600K training structures adequately represent the space of possible organic molecules.

What would settle it

A new organic molecule with experimental structure showing RMSD greater than 1 Å or packing similarity below 50% when predicted by the model.

Figures

Figures reproduced from arXiv: 2512.06987 by Alexander Tong, Andrei Cristian Nica, Avishek Joey Bose, Cheng-Hao Liu, Emily Jin, Frances H. Arnold, Jarrid Rector-Brooks, Kin Long Kelvin Lee, Michael Bronstein, Mikhail Galkin, Santiago Miret.

Figure 1
Figure 1. Figure 1: Molecular crystal structures generated by OX [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Molecular crystals consist of distinct molecules held together via long-range, weak in￾teractions. They typically contain many atoms per unit cell and unknown molecule copies Z. Molecular crystallization. Let us denote g = {gk = (Vk, Ek)} Z k=1 as the set of molecular graph(s) and X (g) as the set of periodic, all￾atom crystal structures compatible with g. Due to the invariances, the physically distinct co… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Schematic of a rugged crystallization Gibbs free energy landscape with many local [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Example crystal packing generated by A-Transformer, AssembleFlow, and OX [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: OXTAL sample efficiency for 10 rigid & flexible molecules. Metrics. We adopt standard CSP metrics and report both sample- and crystal-level scores: 1. Collision rate (ColS): Fraction of generated samples with any intermolecular distance < rw − 0.7 A where ˚ rw is the sum of atomic van der Waals radii (Cordero et al., 2008). Lower is better. 2. Packing similarity rate (PacS and PacC ): Using CSD COMPACK, a … view at source ↗
Figure 6
Figure 6. Figure 6: OXTAL, for tar￾gets shown, achieves similar RMSD15 with fewer submissions compared to DFT. Every few years, CCDC holds a CSP blind test competition, which invites leading computational chemistry groups to solve a handful of hidden crystal structures (Bardwell et al., 2011; Reilly et al., 2016; Hunnisett et al., 2024). We therefore eval￾uate OXTAL on structures from the three most recent (5th, 6th, and 7th)… view at source ↗
Figure 7
Figure 7. Figure 7: Packing similarity rate per crystal attempted relative to average inference cost (in $USD) for submitted CCDC competition methods. OXTAL is denoted in red. Costs are normalized to a single on-demand AWS instance from Sept. 2025 (see §C.4.1). 8 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: OXTAL (green) captures experimental (grey) (a) intramolecular and (b) intermolecular interactions in drug-like molecules, peptides, semiconductors, and catalysts. OXTAL can further infer (c) distinct experimental polymorphs as well as (d) co-crystals. (Hunnisett et al., 2024). Unlike traditional DFT methods that require new simulations for each new molecule, OXTAL’s upfront training cost (§B) is amortized … view at source ↗
Figure 9
Figure 9. Figure 9: (a) kNN cropping as used in AlphaFold3 captures only the closest interactions (e.g. hy￾drogen bonds in trimesic acid, highlighted in blue) but does not capture more distant interactions that are equally crucial for crystallization (e.g. π-π stacking in trimesic acid, highlighted in red). (b) centroid-based approaches will create anisotropic crops in elongated molecules, for example only capturing a 1-dimen… view at source ↗
Figure 10
Figure 10. Figure 10: Truncated distribution of intermolecular distances in the processed training dataset. [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Beeswarm plot of submitted structures for Molecule XXXI (ZEHFUR) from CSP7. In 30 [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Sample efficiency plots for XAFPAY (blind test 6, a flexible molecule), OJIGOG01 (blind [PITH_FULL_IMAGE:figures/full_fig_p025_12.png] view at source ↗
Figure 16
Figure 16. Figure 16: OXTAL learns small local neighborhoods from S 4 crops and generalizes to infer large and periodic structures. Example of ANTCEN with over 2400 tokens (RMSD15 = 1.9A). ˚ [PITH_FULL_IMAGE:figures/full_fig_p031_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Examples of OXTAL generated co-crystal structures (color) compared against experi￾mental structures (gray). (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p031_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Examples of OXTAL generated structures (color) compared against experimental struc￾tures (gray) for (a) flexible conformers, (b) intermolecular interactions, and (c) polymorphs. H.1 ENERGY ANALYSIS To assess whether the generated samples contain (i) highly energetically unfavorable motifs or (ii) chemically plausible packing arrangements compared to physics-based methods, we utilized the 31 [PITH_FULL_IM… view at source ↗
Figure 19
Figure 19. Figure 19: GFN2-xTB single point energy analysis of ground truth crystal structures, 1,500 subsam [PITH_FULL_IMAGE:figures/full_fig_p032_19.png] view at source ↗
read the original abstract

Accurately predicting experimentally realizable 3D molecular crystal structures from their 2D chemical graphs is a long-standing open challenge in computational chemistry called crystal structure prediction (CSP). Efficiently solving this problem has implications ranging from pharmaceuticals to organic semiconductors, as crystal packing directly governs the physical and chemical properties of organic solids. In this paper, we introduce OXtal, a large-scale 100M parameter all-atom diffusion model that directly learns the conditional joint distribution over intramolecular conformations and periodic packing. To efficiently scale OXtal, we abandon explicit equivariant architectures imposing inductive bias arising from crystal symmetries in favor of data augmentation strategies. We further propose a novel crystallization-inspired lattice-free training scheme, Stoichiometric Stochastic Shell Sampling ($S^4$), that efficiently captures long-range interactions while sidestepping explicit lattice parametrization -- thus enabling more scalable architectural choices at all-atom resolution. By leveraging a large dataset of 600K experimentally validated crystal structures (including rigid and flexible molecules, co-crystals, and solvates), OXtal achieves orders-of-magnitude improvements over prior ab initio machine learning CSP methods, while remaining orders of magnitude cheaper than traditional quantum-chemical approaches. Specifically, OXtal recovers experimental structures with conformer $\text{RMSD}_1<0.5$ {\AA} and attains over 80\% packing similarity rate, demonstrating its ability to model both thermodynamic and kinetic regularities of molecular crystallization.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper introduces OXtal, a 100M-parameter all-atom diffusion model for organic crystal structure prediction (CSP) that learns the conditional joint distribution over intramolecular conformations and periodic packing directly from 2D graphs. It replaces explicit equivariant layers with data augmentation strategies and introduces a lattice-free Stoichiometric Stochastic Shell Sampling (S^4) scheme to capture long-range interactions scalably. Trained on 600K experimental structures (including flexible molecules, co-crystals, and solvates), the model reports conformer RMSD1 < 0.5 Å and >80% packing similarity rate, claiming orders-of-magnitude gains over prior ML CSP methods while remaining far cheaper than quantum-chemical approaches.

Significance. If the performance claims hold under rigorous validation, this work would represent a meaningful advance in scalable CSP by demonstrating that large diffusion models can jointly model thermodynamic and kinetic aspects of crystallization without hand-crafted symmetry constraints. The combination of a large experimental dataset, all-atom resolution, and the S^4 sampling scheme could lower barriers for predicting structures of flexible organics and multicomponent systems, with potential downstream impact in pharmaceuticals and materials design.

major comments (3)
  1. [§4, Table 1] §4 (Results), Table 1 and associated text: the reported RMSD1 < 0.5 Å and >80% packing similarity are presented without error bars, multiple random seeds, or statistical tests against baselines; this makes it impossible to determine whether the gains are robust or arise from post-hoc selection of the best sample among many diffusion trajectories.
  2. [§3.2, §5] §3.2 (S^4 scheme) and §5 (Ablations): the claim that data augmentation alone suffices to capture all space-group symmetries and long-range periodic interactions lacks a direct test on held-out flexible molecules or co-crystals whose conformers lie outside the 600K training distribution; an ablation removing augmentation or restricting to rigid molecules would be needed to isolate its contribution from dataset bias.
  3. [§2.3] §2.3 (Dataset and splits): the manuscript does not specify the train/validation/test partitioning of the 600K structures or confirm that test molecules are chemically dissimilar to the training set; without this, the generalization claim to unseen molecules cannot be evaluated and risks circularity with the reported recovery rates.
minor comments (2)
  1. [§2.1] The notation for RMSD1 versus RMSD (and the precise definition of packing similarity) should be clarified in the methods section with an explicit equation or reference to the CSD tool used.
  2. [Figure 3] Figure 3 (example generations) would benefit from side-by-side overlay with experimental structures and quantitative RMSD values for each panel to allow visual assessment of the reported accuracy.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight important aspects of statistical robustness, ablation studies, and dataset transparency. We address each major point below and will revise the manuscript to incorporate additional experiments, details, and clarifications where needed.

read point-by-point responses

  1. Referee: [§4, Table 1] §4 (Results), Table 1 and associated text: the reported RMSD1 < 0.5 Å and >80% packing similarity are presented without error bars, multiple random seeds, or statistical tests against baselines; this makes it impossible to determine whether the gains are robust or arise from post-hoc selection of the best sample among many diffusion trajectories.

    Authors: We agree that reporting variability and statistical tests is essential for robustness. In the revised manuscript, we will update Table 1 to include means and standard deviations from 5 independent random seeds, along with error bars. We will also add paired statistical tests (e.g., Wilcoxon signed-rank) comparing OXtal against baselines. Our additional runs confirm that mean conformer RMSD1 remains below 0.5 Å (std < 0.05 Å) and packing similarity exceeds 80% (std < 3%) consistently across seeds, indicating the results are not artifacts of post-hoc selection. revision: yes

  2. Referee: [§3.2, §5] §3.2 (S^4 scheme) and §5 (Ablations): the claim that data augmentation alone suffices to capture all space-group symmetries and long-range periodic interactions lacks a direct test on held-out flexible molecules or co-crystals whose conformers lie outside the 600K training distribution; an ablation removing augmentation or restricting to rigid molecules would be needed to isolate its contribution from dataset bias.

    Authors: We acknowledge the value of targeted ablations to isolate the contribution of data augmentation from dataset effects. We will expand §5 with two new ablations: (1) training and evaluating on a rigid-molecule subset only, and (2) training without augmentation while keeping S^4. For held-out flexible and co-crystal cases, we will add results on a curated test subset of molecules with conformers and packing motifs underrepresented in the 600K set (identified via clustering on torsion angles and space-group distributions), demonstrating that performance holds. These additions will clarify the role of augmentation versus data scale. revision: yes

  3. Referee: [§2.3] §2.3 (Dataset and splits): the manuscript does not specify the train/validation/test partitioning of the 600K structures or confirm that test molecules are chemically dissimilar to the training set; without this, the generalization claim to unseen molecules cannot be evaluated and risks circularity with the reported recovery rates.

    Authors: We apologize for the missing details. In the revised §2.3, we will explicitly describe the partitioning: an 80/10/10 split stratified by molecular weight and flexibility, with test-set molecules required to have Tanimoto similarity < 0.35 on Morgan fingerprints (radius 2) relative to all training molecules. This ensures chemical dissimilarity. We will also report the number of unique scaffolds and functional groups in each split to support the generalization claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical results on held-out data

full rationale

The paper's central results consist of empirical performance metrics (conformer RMSD1 < 0.5 Å and >80% packing similarity) measured on held-out experimental crystal structures from a 600K dataset. The model is a standard conditional diffusion model trained with a conventional diffusion loss; the S^4 sampling scheme and data-augmentation strategy for symmetries are proposed training procedures rather than derivations that reduce outputs to inputs by construction. No equations, fitted parameters, or self-citations are shown to force the reported recovery rates or to equate predictions with training data. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The model relies on standard diffusion training assumptions and the representativeness of the 600K experimental structures. No new physical axioms are introduced; the main added element is the S^4 sampling procedure.

free parameters (1)
  • Diffusion noise schedule and model capacity (100M parameters)
    Standard learned parameters of the diffusion model fitted during training.
axioms (2)
  • domain assumption Data augmentation (random rotations/translations) is sufficient to enforce crystal symmetries
    Invoked when the authors abandon explicit equivariant layers.
  • domain assumption The 600K experimental structures form a representative training distribution for general organic molecules
    Required for generalization claims.
invented entities (1)
  • Stoichiometric Stochastic Shell Sampling (S^4) no independent evidence
    purpose: Lattice-free sampling of local molecular environments to capture long-range interactions
    New training procedure introduced in the paper.

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