OXtal: An All-Atom Diffusion Model for Organic Crystal Structure Prediction
Authors: Emily Jin
Andrei Cristian Nica
Mikhail Galkin
Jarrid Rector-Brooks
Kin Long Kelvin Lee
Santiago Miret
Frances H. Arnold
Michael M. Bronstein
Joey Bose
Alexander Tong
Cheng-Hao Liu
Venue: ICLR 2026 Poster (2026)
Keywords: Crystal structure prediction
Diffusion models for computational chemistry
AI for science
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
TL;DR: We present an ab-initio all-atom diffusion model for molecular crystal structure prediction and outperform existing machine learning methods by an order of magnitude.

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 $\mathrm{RMSD}_1<0.5$ Å and attains over 80% packing similarity rate, demonstrating its ability to model both thermodynamic and kinetic regularities of molecular crystallization.

Published as a conference paper at ICLR 2026
OXTAL: AN ALL-ATOM DIFFUSION MODEL FOR ORGANIC CRYSTAL STRUCTURE PREDICTION
Emily Jin m Andrei Cristian " Mikhail Galkin Jarrid Rector-Brooks Kin Long Kelvin Lee" Santtiao Miret ; Frances H. Arnold Michael Bronstein 1.9,
Avishek Joey Bose! 1,,11, Alexander Tong", Cheng-Hao Liu 8.00 'University of Oxford, PSynteny, 'Google, *Mila, Universitéé Montréal, CCaltech, "NIIDIA, Lila, "AITHYR,, Futureeouse.. 11 Imperial College London
ABSTRACT
Accurately predicting experimentally realizable 3D molecular crystal structures from their 2D chemical graphs is a long-standing open challenge in computa- tional chemistry called crystal structure prediction (CSP). Efficiently solving this problem has implications ranging from pharmaceuticals to organic semiconduc- tors, as crystal packing directly governs the physical and chemical properties of organic solids. In this paper, we introduce OXTAL, a large-scale 100M parame- ter all-atom diffusion model that directly learns the conditional joint distribution over intramolecular conformations and periodic packing. To efficiently scale OX- TAL, we abandon explicit equivariant architectures imposing inductive bias arising from crystal symmetries in favor of data augmentation strategies. We further pro- pose novel drystallzaationinspiii
lattice-fre training scheme, STOICHIOMET- RIC STOCHASTIC SHELL SAMPLING (S*), that efficiently captures long-range in- teractions while sidestepping explicit lattice parametrization-thee enabling more scalable architectural choices at all-atom resolution. By leveraging large dataset 600K experimentally validated crystal structures (including rigid and flexible molecules, co-crystals, and solvates), OXTAL achieves orders-of-mape magnituge im- provements over prior ab initio machine learning CSP methods, while remain- ing orders of magnitude cheaper than traditional quantum-chemice approaches. Specifically, OXTAL recovers experimental structures with conformer RMSD) < 0.5 Å and attains over 80% packing similarity rate, demonstrating its ability model both thermodynamic and kinetic regularities of molecular crystallization.
INTRODUCTION
A landmark open challenge in computational chemistry is identifying a molecule's 3D crystal structure given knowledge of its chemical composition (Bardwell et al., 2011; Reilly et al., 2016; Hunnisett et al., 2024). In particular, given only molecule's 2D chemical graph, ab initio molecular crystal structure prediction (CSP) seeks to estimate the distribution of experimentally realizable crystal packings in accurate and scalable manner. This 3D arrangement of molecules within a periodic lattice dictates the macroscopic behavior of organic solids. For instance, in phar- maceuticals, crystal packing governs solubility, bioavailability, and the long-term stability of active ingredients (Schultheiss & Newman, 2009; Chen et al., 2011); in material science, intermolecular geometry dictates charge transport, porosity, and optical response enabling applications across electronics, photonics, sensing, and energy storage (Zhang et al., 2018; Wang et al., 2019).
The complexity of CSP is underscored by the nature of crystal formation, wherein experimentally realized structures often occupy local minima of highly non-smooth and well-separated Gibbs free energy landscape (Figure 3(a)). This thermodynamic energy landscape is determined by the com- petition between the intramolecular interactions that set the molecule's ' own (flexible) conformation
'Equal Contribution.
1 Corresppnniigg authors: emi 1y. jiné cs ox.oox....... ac..ac.uu uk; chl@caltech. I Work completed while at Mila.
Work completed while Intel Labs.

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QOOCIG RM.55FF0.55.
HURYUQ RMMDD.F0.85
TPHPOR RVSD,,-1233
UMIMIO RMSD
POOPP PODNO PAPPO
GLYCIN 70.74
ACACPD RMSD 13
CAPRYL RMSD,F=0.73. A
QAXMEH
RMSD,FF1.24 A
Figure 1: Molecular crystal structures generated by OXTAL (color) compared to ground truth (grey).
and the long-range and weak intermolecular forces that dictate how molecules pack together peri- odically (Chernov, 2012). As a result, classical CSP approaches combine a search procedure (e.g., enumeration evolutionary algorithms) with oracle access energy/ranking models, such force fields or quantum-chemical density functional theory (DFT) (Engel & Dreizler, 2011: Hunnisett al., 2024). However, classical CSP approaches often fail to capture realistic kinetic conditions that lead to the distribution of experimentally sampled energy minima. Consequently, these methods require the generation and optimization of ~1,000 100,000 structures per molecule-the the majority of which struggle to go beyond unfavourable local energy minima despite extensive computation.
Recently, generative approaches to modeling atomic systems-e., e.g.. AlphaFold3 (Abramson et al., 2024) for biomolecules and MatterGen (Zeni et al., 2025) for inorganic materials- have demon- strated their ability to capture intricate 3D atomistic interactions directly from data. Molecular CSP generalizes both of these, as proteins and inorganic crystals have smaller set of interactions; pro- teins pack into lattices under strong intramolecular constraints mostly governed by their backbones (Branden & Tooze, 2012), and inorganic crystals possess strong covalent ionic bonds across smaller number atoms (Figure 2a). Protein generative models also heavily rely on biological priors based evolutionary information captured by multiple-sequence alignment (Jumper et al., 2021). In contrast, small-molecule crystals span chemically diverse scaffolds, exhibit rich conformational flexibility, and often contain many molecular copies within unit cell (Figure 2b). Accurately capturing these interactions requires large and diverse training set, highly expressive yet efficient to sample models, and training schemes that consider periodic interactions in crystal lattice without impeding scalability for large model training.
Main contributions. this paper. we introduce OXTAL, an all-atom diffusion transformer model for molecular CSP. Conditioned solely on the 2D molecular graph, OXTAL learns to sample exper- imentally realistic crystal structures with accurate deseriptions of molecular conformers as well as their periodic packing. To enable large-scale modeling, we train OXTAL on over 600k experimental molecular crystal structures spanning rigid and flexible molecules, co-crystals, and solvates. OXTAL builds recent advances in all-atom generative modeling (Abramson et al., 2024), discarding sym- metry representations of lattice vectors and associated crystal symmetries favor of training directly on Cartesian coordinates and employing SE(3) data augmentation. We further introduce STOICHIO- METRIC STOCHASTIC SHELL SAMPLING (S²). a novel lattice-free training scheme that retains the rich information of long-range interactions. We summarize key contributions follows:
We present OXTAL, the first large-scale all-atom diffusion model for molecular CSP, that samples molecular crystal packing directly from 2D molecular graphs ($3).
We introduce a crystaliiaaionninssire training scheme for periodic structures, 51, which removes explicit lattice parametrization and enables more scalable training ($3.1).
Empirically, OXTAL significantly outperforms existing ML-based ab initio CSP methods, achiev- ing RMSD, 0.5 Á and packing similarity rates above 80% within 30 samples ($4.1), while be- ing several orders of magnitude cheaper than traditional quantum chemical methods in DFT ($4.2). We provide additional chemical analysis highlighting OXTAL's ability capture diverse intramolecular and intermolecular interactions, including crystal polymorphs, and generalize to complex co-crystal and biomolecular interactions ($4.3).
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2 BACKGROUND AND PRELIMINARIES
2.1 CRYSTAL REPRESENTATIONS
Formally, periodic crystal structure C is defined by a pair (L, The first component L E 3 defines the lattice vectors forming parallelepiped known the unit cell. The second component B = {( ] is the basis, which consists of the N atoms within this unit cell. Each atom described by its species { and its fractional coordinates {u, E [0, 10,1) relative to the lattice vectors,
equivalently, its Cartesian coordinates Lu,, For molecular crystals, B naturally decomposes into molecules. The connectivity of each molecule my is given by graph {9i (Vi, Ex) E=) (vertices/atoms Ví and edges Ex: species labels We next recall the symmetries present in the periodic crystal structure C.
carried by the vertices).
Symmetries. Given C (L, B) where (u: T R2/Z²) the Cartesian positions of atoms are,
X B) = [L + uz) n E 2 i= 1..,.,,
(1)
Furthermore, two descriptions (I. .3) and (I', encode the same structure if and only if there is group action in 3D, g tR SE(3) such that, X(I', B²) g (II,
A periodic crystal admits an asymmetric unit A, the minimal subset that recovers the entire unit cell by applying symmetry transformations of the crystal's space group. Conversely, supercell can be obtained by integer matrix U Z3x3 with m det U| 2 1, yielding C(C) (LU, B(),, the same infinite crystal in a differing tiling. For example, U = mla yields a cubic m x m X m. supercell. A formal summary of crystal symmetries is outlined below.
Crystal representation invariances
(S1) Global translation. For i T,, (L, ((),, (L, ((z), us + ()}).
(S2) Globul rotation. For R E SO(3), (L, {(z,, u:))) + (RL, ((z,, us)))-
(S3) Permutation (reindexing). For Ç E (L,(L, {(z,, u))) + (L, {(((()) (c())))
(S4) Unit-cell change. Let U g3x3 with m == det U| 2 1. Unimodular basis change (m = 1, E GL 2)):
(T., ((z, + (LU, ((=, U (.))) w)))), (LU) U-) = L(Un + uz).
Supercell expansion (m > 1): Let R(U) c T be fixed set of coset representatives for 2 /UZ/ (so (R( m.. Then
(L, (22, u,
LU, {(z, U- + +r)) i= 1,... N, re R(U))).
since (LU) + U + r)) = L(Un u4 +r)
Molecular crystallization. Let denote g {gk = (Vi, Ex) as the set of molecular graph(s) and X(g) the of periodic, all- atom crystal structures compatible with g.
Due to the invariances, the physically distinct configurations form a quotient space M(g) / ~, Ab inãtio CSP can then be posed as conditional probabilistic inference over equiva- lence classes [C] = (L, B) E M(g). An ap- proximation of the experimentally realized dis- tribution under crystallization conditions is:
(a) CaTiOs (inorganic) Figure 2:
(b) Asprin (organic)
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.
Ps ([C) g) x Ax ([C] g) exp (-BAG((C))
where AG is the Gibbs free energy (thermodynamiccs) Ki summarizes kinetic accessibility (nucle- ation and growth pathways), / T kn is the Boltzmann constant, and T is temperature.
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In practice, learning and sampling must respect the symmetry of MMg). handle strong coupling between intramolecular conformation and intermolecular packing (especially in flexible molecules), navigate rugged kinetic and energy landscapes arising from large unit cells (often > 100 atoms) and weak, long-range interactions, and marginalize over unknown Z.
These challenges are distinct from inorganic erystals, which are characterized by continuous, strong ionic and covalent bonds, no molecular conformers, and often < 30 atoms per unit cell (Figure 2).
2.2 CONTINUOUS- TIME DIFFUSION MODELS
diffusion model solves the generative modeling problem by being the solution to a (Itô) stochastic differential equation (SDE) (Øksendal, 2003),
dX, fx( dt + o,dW,, Xo po-
In Equation (2), we use boldface to denote random variables and normal script to denote functions or samples. The function ft R + R corresponds to the average direction of evolution, while Te : IR + R is the diffusion coefficient for the Wiener process W.. r. By convention, this is termed the forward noising process that starts from time L = 0 and progressively corrupts data until the terminal time t where we reach a structureless prior p1 (z1) == (0, I).
Under mild regularity assumptions, forward SDEs of the form of Equation (2) admit time reversal, which itself is another SDE in the reverse direction & to t and transmutes prior sample In ~ P1 to a sample from the target distribution 2g Po (Anderson, 1982).
dx, (X)(X) dt V log (X.)) dt + a,dW,, ~1
(3)
Here W, another standard Wiener process, and the reverse-time SDE shares the same time marginal density as the forward SDE. Critically, the forward and reverse SDEs are linked via the Stein score V log Pe (are), which is the key quantity of interest in the design of diffusion models. More precisely, diffusion models estimate the score function by forming an Ez-regression objective using a denoising network Do(r,, l). For example, for the variance exploding (VE) SDE family of forward processes: Pt Po (O, (O, this corresponds to learning the set of optimal denoisers,
ie., the set of conditional expectations, across time (z,, t) E [ X, = zz] Vt e [0, 1]. Owing convert this simple simulation-free training ditional objective for any Bregman divergence with convex F, 18, (Holderrieth et al., 2025, Prop. 2)
to the nature of Gaussian convolution,
(0) = Ex..((0.))eoo-pptsaaaa/r....a.e
[A(t) Do f))]
(4)
where A(1) : [0, 1] R., any weighting function. For a sufficiently expressive family of denois- ers 71 = {Do: 0 θ}. the minimizer to Equation (4) is (i = D(x,, E [X XX xn). Given a trained denoising model, diffusion models generate samples at inference by simulating the reverse-time dynamics of (3) with the learned score 8o computed as < (Do(x,,() - x: 2z)/ot-
3 OXTAL
We now describe OXTAL, our all-atom diffusion model for molecular CSP. As outlined in $2.1, existing inorganic CSP models (Miller et al., 2024; Gasteiger al., 2021) that rely equivariant architectures and explicit unit-cell parametrizations face scalability challenges for large molecular crystals with unknown multiplicity Z. We thus introduce 5 training, which exposes the model to long-range periodic cues without ever parametrizing lattice 1$).1). Second, we implement a high- capacity, non-equivariant Transformer with data augmentation and strong molecular embeddings to capture symmetries ($3.2). Together, these choices decouple what to generate (conformations and packing) from how the crystal is represented during training (unit cell, Z, etc.).
3.1 STOICHIOMETRIC STOCHASTIC SHELL SAMPLING (S*)
Crystallization is local-to-global process: once molecules approach contact distances, weak but specific interactions induce recurring motifs that propagate periodically. Learning to denoise such local consistent neighborhoods should therefore recover larger periodicity inference time. Training on such subsampled blocks reduces token size, provides natural augmentation, and mirrors the partial observability of nucleation and growth (Figure 3(b)).
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(a)
(b)
(c)
Energy
Energy Kinetics
brick-wall, 1:1
herringbone, 2:1
(d)
Predicted crystal
SMILES sequenice(s) CHCOOC-M.COM Molecular feat.
Single
S" crop
Conformer
Atom
Pairorrmr blocks
Diflus Module
optimization
Encoder
Pair repr.
Conformer feat.
Recydling (x2)
Diflusion steps
Predicted conformer
Figure 3: (a) Schematic of rugged crystallization Gibbs free energy landscape with many local minima. Kinetic conditions often dictate which experimental minimum is formed. (b) Molecular crystallization, showing nucleation and growth in successive layers, which is the inspiration for S* (c) Common packing motifs exemplified in co-crystal polymorphs with 1:1 and 2:1 stoichiometric ratio. (d) Overview OXTAL. architecture.
We formalize this idea in 5 Let ((V) = (LU, B(U) be a supercell with molecules m E M, where (m) C R denotes m's non-hydrogen Cartesian coordinates. We next define the minimum-imag intermolecular distance between two molecules, duan (m, m') = min, (m)) e X (m²) || x 1|2-
Given a fixed contact radius reut, 5tt builds concentric shells S around a mniformly-samplee central molecule m. Uniform(A)) based the molecular contact graph induced by dmiin (:, I Yout
(m {m+ E M kreat S dmin (min m.) (k- 1)reurh
= 0,,,,,
Pmmax), and define the block of molecules Vx = -K We cap block size by token budget Tmax (atoms).
We sample the number of shells K Uniform(O, kimax) with probability
|Vxl < Taax we accept Vx: otherwise we choose the smallest K* with [V > Tmax and no full shells fit, we subsample the frontier Sx- to meet the budget while preserving the crystal's molecular stoichiometry (Figure 3(c)). For example, if molecule type i appears N:AS times in A and N; times in SK*, we sample molecules of type in Sx- with weight w; x (NASU/No /N,). The resulting set is our training crop, denoted Aerop-
Compared to centroid- or i:NN-based heuristics, this "shell cropping" better respects local interac- tion networks by respecting anisotropic packing motifs and interactions beyond the strongest ones (Figure 9), while mitigating truncation biases common in large-graph learning (Zeng et al., 2020). $D.1 shows that training with S outperforms kNN and centroid cropping methods, and $F.1 shows that training with S can generalize to long- range periodicity beyond training token sizes. Hyper- parameter ablations of Tem can be found in $D.2. Finally, we bound the error due to cropping. In the next proposition (see SA for proof), we show that the enror in the loss due to cropping with $ decreases with the cube root of the number of tokens.
Proposition 1. Let AA ((u, v) E F. E Acmo, & Acrop] represent the bound- ary of Aemp- Denote the number of atoms in volume C as T(C).. Let La (cmm))))) Elu,o) L(u, v) be the boundary loss. Assuming 3 s.t. L(u, v) 0, Vu, s.t. ||u [ ||| 10 Le. L is local, and there exist 0 <a a 00 s. S|S1 < T(S) I b)S) for any S C V. Then,
Lo( (p(p)))))) O((1 Temr) T ((A T T(Acmp)
(6)
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3.2 MODEL ARCHITECTURE
OXTAL is comprised of: (1) an Atom encoder that embeds both physical and structural information: (2) a Pairformer trunk that propagates information across all atoms in the crop; (3) a Diffusion module that takes in the single and pairwise representations and outputs generated crystal struc- ture. The overall architecture of OXTAL is depicted in Figure 3(d).
Atom encoder. Given an input SMILES sequence 8, we generate a 3D conformer with RDKit ETKDG followed by relaxation by the semi-empirical quantum chemical method GFN2-xTB (Pracht et al., 2020). The atomic number, positions, formal charges. Mulliken partial charges, and bond information are used as feature embeddings for the model. OXTAL is not particularly sensitive to the feature conditioning conformer coordinates (SE). Finally, we resolve ambiguity of identical molecular copies via relative position encoding on entity identifiers (Abramson et al., 2024).
Pairformer trunk. We adapt existing state-of-the-art architectures for protein folding to generate single and pair representations for each molecular crystal (Abramson et al., 2024). Instead of tokenizing protein residues, we simplify the tokenization such that each token directly represents a single atom Og in the molecule. We then apply the Pairformer stack from AlphaFold3, which leverages triangular self self-attention to update the single and pair representations. Unlike AlphaFold2, which relied on the equivariant Evoformer (Jumper et al., 2021) architecture, this simpler Pairformer module is not explicitly equivariant, allowing for training larger sequences.
Diffusion module. The design of our diffusion module follows that of AlphaFold3 (Abramson al., 2024), consisting of an atom attention encoder which combines token information given by the pairformer with an encoded representation of T₁. This is followed by a large 70M parameter diffusion transformer (Peebles & Xie, 2023), before final atom attention decoder predicts the denoised atomic positions. We broadly follow Karras et al. (2022) for pre-conditioning of model inputs. A diffusion module size ablation is further provided in $D.3.
3.3 TRAINING
OXTAL is trained using a procedure similar to those successfully employed for protein structure prediction (Abramson et al., 2024). The training objective a composite loss designed to capture both the global structure and the accuracy of the local chemical environment. This loss is comprised of two main components:
(1) mean squared error loss Lme, (2) a smooth local difference distance test DDD as defined in Abramson et al. (2024). Both losses compare the predicted structure align al i (20, and the latter emphasizes the pairwise interactions within the crop via a surrogate of the interatomic distances. To round off our training, we also include a distogram loss on separate head branching from the trunk Edist (d, d) to ensure the trunk output contains binned pairwise distance information. Additional details for computing component losses are provided in $B.2.3. The final loss is then a weighted sum of these components:
to Do and aligned ground truth structure 20
align) + Cavbrr(eo, 20 align + Aaisa Lasa d). [(0) = E (, (x.lxgg)) (Cmse To
We next curate training dataset from the Cambridge Structural Database (CSD) that contains ~ 600k crystals. Specific details regarding model training and configuration are outlined in $B.
4 EXPERIMENTS
We evaluate OXTAL on several different datasets for molecular CSP, comparing against a range of ML-based ($4.1) and DFT energy-based methods ($4.2). These results are complemented with broader chemical survey ($4.3). See $C for exact specifications.
Baselines. We compare against ab initio ML methods and mased methods. For ML methods, most models for inorganic CSP are incompatible, so we evaluate against the pre-trained Assem- bleflow, molecular CSP method that infers crystal packing from rigid-body molecules (Guo et al., 2025) and A- Transformer, an all-atom transformer flow matching model (SC.3.1). Additional results for zero-shot inference from AlphaFold3 are presented in SC.3.3. For energy-based methods, we compare against computational chemistry baselines that submitted to CCDC's 5th, 6th, and 7th CSP blind tests (Bardwell et al., 2011; Reilly al., 2016; Hunnisett et al., 2024).

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Ground Truth
A-Transformer
AssembleFlow
OXtal (ours)
PUBMUU (rigid)
Figure 4: Example crystal packing generated by A-Transformer, AssembleFlow, and OXTAL.
Table I: Performance of ab initio ML models on rigid and
flexible molecular CSP in 30 samples. OXTAL achieves an order of magnitude improvement and the only model able approximately solve any crystals in the flexible dataset.
Rigid Flexible ele
8
Avg. RM (A)
Model
Cols 4 Pacs
Paec t Rees 1 Rece f Sole 1
Rigid Dataset
4
A-Transformer
0.731
0.015
0.060
0.033
0.120
0.060
2
AssembleFlow
0.524
0.001
0.040
0.211
0.760
OXTAL
0.011
0.873
1.000
0.737
0.960
0.300
1
10
100
500
Flexible Dataset
N samples
A-Transformer
0.900
0.001
0.020
AssembleFlow
0.883
0.021
0.140
Figure 5: OXTAL sample efficiency for 10 rigid & flexible molecules.
OXTAL
0.097
0.291
0.900
0.048
0,400
0.220
Metries. 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 < Two
0.7 A where r'e the sum of atomic van der Waals radii (Cordero al., 2008). Lower better.
2. Packing similarity rate (Pacy and Pacc): Using CSD COMPACK, sample's 's packing is partially similar if at least 8 of 15 molecules could be aligned to an experimental cluster (cluster size per match.
CSP5; SC). Pace is the fraction of targets with least
3. Conformer recovery (Recy and Recc): RMSD, < 0.5 Å (non-hydrogen) to a solid-state con- former. Recs averages over all samples; Rece is the fraction of targets with at least one match. Approximately solved (Solc): Any collision-free, packing-similar similar sample with RMSD11 2 on a 15-molecule cluster.
4.1 CSP FOR RIGID AND FLEXIBLE MOLECULES
First, we compare OXTAL to ab initio ML models two different test sets comprised of repre- sentative rigid and flexible molecules with ground-truth structures in CSD (see $C.2 for details). For each crystal target, we generate n2 = 30 samples using each model. Training-time exclusions ensure no target appears in the training sets of OXTAL or A- T-Trnsformmr; AssembleFlow uses a public checkpoint that may include overlap. DFT baselines are omitted here due prohibitive cost.
Results. Table shows OXTAL outperforms existing ML methods across all metrics on both datasets. Intramolecularly (Recc), OX TAL recovers up to 90% of solid-state molecular conformers; intermolecularly. Colg is near zero on rigid targets and low on flexible ones. OXTAL's predicted packings also attain strong packing similarity rate against experimental structures, with approximate solves for both rigid and flexible molecules. Qualitatively (Figure 4), A- A-Transformer struggles to capture meaningful conformers despite being given Z. highlighting the limitations of unit cell based model. AssembleFlow generates molecular assemblies with large spatial separations that lack periodicity (also reflected in low Pacç and Pacş scores). along with frequent interatomic clashes.
Sample efficiency. For downstream screening and design, few-sample success is critical. OXTAL exhibits log-linear improvement in RMSD1s among packing-sime
predictions as increases (Figure 5), with several rigid targets reaching Pace and Solç with n < 10. This suggests the sampler (i) often lands near the correct motif and (ii) refines global periodicity with additional draws.
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4.2 CCDC CSP BLIND TESTS
Every few years, CCDC holds CSP blind test competition. which invites leading computational chemistry groups to solve handful of hidden crystal structures (Bardwell al., 201 I; Reilly et al., 2016; Hunnisett et al., 2024). We therefore eval- uate OXTAL on structures from the three most recent (5th, 6th, and 7th) blind tests. Metrics and experiment set up follow $4.1. We compare OXTAL and other ab initio ML baselines against the aggregate of reported expensive DFT- based submis- sions (DFTavg). See $C.4 for additional details and ȘI for per- structure DFT results.
10
8
RMSD,s (A)
NACJAF
2
Oxtal
Others
Results. Table 2 shows that OXTAL strongly outperforms ab initio ML baselines, and achieves the best second best per- formance across all three tests using only 30 samples per target. While DFT methods attain higher approximate solve rates, when OXTAL is allowed to generate the same number of samples as the DFT methods for CSP Blind Test 5, it matches the approx- imate solve rate of DFT avg ($F2). OXTAL consistently scores the best terms of packing similarity rate. From par-sample basis, only 6 30% of DFT samples match the packing cluster, whereas OXTAL generally recapitulates the packing structure (48 118-677 67%). This suggests that while DFT identifies many local energetic minima, OXTAL can better capture the joint energy and kinetic features that determine which motifs are more likely to be formed. Of the hundreds of submitted predictions (and po- tentially many more generated but unsubmitted structures), only a small percentage of DDFT-identified minima are close to ground truth structures (Figure 6). Predicting the correct experimental structure in few shots is crucial for downstream discovery ap- plications, and OXTAL reliably approximates crystal packings sans any ranking methods.
0
10
10a
10a
Submission
10
8-
RMSD (A)
OJIGOG01
OXtal
Others
2
0
100
10a
102
10a
Submission
Figure 6: OXTAL, for tar- gets shown, achieves similar RMSD11 with fewer submis- sions compared to DFT.
Inference cost. A major pitfall of DFT-based methods is the extremely high computational cost required to run the atomistic simulations. Recently, CCDC raised concerns over the 46 million CPU core hours that were reportedly utilized by submitted methods in CSP7 solve only 8 crystal targets
Table 2: Results for the 5th, 6th, and 7th CCDC CSP blind tests. Classical chemistry methods are aggregated DFT avg. The best model is bolded, and the second best is underlined.
TXtal
CSP-6
10a
CSP-5
CSP-7
Average cost (USD)
10a
Model
us Cols + Pacs Pace 1 Recs t Reco 1 Sole
10a
CSP Blind Test 5
10a
A-Trnsfformrr
30
0.833
0
10a
AssembleFlow
30
0.717
0
0
0.150
0.500
0
10a
DFT
464
0.039
0.323
0.661
0.784
0.733
0.544
OXTAL
30
0.006
0.667
0.833
0.572
0.833
0.167
10-1
CSP Blind Test 6
0.0
Packing similarity rate (Pacs)
A- A-Transformer
30
0.967
0
0
AssembleFlow
30
0.800
0
0
0.073
0.200
0
DFT.vg
83
0.067
0.183
0.520
0.655
0.560
0.496
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 single on-demand AWS instance from Sept. 2025 (see $C.4.1).
OXTAL
30
0.013
0.660
1.000
0.160
0.600
0.200
CSP Blind Test 7
A- A-Transformer 30
0.950
0
0
0
0
0
AssembleFlow
30
0.808
0
0.063
0.250
0
DFT.
868
0.072
0.058
0.511
0.337
0.449
0.421
OXTAL
30
0.021
0.483
0.875
0.129
0.375
0.125
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(a)
(b)
(c)
(d)
OBEGIX
DORDUMO!
NAD10 RMISI,
RM8D,=0.811
RMSD 28
RMSD,
XAFQIH RMSD,-0079
OJIGOG01
HMSD,-0
DORDUMO5 RM5D
PDB: 2OKZ
RMSD,=1.331
TEPNITOS RM60,-0.25
Figure 8: OXTAL (green) captures experimental (grey) (a) intramolecular and (b) intermolecular interactions in drug-like molecules, peptides, semiconductors, and catalysts. OXTAL can further infer (c) distinct experimental polymorphs as well as (d) co-crystals.
(Humnisett al.. 2024). Unlike traditional DFT methods that require simulations for each new molecule, OXTAL'S upfront training cost ($B) is amortized at inference, enabling efficiently sampling for new molecules. Using standardized on-demand cloud pricing (SC.4.1), OXTAL is over an order of magnitude cheaper at inference time, while maintaining strong packing similarity rates (Figure 7). Given CCDC's call for more efficient CSP algorithms, OXTAL'S cost profile enables broad screening and dense posterior sampling before optional physics-based refinement.
4.3 SURVEY OF CHEMICAL INTERPRETABILITY
Beyond benchmark metrics, we examine OXTAL's ' ability to reproduce chemically meaningful in- tramolecular and intermolecular features in practically relevant crystals. Figures and 8 and SH highlight accurate packings (RMSD15 < Å) across diverse rigid and flexible chemotypes: drug-like molecules (HURYUQ), polymer precursors (CAPRYL), organometallies (ACACPD), m conjugated materials (QQQCIG), and ROY (QAXMEH), the molecule which the most known polymorphs.
Molecular interactions. For intramolecular interactions, OXTAL recovers solid-state geometries for highly flexible molecules (which are highly influenced by packing), including small-molecule drugs as well as biomolecular fragments in the Protein DataBank (e.g. RMSD, = 1.3 A for a 6-mer peptide with 17 rotatable bonds (2OKZ) in Figure 8(a)). For intermolecular interactions, OXTAL accurately captures both strong and weak interactions, and both in registry and lengths. Examples in Figure 8(b) include complementary hydrogen bonds in semiconducting crystal (XIJOOT), weak CI-H halogen bonds in organometallic catalyst (OJIGOG), π- stacking in --functional molecule (TEPNIT), and multiple weak contacts in a cluster of the flexible drug aripiprazole (MELFIT) (Fig- ure 18(b).. Zooming out, while OXTAL may prefer planar motifs, it can still reproduce diverse pack- ing motifs, including ID columnar structures (e.g. BALNAD in Figure 8(d)), quasi-2D herringbone structures (e.g. ANTCEN in Figure 16), and 2D brickwork structures (e.g. UMIMIO in Figure 1).
Polymorphs. For molecules with many known polymorphs (including highly rotatable scaffolds), independent OXTAL samples predict distinct experimental polymorphs (e.g., the drugs galunisertib DORDUM in Figure 8(c) and indomethacin INDMET in Figure 18(c)). This suggests the sampler explore multiple kinetic and thermodynamic basins rather than collapsing to single motif. The diversity of sampled polymorphs shown in Figure 20.
Multi-component systems. OXTAL is not restricted to single-component systems. OXTAL can correctly predict the interactions between electron donor and acceptors (Figures 8 and 17), which dictate these crystals' electronic properties. For the charge-transfer semiconducting co-crystals BALNAD and PERTCQ, OXTAL correctly reproduces the ID --stacked columns with alternating donors and acceptors, the inter-columnar brick-wall registry, well as the stacking distances.

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Energy analysis. Finally, probe the energetic plausibility of OXTAL samples using single-point GFN2-xTB calculations ($H.1). Compared to the physics-based submissions to the CSD blind tests, OXTAL samples occupy similar, relatively tight energy basin. This indicates that even without any geometry relaxations, OXTAL learns to avoid unphysical motifs and respects the coarse thermody- namic landscapes.
RELATED WORKS
Physical approaches to crystal structure prediction. Classical crystal structure prediction (CSP) mostly applied search-based algorithms to sample pre-defined search space (Hunnisett et al., 2024). While many such methods have shown varied degrees of success for different applications (van Eijck, 2002; Pickard & Needs, 2011: Case et al., 2016; Tom et al., 2020; Banerjee et al., 2021), they fundamentally rely on many calls to an expensive evaluation function (e.g., energy computation using DFT) and struggle to leverage prior data effectively. Recent search and optimization approaches replace DFT with machine learning interatomic potentials (Batatia et al., 2025; Wood al., 2025; Gharakhanyan et al., 2025). In contrast, OXTAL does not require explicit energy function calls and brings orders of magnitude improvements in speed and inference costs.
Generative models for inorganic crystal structure generation. Generative models have been applied for unconditional de novo generation of inorganic periodic crystals (Xie et al., 2022) and later used for generation conditioned on crystal composition (Jiao al., 2023; 2024; Yang et al., 2024; Miller et al., 2024; Levy et al., 2025). In contrast to molecular crystals, inorganic crystals typically comprise smaller unit cells governed by strong inter-atomic bonding, resulting in rigid continuous lattices rather than flexible molecular packing.
Protein structure prediction. In computational structural biology, the analogous task of protein structure prediction (PSP) conditioned on protein sequence has seen transformative progress with landmark models like AlphaFold (Jumper et al., 2021; Abramson et al., 2024) and ESMFold (Lin et al., 2023), followed by de novo protein design approaches (Watson et al., 2023; Yim et al., 2023; Bose et al.. 2024). These models work with a few dozen residue types, compared to a larger chemical space in general molecular CSP, and use evolutionary information not present in molecular crystals. A more detailed discussion of related work can be found in $G.
DISCUSSION
In this paper, we introduce OXTAL, a large-scale all-atom diffusion model for 3D molecular CSP that learns the joint distribution of molecular conformations and periodic packing conditioned on 2D graphs. Discarding explicit equivariance and unit-cell parametrization for symmetry-aware augmentation and St, OXTAL learns periodic motifs from locally consistent neighborhoods at scale, enabling efficient sampling at all-atom resolution. Empirically, OXTAL achieves state-of- the-art results among ab initio ML methods, and attains competitive packing similarity at several orders of magnitude lower cost compared to DFT- based methods. Our chemical survey supports OXTAL's ability to capture diverse intra- and intermolecular interactions while avoiding unphysical motifs. Nevertheless, many improvements still remain. These include integrating reliable ranking, incorporation of local relaxation, conditioning on crystallization context (i.e. solvent, temperature), and further improving solve rate and sample efficiency.
CONTRIBUTIONS STATEMENT
CL and AN conceived the idea for this project. CL, EJ, and AN led the project development. An earlier version of the model was developed by AN, CL, and MG. The current model was developed by EJ, CL, and JRB. The theoretical work was led by AT and AN, with help from EJ, ABJ, and CL. Data processing was led by CL. Baseline experiments were led by AN, CL, and EJ. Inference and chemical/energy analysis were led by CL, KL, and EJ. CL, AJB, EJ, and AT led the writing with help from all authors. CL., AT, and AJB supervised the project with input from MB, SM, and FA.
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ACKNOWLEDGMENTS
The authors thank fruitful discussions with Tara Akhound-Sadegh, Xiang Fu, Francesca-Zhouffn Li, Dinghuai Zhang, and Hatem Titi. EJ partially funded by AstraZeneca and the UKRI Engineering and Physical Sciences Research Council (EPSRC) with grant code EP/S024093/1. AJB acknowl- edges partial funding through an NSERC PDF scholarship. This research is partially supported by EPSRC Turing AI World-Leading Research Fellowship No. EP/X040062/1 and EPSRC AI Hub on Mathematical Foundations of Intelligence: An "Erlangen Programme" for Al No. EP/Y028872/1. AJB is partially supported by NSERC PDF. The authors acknowledge funding from UNIQUE, CIFAR, Amgen, NSERC, Intel, and Samsung. The research was enabled in part by computational resources provided by the Digital Research Alliance of Canada (attps: // al iancecan. ca), Mila (https:/ / /mi la. quebec), and NVIDIA.

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APPENDIX
A THEORY
Proposition 1. Let A {{u,0} E F. : E Amp, & Acop) represent the bound- ary of Acop- Denote the number of atoms in a volume C as T(C). Let La (o(p)))) = E(a,0EEAA... C(u, v) be the boundary loss. Assuming 3r s.t. [(u, u) O, Vu, U.t. S.t. I|u 1/ > r Le. L is local, and there exist 0 < a < 00 s.t. S| - T(S) I f any S C V. Then,
Lo( (opp) ((11 Tear) T cmp))) 11/3) T T(Acop)
(6)
To prove this proposition, we first label our assumptions.
A1 Locality. 3ng s.t. L(u, v) = 0 for all u, v s.t. ||u - U| > ro
A2 Uniform Density, there exist 0 S b < s. alS| T(S) S b|S| for any 8 S V.
Next we investigate the S algorithm. We first recall the definition of shells and Acrop:
Sx(ga) (g. E C(U)) krow S d(ges 9i) < (A + 1)raat.
k = 0, 1,
(8)
where is the distance between molecules ge and gi in the infinitely repeating lattice. and Teut is some predefined contact radius. Molecules from each subsequent full shell k are added until [Vk+al T muxx where T Tiaa the crop budget. If least one full shell fits, we train on the crop Acou = {9e} U UREx Sg. This implies that Acrop can be well approximated by ball centered around of radius (k + 1)
We define the ball of radius rы raak k Be UnEX Sg. First, present short lemma show the number of neighbors of a node is bounded.
Lemma 1. We define the edge neighborhood of g as N()) = {(u, v} s.t. a = g C(u, v) 2 0}. Assuming [AI] ] and [A2], we have a uniform bound on the degree
[W(g)) c
for some C' independent of g.
Proof. This follows from considering a ball of radius around g. That ball has volume V = - Using [A2], have that the token count (B) <
3 4hy3 and therefore ((gg) 2, which is
independent of
We next note that for regular lattice structure we have the following inequality for the size of the boundary relative to the total volume. Specifically for a lattice we have:
Lemma 2. For < a < < oo on a 3D lattice, we have the following relationship between a sphere's 's surface area and volume: Bx 2/3 < |aBel= < 1//3.
We note that the constants are due to discretization error and locality. As approach the continuous limit (i.e. k + oo), the bounds become tight.
Next, we have to bound how well Acrop is approximated by ball of radius A.
Lemma 3. For some constant 0 < c < oo, AAmmp < 0B + cread |2/
Proof. We first note that Bg C Acrop by construction of Acuu. This means that we can consider
Acoup as all the molecules in B& plus (possibly) some additional molecules in Se(ge). We can then bound the total surface area as
Am < =|0Bal (g.))
(10)
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however we know that the surface area of molecules in (g()e) is bounded by the number of nodes in Sy and some constant.
[aS)(o))l S c|Sa
(11)
c((rounk + 1))² (F)
(12)
or (3k2 + 3k + 1)
(13)
S 3 hu
(14)
cT cut /
(15)
which combined with equation 10 proves the lemma.
We are now ready to prove the main proposition.
Proof. Assuming La (rop)))) is based on a sum of pairwise interaction terms i.e.
(A(p)))))
Σ
C(u, v)
(16)
(u.t)eAA.m
Lemma 3 allows us first analyze Ca(Bx) then Lemma 3 for the final bound.
(a(Bx)
Σ C(u,v)
(17)
E0B.
< c|00Ba] (un)
max
L(u, v)
(18)
using Lemma 2,
S c||Ba|2/8 (u,0) E8B;
max C(u, v)
(19)
Assuming [A1], [A2], and Lemma 1,
S ccTT
(20)
Combining this with Lemma 3 we have the final result
Lo (a)))) = O((1 + TTw) (AA
T (rop))))
As reminder, this proposition implies that the boundary surface becomes less of issue as the number of tokens grows.
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(a)
(b)
RAR
Figure 9: (a) KNN cropping as used 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. म-т stacking in trimesic acid, highlighted in red). (b) centroid- brrrodddbaaedddeeo approaches will create anisotropic crops in elongated molecules, for example only capturing a I-dimensional column (grey) in the ellipsoid p-quinquephenyl, while missing peripheral interactions (red).
B TECHNICAL DETAILS
Experiments were performed on heterogenous GPU clusters consisting of NVIDIA L40S and H100 GPUs. Models were primarily trained using multinode DDP training on L40S GPUs as cluster availability permitted. Inference is performed across all available hardware. Our model code is available to use here: https//gitabb.om/XXXx/O/XXK
B. TRAINING DATA PROCESSING
curate training data from the Cambridge Structural Database (CSD, including releases up to May 1, 2025) under the following criteria: (i) 3D coordinates are present, (ii) the conventional R-factor < 9%, (iii) the structure is derived from single crystal diffraction at ambient pressure, (iv) be sanitized RDKit with missing heavy known space group, and (vii) at most 250 non-hydrogen atoms are present per unit cell. To avoid leakage, we exclude any entry belonging entry containing molecular component that appears in test sets. To avoid oversampling certain clusters within each crystal family, near-duplicate polymorphs are collapsed using RMSD1s 0.25 Å, retaining the entry with the lowest R. Our final training dataset contains 594,202 crystals in total.
the structure is not polymeric, (v) the structure atoms, (vi) there
crystal family and any
For data preparation, crystallographic disorder resolved by selecting the disorder group with the highest occupancy. We remove hydrogens for training and extract kekulized bonds from crystallo- graphic metadata. Prior to building supercells, molecules of the crystals are centered to lie within the unit cell, and the unit cells are transformed to their unique Niggli-reduced forms. Supercells are constructed by tile translation Tyyk = ia + jb + ko for i, & E 1,, 0, such that molecules with centroids inside the supercell boundary are included.
B.2 ADDITIONAL MODEL DETAILS
B.2.1 STOICHOMETRIC STOCHASTIC SHELL SAMPLING (S*)
We provide the full algorithm for S cropping in Algorithm 1. Recall that for crystal C, M denotes the set of molecules within the crystal, A denotes the tokenized atom array for all molecules m E M, and X R3 denotes the Cartesian coordinates of each atom Note that for practical purposes, we assume M has finite size. Additionally, A is the crys- tal's minimal asymmetric unit, and d is a pre-computed intermolecular distance matrix, where d(i,j) X(m),,,((m)))))xxpp.
A.
||æ; 12112-
Given a specified shell radius Tem. we first sample central molecule m. Uniform(A)) Then, we assign all other molecules m7, E M \ m. to shell layer, as defined by Yeut- Note that each molecule m. only belong to one shell layer. Next, with probability (1 Pmax), we randomly sample how many shells to keep. We then add complete shells of molecules to our selected set until the maximum token budget T Tmax is reached. If no complete shell can fit within the token budget, we adaptively sample molecules the first shell according to Algorithm order to preserve the stoichiometric ratios of the molecules in A.
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Implementation details. In practice, begin by first considering ((O), where U = 3T3. For each input crystal, sample molecule from the asymmetric unit of the central unit cell. After analysing the distribution of intermolecular distances for all erystals in the training set, we select Tout 4.5 A (see Figure 10 and $D.2). Furthermore, in order to encourage the selection of larger Acro blocks, we set Pmax 0.8 and T max = 640.
x 3 crystal supercell
4 10
10
10
Frequency
10c
10
2
5
8
10
Distances/A
Figure 10: Truncated distribution of intermolecular distances in the processed training dataset.
Algorithm STOICHIMMTTRC STOCIASTIC SHELL SAMPLING
1: Input: M, A, A, d, Teuts Tmaxx Pmax
2: me Uniform(A)
Sample central molecule
3: M + M {mc}
4: Initialize S = 0, k +-1
5: while M + do
Compute shell layers around me
6: Sa < (m; E M d(me, (m)) S remt)
7: S S M t M Sk, + to ++1
8: end while
9:
10: Dmax Bernoulli Pmax)
> Sample maximum number of shells Skmav to keep
11: if fmax False then
12: kmax Uniform/ 11....,k 1}
13: S (S, ........ Skmean
14: end if
16: Initialize A f- Amec) 1, T max do AA(S)) Tmax then
while |Acrop
D Add full integer shells within token budget T max
18:
if [Acopp
19:
break end if
20:
21:
Acrop < A U A(S)), i i+t
22:
end while
23:
24: if i 1 then
If no full shell fits, sample molecules according stoichiometry Agrop < ADAPTIVE STOICHIOMETRIC SAMPLING(A, AA, m A, Tmax. S2)
25:
end if
27: return Agrop
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Algorithm 2 ADAPTIVE STOICHOMMETRIE SAMPLING
1: Input: A, mc. A, Timx. S
2: Calculate proportion of each molecule type Pt 1 Aaypo((m))))
[A]
3: Initialize ideal targets: R2 t round(p: (S]) for each type
4: Acoo f- Ame)), Riype(m.) Rypp((m.)
b me is already pre selected
5:
6: while AAcupl < max do
7: Bucket remaining molecules by type: B, = {m E S: type(m) =
8: Compute adaptive weights for each type:
9:
for all E 7 with B, & 0 do
W/ R.
11: end for
Normalize weights to probabilities: P/ wt/ wt
13: Select type l' randomly according to probabilities P% Sample m' Uniform Bp)
15:
if [Acrop +A(mm') > Tmax then
16:
break
b Stop adding this molecule exceeds token budget
17: end if
18:
Acrop < Acpp (mmmm)
19:
S-S (m'), Br By \ {m'}, Ry t Ry
20:
end while
21:
return Acro
B.2.2 ARCHITECTURE
Our model adopts the AlphaFold3 (AF3) architecture via the public Protenix implementation (Team et al., 2025). We adopt Algorithm from Abramson et al. (2024) to embed the reference conformer into the atom encoder. Atom-level tokens with relative position and entity encodings are processed by an AF3-style Pairformer trunk with recycling to produce single and pair representations; the mul- tiple sequence alignment (MSA) pathways are disabled. These representations condition structure- denoising head consisting of an atom diom-attention encoder, a transformer-bas diffusion module, and an atom-attention decoder that outputs 3D coordinates.
B.2.3 LOSSES
We use combination of losses encourage accurate structure prediction both the global and local scales. Here we enumerate what the different losses are, how they are formulated, what they are useful for and how they lead to correct diffusion model.
SmoothLDDTLoss: The Smooth local distance difference test (SmoothLDDT) loss is a smooth form of existing LDDT loss (Mariani et al., 2013). The LDDT measures how well two structures align over all pairs of atoms at distance closer than some predefined threshold. For us, this is Ru 15A. These pairs of atoms form set of local distances L. The LDDT score the average of fractions at four distance thresholds: [0.5, 1.0, 2.0, 4.0] Angstroms. The Smooth LDDT test, instead of using a binary test of whether or not the local distances are on the same side of the threshold, uses sigmoid function. Let
L | - I=1l
(21)
L Gr G2
(22)
8 abs(L GTT
(23)
c = 4
sigmoid(
2 - 6) + sigmoid(1 - 6) + sigmoid(2 6) + sigmoid
(24)
mask
(25)
Then the SMO between two molecules of size d is:
SMooTHLDDT(2,, (T) Σ mask)/(d(d)
(26)
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Our SmoothLDDT loss is then equal to
LLDDT (z, x = = SMooTHLDDT(r, ALIGN
(27)
where ALIGN(a, (a, b) performs an optimal rigid alignment of to b in 3D.
B.2.4 MODEL HYPERPARAMETERS
Training. Our training implementation is based off of the open-source Protenix model (Team et al., 2025). We disabled all MSA components. For training, we use Adam optimizer with 31 0.9, 32 = 0.95, a learning rate of 0.0018, and a weight decay of 1e-8. The learning rate is additionally set to scheduler with 1,000 warmup steps and decay factor of 0.95 for every 50,000 steps. We report results for our model trained at 110,000 steps.
The atom encoder has 3 blocks with 4 heads. The atom embedding size is 128, whereas the pair emhedding is size is 16. In terms of the main Pairformer trunk, we use Pairformer blocks, each with 16 attention heads and dropout rate of 0.25. The hidden dimension for the pair representation is 128, and the hidden dimension for the single representations are 384. Furthermore, we do rounds of recycling. For the diffusion block, we use diffusion batch size of 32 and a chunk size of 1. The actual diffusion transformer has 12 transformer blocks, with 8 attention heads. Crop size (and therefore token size for the diffusion transformer) is set to 640, with 50/50 ratio of 5 and &NN cropping for training. All components are set to seed 42.
Inference. At inference time, we use the following hyperparameters for our diffusion sampling: To 0.8, noise scale lambda 1.003, steps 200, and step scale eta = 1.5. When generating samples, we generate sample from 30 different seeds for each target crystal structure. Seeds are set from 0 to 29.
C EXPERIMENTAL DETAILS
C.I SELECTION OF PERFORMANCE METRICS
The four metrics in the main text jointly probe physical plausibility (Colg), rough packing sim- ilarity (Pacs, Pacc), intramolecular fidelity (Recs, Recc), and a holistic solve indicator (Solc). Reporting both sample-level and crystal-level aggregates essential: the former characterizes the distributional quality of all proposals, while the latter answers whether a target was recovered at least once. Concretely, crystal-level rates are an OR-aggregation over target's ' samples, Evaluating both crystal and sample level metrics together helps diagnose failure modes such as mode collapse (high Pacc with low Pacs) and low recall (the reverse).
Thresholds and interpretability. We adopt community conventions for RMSD; (Nessler et al., 2022):
RMSD15 < 1.0 typically indicates the predicted packing reproduces the experimental match and lies in the exact energy basin as the experimental structure. This metric is the one used by the 5th CSP blind test (Bardwell et al., 2011).
1.0-2.0 usually indicates the prediction shares the correct topology with mild lattice strain small reorientations. If the H-bond graph. Z/Z', density, and PXRD are consistent, this is very likely recoverable to < Á with brief local relaxation. Otherwise, the structure is often structurally related the ground truth (i.e. in or near the correct packing motif/topology or space group but with slip, molecular misorientation, or cell mismatch). It demonstratess that the method can correctly identify the neighborhood of the global energy minimum, even can't 't pinpoint the exact minimum itself.
2.0-3.0 typically indicate a significant mismatch. At this level of deviation, key intermolecular interactions, like hydrogen bonds, may be incorrect. The overall packing symmetry might also be different. However, the prediction might still capture general feature of the packing (c.g., identifying a layered structure vs. a herringbone packing).
above 3.0 A. these values generally not considered useful. The deviation is so large that the predicted structure is almost certainly in a completely different and incorrect energy basin. Any similarity the experimental structure is likely coincidental.
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Our Sole (collision-free packing-simila RMSD1s < 2A) is thus strict, early-stage indicator: not "solved," but reliably near-correct for downstream relaxation and re-ranking.
Packing matching for non non-periodic predictions. Our generators output finite blocks without pe- riodic conditions. For large inference blocks, is possible to identify translation vectors that map the finite cluster onto itself (e.g., by correlating molecular centroids local environments), least- squares fit three independent vectors to define a primitive lattice, and convert atoms to fractional coordinates. Nevertheless, CSD COMPACK can be directly used for robust alignment of block against a crystal structure while preserving standard CSP rigor. First, we employ standard practices of avoiding hydrogen-atos atom alignment and allowing mismatches in connectivity annotations (e.g., bond orders). In the absence of periodic images, greedy pruning can miss valid correspondences; therefore for all methods (including DFT baselines) we use a search time of 10 seconds with a dis- tance and angle threshold of 50%. This enables reliable COMPACK outputs on non-periodic inputs without diluting the criterion: acceptance still hinges on multi multi-molecule superposition (15-molecule cluster, 2 8 matched) and the same RMSD,, thresholds used in periodic CSP benchmarks. Lastly, we note that is possible to deduce the underlying Bravais lattice of a large periodic point cloud by analyzing the set of interatomic difference vectors (a Patterson analysis): in the resulting Patter- son function, lattice translation vectors appear as a high-multiplicity, regularly spaced subset of the interatomic vectors, from which the lattice parameters (and hence primitive cell) can be recovered.
C.2 MOLECULAR CSP ON RIGID AND FLEXIBLE DATASETS
We construct our rigid and flexible test datasets using crystals from the Cambridge Crystal Structure Database (CCDC), following the same processing procedure outlined in $B.1. Both rigid and flexi- ble datasets are comprised 50 molecular crystals. These are generally crystals with practical rele- vance or newly-released crystals. We generally define rigid molecules to contain 0-3 rotatable bonds, and flexible molecules to contain more than that. We note there is small nuance flexibility, as refine it in the molecular context (by ring restriction or number of known polymorphs, etc.), this means crystals such as rubrene (QQQCIG), seraphenyylpophhrii (TPHPOR), CL-20 (PUBMUU) defined as "rigid;" ROY (QAXMEH), galunisertib (DORDUM), sulfathizaole (SUTHAZ), and flufenamic acid (FPAMCA) are defined as "flexible." " The exact CSD identifiers are provided below for reference.
Molecules in the rigid dataset: XULDUD, GUFJOG, QAMTAZ, BOQQUT, BOQWIN, UJRIO, PAHYON, XATMIP, HAMTIZ, XATMOV, AXOSOW, SOXLEX, WIDBAO, HXACAN, AC- SALA, PUBMUU, GLYCIN, TEPNIT, QQQCIG, ZZZMUC, FOYNEO, ANTCEN, URACIL, BT- COAC, CORONE, GUJTOX, TPHPOR, ACETAC, IMAZOL, CEBYUD, CILJIQ, CUMJOJ, DEZ- DUH, DOHFEM, GACGAU, GOLHIB, HURYUQ, IHEPUG, LECZOL, NICOAM, ROHBUL, UMIMIO, WEXREY, CAPRYL. ACACPD, BPYRUF, JIVNOV, MUBXAM, VUBUB, NAVZAO.
Molecules in the flexible dataset: QAXMEH, DORDUM, BOTHUR, MOVZUW, SUTHAZ,
TPPRHC, FPAMCA, INDMET, MELFIT, YIGPIO. TEHZIP, DMANTL, YIGDUP UWE-
QUL, COWZIA, FUVLAN, RUTJUP, MUYRIL, QUTZUE, MURQUP. CUWLIT, QUR-
PUS, DUZTOL, VUZQUG, MUZKOL, YUYLAJ, BUYWUR, HABMUX, QURBEO, HUT-
DOT, CUYGEM, MUSTIH, MUSXUX, DABHIC, FACDOH, RUWFAU, CAFHUR, HUW-
PUO, CAFHEB, HUTKOA, DUVCOQ, QUXHAW, CABFIZ, QUSQAA, MUSYAE, CUYVUR, JABXIY, RUSXEM, CUYWAY, YABFAN.
C.3 Ab initio MACHINE LEARNING BASELINES
We compare OXTAL against three ab initio machine learning baselines: (i) lightweight transformer trained with flow matching on our dataset ($C.3.1), (ii) the publicly released SSEMBIEFFL.W ATOM model (Guo al., 2025), and (iñ) ALPHAFOLD3 (Abramson et al., 2024) used as a generative baseline. Our complete table of results are reported in Table 3 on both rigid and flexible molecular CSP benchmarks using n 30 samples per crystal target.
C.3.1 A A-TRANSFORMER (OURS)
Model. A-Transformer is a lightweight transformer encoder operating on atom tokens with unit- cell features. The model PyTorch nn. Trans forme rEncoder with hidden size de 512,
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Table 3: Performance of ab-initio machine learning models, including AlphaFold3, on the Rigid molecular CSP dataset. For each model, results are calculated using 30 samples for each erystal target.
Model
Cols +
Pacs 1
Pace t
Recs t
Rece
Sole
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
AlphaFold3
0.114
0.089
0.340
0.133
0,480
0
OXTAL
0.011
0.873
1.000
0.737
0.960
0.300
= 13 layers, and = 4 heads. Each atom embedding includes element and charge information, time & E (0, 1]. molecular fingerprints, and, when enabled, unit-cell lengths (a, (a,b,c) and angles (a, 7) Two output heads are used: a coordinate head (I&3 per token) and, optionally, a rotation head (unit quaternion, disabled in main runs).
Training. The objective is rigid-cluster translation flow matching R We linearly interpolate between ground-truth translations sq and random in-cell starts 81,
$ (1 t) so + ts,, to Unif(tmin 1},
and predict denoised coordinates dn- The loss is æp regression term:
1:0 (0) = Amans Σ
200
Inference and Evaluation. At inference integrate from t=1 1 to fmin with Euler steps, producing clusters PI box. This baseline is deliberately minimal: ignores rotation flow matching and lattice prediction, relying solely translation flow matching and unit-cell features. It provides a capacity-matchat reference against which to measure the benefits of OXTAL's architecture and training.
C.3.2 ASSEMBLEFLOW
We evaluate the newly released ASSEMBLEFLOW ATOM model (Guo et al., 2025) using the authors' checkpoints without re- re-training fine-tuning. For each molecule we generate clusters of 15 rigid copies from an RDKit ETKDG conformer, applying random rotations and translations with uniform offsets S), where S (10, 15, 20} Á. Three seeds (42, 7, 20243 and seven checkpoints yield 63 runs per molccule. To standardize evaluation, we randomly sample 30 outputs per crystal and compute metrics those. AssembleFlow enforces rigid- moleclle assembly and provides strong baseline for rigid-packing quality, but is unable to handle flexible molecules, as reflected in the results presented in Table 3.
C.3.3 ALPHAFOLD3
We additionally evaluate ALPHAFOLD3 as structural generative baseline for the Rigid molecule dataset. For each target molecule, we generate conformations using default protein-ligand genera- tive settings, treating each conformer as a candidate crystal packing. Inference is performed based on 30 counts of the molecule, and thirty samples per target are evaluated in the same way as for other baselines. While ALPIIAFOLD3 was not designed for crystal structure prediction, including it highlights the gap between general-purpose biomolecular structure generators and CSP-specific models.
C.4 CCDC CSP BLIND TEST DETAILS
To contextualize our work, we provide summary of the 5th, 6th, and 7th CCDC CSP blind tests. These community-widd challenges have benchmarked the of-t-oofthheann in predicting the crystal structures of organic molecules from their chemical graphs alone, primarily relying on density func- tional theory (DFT). Here, provide brief descriptions of these tests, and refer the audience to
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CSD7 ZEHFUR
RMSD 15/11///
-3
Gurs
Group10 XtaPP
Group16 Maram bayey
Groupt8 SMohamed
Groupt I, Adjmaan Pantalidee
Group Miluuann
Group2 Obsta Goto
Groupz4 Strvice
Groupt5 [Shang
Group88, Gzhu
Grup3 DBosse
Group5 gbay
Groupe BEjcck
Figure 11: Beeswarm plot of submitted structures for Molccule XXXI (ZEHFUR) from CSD7. In 30 inference samples, OXTAL obtains performance comparable to some DFT groups with thousands of submitted samples. Colored points signify a partial packing similarity and gray points signify packing mismatch (e.g. out of 15 molecules match with low RMSD, i.e. overall packing is significantly different).
Bardwell et al. (2011); Reilly et al. (2016); Hunnisett et al. (2024) for details. Performance is as- sessed using the COMPACK algorithm, which quantifies structural similarity through root mean square deviation (RMSD) of molecular clusters.
In the first four CSP blind tests, the field evolved from force-field landscapes to the first widespread use of periodic dispersion-correctedd DFT (DFT-D), which proved decisive in 4th blind test and set the stage for DFT to become the de facto standard for final lattice-energy evaluation. The 5th blind test (Bardwell al., 2011) marked significant increase in the complexity of the tar- get molecules. The six targets included rigid molecules, semi-flexible molecules, 1:1 salt, a highly flexible pharmaceutical-like compound, and two co-crystals. This test highlighted what has be- come a standard workflow in CSP: broad structure generation (e.g., grid or quasi-random sampling, parallel tempering), followed by local minimization and hierarchical re-ranking. While at least one successful prediction was submitted for each target, the success rate was lower than in previous tests, underscoring the increased difficulty. DFT-D demonstrated its reliability for discriminating between competing structures for small and moderately flexible molecules, but handling high flexibility and complex solid forms remained a major challenge. total of 15 groups submitted structures for this blind test, although the report contains only 14 groups
The 6th blind test (Reilly et al., 2016) continued with five challenging targets: a small, nearly rigid molecule; a polymorphic former drug candidate; chloride salt hydrate; co-crystal; and large, flexible molecule. This test solidifed the "scarch-optimizzrrnnk" pipeline. On the search side, more than half of the methods allowed intramolecular flexibility during exploration, and many adopted hi- erarchical filtering starting with generating conformer and packing, followed by progressively tighter optimization and pruning. In optimization and ranking, dispersion-coorrcted periodic DFT became mainstream, with van der Waals (vdW) models (e.g., D3/D3(BJJ, MBD) and multipole-based elec- trostatics or SAPT-derived potentials used refine close competitors. All experimental structures were predicted by at least one submission except potentially disordered Z' 2 polymorph. The results demonstrated that while DFT-D provided reliable baseline energetics, accurate treatment of conformational flexibility remained the primary bottleneck. A total of 25 groups participated in this blind test.
The 7th blind test (Hunnisett et al., 2024) introduced a two-phase structure to separate structure gen- eration from ranking challenges. The seven targets featured a silicon-iodine containing molecule, a copper coordination complex, a near-rigid molecule, co-crystal, polymorphic small agrochem- ical, a highly flexible polymorphic drug candidate, and a polymorphic morpholine salt. The test also featured one of the most challenging systems in the history of the blind tests: large, highly polymorphic pharmaceutical drug candidate. A key finding from the structure generation phase was that while different search methods often identified overlapping sets of low-energy structures,
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10
10
1.25
1.25
RMSD, (A)
1.00
RMSD. (4)
1.00
GJ6G0511
Oxtal
RMSD: (0
RMSD: (A)
ZEH UN
Oxtal
0.75
0.75
Others
0.50
XATRW
XATWW Oittl Others
0.25
ORtal
0.25
8.00
0.00
107
10
10
10"
16
10a
10a
10P
10:
10a
10P
10a
100
10a
Submission
Submiission
Submission
Submissson
Figure 12: Sample efficiency plots for XAFPAY (blind test a flexible molecule), OJIGOGOI (blind test 7), and ZEHFUR (blind test 7). OXTAL is able to quickly recover both molecular conformers (RMSD,) and periodicity (RMSD1s).
their success rates tended to decrease as the complexity of the target molecule increased. For rank- ing, periodic dispersion-correns corrected GGA DFT methods produced results in excellent agreement with experiments across most targets, whereas higher-level corrections, full free-energy treatments, and ML on DFT potentials were less decisive for these specific systems than expected. Additionally, dynamic and static disorder (and high Z.) remained difficult. A total of 22 groups participated in the structure generation phase of this blind test.
These blind tests shows clear trend that DFT-based ranking has become reliable, but limitations persist: computational expense, difficulty capturing kinetic effects, challenges with disorder and flexibility and high Z' number, and the fundamental limitation that thermodynamic ranking often fails to predict which polymorphs are experimentally observable. Our approach aims to address these limitations by directly learning both thermodynamic and kinetic regularities from data, with the hope of eventually eliminating the need for extensive search, local optimization, and post-hoc ranking altogether. By generating small number of high-quality structures directly, we bypass the traditional
raank pipeline that has dominated CSP. Tables 8, 9, and 10 in $I show comparisons for all submitted structures by each group (sans ranking)The beeswarm plot (Figure 11) of submissions for molecule XXXI further highlights the extensive sampling currently required by DFT methods compared to OXTAL. This point is further emphasized in Figure 12, which plots the best RMSD achieved at given n submission size for a few blind test crystals.
Result computation. Because each submission group can choose which crystals attempt, in $4.2 we report metries that are averaged over submission groups. For sample-level metrics, we first compute each rate separately for every group, then take the mean of these per-group rates across all groups. ng is the average number of samples per group per target. For crystal-level metrics, average the rates over each group, and across all available targets for that competition. We count groups who did not submit any submissions for crystal miss, since they did not show evidence of successfully solving it.
Note that in blind test 7 (Hunnisett al., 2024), Target XXX has two forms with different stoi- chiometries (MIVZEA and MIVZIE). For evaluation purposes, ab initio machine learning methods attempted 30 structures for each stoichiometry. As such, per-sample metrics for competition 7 are computed with these additional samples, and we consider 8 total targets for per-crystal metrics.
C.4.1 INFERENCE TIME COST
We compute computational costs by multiplying the reported wall-clock compute time by an AWS on-demand unit price with hours taken directly from the three blind tests references (Bardwell et al., 2011; Reilly et al., 2016; Hunnisett et al., 2024). Because the papers report heterogeneous processors and often normalize times to ~3.0 GHz core-hours, we treat one normalized CPU hour as one AWS vCPU-hour; we then price CPU time at the c5. large on-demand rate in Sept. 2025, i.e., $0.085 per vCPUs + $0.0425 per -hpu-hour, so CPU cost hours x $0.0425. For L40S GPU runs, we map directly to g5e. xlarge instances (which contains one NVIDIA L40S) and are priced at $1.861 per instance-hour so GPU cost hours x $1.861. We apply the rates pro-rata without further rounding. All prices are on de-demand EC2 instances as of September 2025. For reference, exact reported times used presented in Tables 11, 12, and 13.
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D MODEL ABLATION STUDIES
Here, provide series of different model ablation studies. Due to the high computational demand of training OXTAL, all results in this section are reported at 50k training steps instead of the 110k reported in the main body of the paper. Following our predefined evaluation protocol, we evaluate nss = 30 generated samples with 30 molecular copies for each crystal target.
D.1 CROPPING METHOD ABLATION
In order isolate the performance gain from St, we directly compare against other standard cropping methods. Overall, Stt performs the best across all metrics and datasets with centroid radius performing the second best, indicating that there may not be many oblong molecules in the evalua- tion datasets. However, these results support the benefits of using S4, since it is not subject to the same pitfalls of ANN and centroid radius cropping as illustrated Figure 9.
Also, note that our implementation of centroid radius cropping is more generous than the standard one used in the literature (Abramson et al., 2024). Specifically, naive radius cropping selects any atom that lies within pre-defined spatial radius. However, this often results in partial molecules being cropped, which naturally leads to lower performance. Instead, we consider all atoms in a given molecule if its centroid lies within 15 Å of randomly sampled central molecule, and only consider complete molecules up to our token budget, which mitigates the issue of fragmented molecules during training. ANN is also implemented such that it only considers complete molecules up the token budget, ordered by neighbor distance from randomly sampled central molecule.
Table Results for different cropping methods with best results bolded and second best underlined.
Crop Method
Dataset
Cols
Pacs
Pace
Recs 1
Rece
Sole f
Rigid
0.086
0.631
0.920
0.520
0.780
0.220
Flexible
0.444
0.123
0.700
0
0
0.020
ANN
CSP5
0.085
0.470
0.667
0.433
0.833
CSP6
0.132
0.353
0.800
0.007
0,200
0.200
CSP7
0.312
0.165
0.750
0.005
0.125
Rigid
0.040
0.669
0.980
0.591
0.940
0.340
Flexible
0.223
0.184
0.720
0.033
0.300
0.040
Centroid Radius
CSP5
0.054
0.470
0.833
0.429
0.833
CSP6
0.151
0.324
1.000
0.173
0.400
CSP7
0.104
0.225
0.750
0.104
0.250
Rigid
0.026
0.688
0.940
0.629
0.940
0.280
Flexible
0.143
0.260
0.800
0.031
0.360
0.140
Ours (S*)
CSP5
0.000
0.500
0.833
0.478
1.000
0
CSP6
0.047
0.440
1.000
0.107
0.800
0.200
CSP7
0.033
0.221
0.625
0.104
0.500
D.2 S RADIUS SIZE ABLATION
Next, we investigate the sensitivity of OXTAL the choice of 5 shell radius size. From our results in Table 5, we see that there are generally minimal changes in performance across three different choices of radius size. Recall that our main OXTAL model uses a shell radius size of 4.5, which was selected from analyzing the distribution of intermolecular distances presented in Figure 10. From this figure, both 4.5 and 5 À are natural choices for the first shell, however due to the "layered" nature of crystallization,
consider second shell at 9 rather than 10 Á to be more fitting.
Overall, our current implementation of 5 may slightly favor smaller shell radius sizes due to the able to accommodate.
overall token budget constraint, which limits the number of full shells Regardless, we see that all three radius settings for 4 outperform existing cropping methods from 'abble suggesting that OXTAL is somewhat robust reasonable choices in S radius size.
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Table 5: Effect of 5t shell radius size, with best results bolded and second best underlined.
Radius Size
Dataset
Colg 4
Pacs
Pacc
Recs f
Rece
Sole 1
Rigid
0.015
0.694
0.980
0.596
0.920
0.320
Flexible
0.109
0.290
0.820
0.049
0.380
0.140
3.5 A
CSP5
0.006
0.439
0.833
0.433
0.833
CSP6
0.068
0.409
1.000
0.174
0.600
0.400
CSP7
0.095
0.238
0.750
0.110
0.500
Rigid
0.026
0.688
0.940
0.629
0,940
0,280
Flexible
0.143
0.260
0.800
0.031
0.360
0.140
4.5 Å
CSP5
0.000
0,500
0.833
0.478
1.000
CSP6
0.047
0.440
1.000
0.107
0.800
0,200
CSP7
0.033
0.221
0.625
0.104
0.500
Rigid
0.047
0.690
0.940
0.625
0.960
0.220
Flexible
0.216
0.241
0.740
0.021
0,300
0.080
5.5 Á
CSP5
0.012
0.470
0.667
0.439
0.667
0
CSP6
0.147
0.375
1.000
0.147
0.600
0,200
CSP7
0.101
0.234
0.750
0.142
0.375
0
D.3
MODEL SIZE ABLATION
To further investigate the effect of model size, we train a smaller version OXTAL that contains roughly 50M total parameters, which is half the size of the one report in the main paper.
Table 6: Effect of OXTAL model size, with best results highlighted in bold.
Model
Dataset
Colg +
Pacs
Pace
Recy f
Rece
Sole
Rigid
0.731
0.015
0,060
0.033
0.120
0,060
Flexible
0.900
0.001
0.020
0
0.020
A-Transformer
CSP5
0.833
0
0
0
CSP6
0.967
0
0
0
0
CSP7
0.950
0
0
0
Rigid
0.524
0.001
0.040
0.211
0.760
Flexible
0.883
0
0
0.021
0.140
AssembleFlow
CSP5
0.717
0
0
0.150
0.500
CSP6
0.800
0
0
0.073
0.200
CSP7
0.808
0
0
0.063
0.250
Rigid
0.066
0.712
0.980
0.621
0.940
0.320
Flexible
0.281
0.221
0.700
0.017
0.240
0.060
OXTAL (50M)
CSP5
0.170
0.491
1.000
0.400
0.833
0
CSP6
0.261
0.370
1.000
0.094
0.400
0.200
CSP7
0.159
0.173
0.750
0.105
0.250
0.125
As shown in Table 6, the smaller 50M parameter version of OXTAL still outperforms existing ab- initio ML methods, which we have provided again here for reference. This result reinforces the benefits of OXTAL's lattice-free and non-equivariant architecture at smaller scale.
CONFORMER ANALYSIS
We molecule, the model is conditioned (i) its bond information and (ii) 3D structure obtained using RDKit ETKDG followed by relaxation with the semi-empirical quantum- GFN2-xTB. This conformer serves solely feature conditioning signal for the computational
now investigate the influence of the feature molecular conformer used by OXTAL. For each
method
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(a)
(b)
CUTTES
COUZEL
GASAER TEPMEE4 SODUP
QAAMINN
VISSUP
Onil Faccba
Cysler Cueownty
Hahh
Gyel deanary
Figure 13: Analysis of input and final conformer in ten crystals for which OXTAL obtains RMSD, 0.5A. (a) Different input conditioning conformers and their differences with the ground truth. Gen- erally, flexible molecules' conformers have significant deviations to the crystal geometry. (b) Differ- input conditioning conformers and their differences with the final, model-predine conformer. Generally, the model final conformers that are significantly from the conditioning.
prior, rather than as an experimental oracle: the generative process always starts denoising from random atomic coordinates, with the conformer providing only reference for physically plausible initialization derived from quantum-chemin approximations as a feature input. To quantify how this initialization influences generation quality, we perform the following targeted analyses:
1. Distance of the feature conformer relative to ground truth. In Figure 13(a), we show that the feature conditioning conformers for flexible molecules can be significantly different than the ground truth crystal conformation. This shows how often the model must depart from or refine the initial geometry.
2. Distance of the feature conformer relative to the prediction. Figure 13(b), we show that there are significant differences between the feature conformer with the final, model- predicted conformer. Structures predicted by the diffusion process is different than the one conditioned in the input embedding, i.e. it is not merely reproducing the structure used in input embedding.
3. Robustness feature conformer quality. We assess robustness by replacing the GFN2-xTB initialization with alternative or deliberately perturbed conformers,
RDKi--ETKDG conformers
Universal forcefield conformers
MMFF94 conformers
GFN2-xTB conformers
Ground truth crystal conformers.
In Figure 14(b), we plot generation performance (e.g., RMSD1s) as a function of input distortion level. We also plot the best RMSD11 for each in Figure 14(a). These plots show that the model's 's predicted crystal packing not significantly affected by the different conformers or their differences with the ground truth crystal conformation.
4. The issue of Z'. When > 1, the asymmetric unit contains several symmetry- independent molecules. These molecules can have similar conformation (but in different orientation) or genuinely different conformers. ~ 10% the training set contains such examples, and in this subset, mean Z' is 2.14. OXTAL conditions every molecular copy with the same feature conformer, and can occasionally approximately solve crystals with 7' (e.g. Target XXIII in CSP 6, XAFPAY02, RMSD1s 1.91Å.)
Together, these analyses provide a clear and quantitative view how the initial conformer affects OXTAL: how different it is from the target, how effectively the model corrects it, how robust gener- ation is to poor or perturbed inputs, and whether supplying multiple conformers per 4 unit impacts performance.
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(a)
(b)
233
ANTOZN
CORDUMELL
Phoikke
LECELR
24-
HEUUTT
COCCIOSS
UNID
Grous
0082
1009
aracaar
Crysas Deconeryy
RM50 col-rvi car
Figure 14: Analysis of input conformer with the final predicted crystal packing. (a) Best RMSD 15 from 30 samples per target when using different initial conformers. Generally, the model robust against different sources of the input conditioning conformer. (b) All RMSD1s across ten targets relative to the difference in input conditioning and crystal conformer differences. This shows the model can still produce good packings even if the input conditioning conformer there is very differ- ent from the crystal conformation
F INFERENCE ANALYSIS
In this section, provide deeper analysis into the inference and generation capabilities of OXTAL. Specifically, we investigate the performance of OXTAL on generating significantly larger crystal blocks, evaluate how the model performs when allowing for additional sampling, and provide small qualitative analysis on the diversity of generated samples.
F.1 INFERENCE ON LARGER CRYSTAL BLOCKS
To evaluate the long-range periodicity of OXTAL, we perform inference on increasingly larger crys- tal blocks for handful of different crystals (Figure 15). The respective number of atoms, and there- fore tokens, for each molecule are provided in parentheses as follows: CAPRYL (10), CUYVUR (18), HURYUQ (14), QQQCIG05 (42), UMIMIO (12). Recall that OXTAL is trained with maxi- mum token budget of 640 (.2...4) hence generating 200 copies of CAPRYL requires 2,000 tokens and 100 copies of QQQCIGO5 requires 4,200 tokens, which are far beyond anything the training dataset would have seen.
In general, conformer recovery (denoted by RMSD;) remains somewhat constant as more molecule copies are generated. This makes sense because if the model is already able to capture the correct crystal conformer, generating more copies of that should not change the conformer itself signifi- cantly. In terms of lattice periodicity (denoted by RMSDis), OXTAL does struggle slightly with generating more molecules, since the packing arrangements cover distances that are further away. However, we note that although the RMSDis does increase for these larger blocks, they still mostly remain under the 2.0 Á threshold to be considered "approximately solved."
This analysis supports the long-range generalizability of OXTAL to generate larger periodic pack- ings, and we provide a visualization of the approximately solved larger packing for ANTCEN in Figure 16, which contains over 2,400 tokens.
F.2 ADDITIONAL SAMPLE EVALUATION FOR CSP BLIND TEST 5
For all previously reported results, we evaluate OXTAL using 30 generated samples per crystal target. This is done in order to highlight the sample efficiency of OXTAL (cf. Figures 5 and 6), since few-sample success is critical for downstream screening and design. However, we note that this puts OXTAL at somewhat of a disadvantage when comparing against traditional DFT methods, which often generate hundreds thousands of candidate packings. Here, we provide more direct comparison of OXTAL to DFT methods by evaluating OXTAL using the same number of generated samples on the CSP Blind Test 5 dataset.
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2.00
refcode
1.75
CAPRYL
3.5
CAPRYL
CUrvUR
CUYViR
HURYUO
HURYUO UHIIOO
1.50
3.0
1.25
2.5
RMSDas
RMSD.
1.00
2.0
0.75
0.25
0.00
0.0
25
75
100
125
150
175
200
25
50
100
150
175
200
Number of molecules
Number of moleculles
Performance of OXTAL on increasingly larger inference crystal blocks (denoted by the number of molecule copies generated). RMSD, (left) remains roughly constant, whereas RMSD increases slightly for larger predicted packings. Note that QQQCIGOS, which contains 42 heavy atoms (i.e. tokens) per molecules, goes of memory past 100 molecules.
Figure 15:
Table Evaluation of OXTAL on CSP Blind Test 5 with the same number of generated samples per crystal target (ng) as DFT avg.
Model
Colg
Pacs f
Pace f
Recs
Rece f
Sole 1
DFT avg
464
0.039
0.323
0.611
0.784
0.733
0.544
OXTAL
30
0.006
0.667
0.833
0.572
0.833
0.167
OXTAL
500
0.009
0.536
1.000
0.548
1.000
0.500
As expected, allowing OXTAL to generate more candidate packings increases its performance on our per-crystal evaluation metrics, while remaining roughly the same per-sample metrics. Notably, we also see that increasing the number of generated samples bring the approximate solve rate of OXTAL equal to that of DFT wwg. This suggests that the model sampler is indeed able to generate accurate crystal packings and compete with traditional DFT methods.
G ADDITIONAL RELATED WORK
Physical approaches to crystal structure prediction. Physical approaches mostly rely on search and sampling using energy function. Some classical methods infused domain knowledge, such as starting with initial guesses like a unit cell, and employed varying parameters, random sampling (Case al., 2016; Pickard & Needs, 2011; Tom et al., 2020), guidance from force-fields (van Eijck, 2002), or constructed guesses based on chemical principles (Ganguly & Desiraju, 2010). Recent methods have also applied more structured search algorithms, such simulated annealing (Reinaudi et al., 2000; Earl & Deem, 2005), genetic algorithms (Curtis et al., 2018; Lyakhov et al., 2013), particle swarm optimization (Wang et al., 2010), and basin- masin-hopping (Banerjee et al., 2021).
ML potentials. Computational complexity of DFT and availability of large datasets (Levine et al., 2025: Sriram al., 2024; Barroso-Luque et al., 2024; Smith et al., 2020) enabled the development of universal machine learning interatomic potentials (MLIP) (Gasteiger et al., 2021; 2022; Batatia al., 2022; Liao et al., 2024; Batatia et al., 2025; Wood al., 2025) to predict energy and forces of different atomistic systems (from small molccules inorganic crystals) at fraction of DFT costs. The next generation of physical approaches to CSP replaced DFT with MLIPs and showed benefits in material discovery (Merchant et al., 2023) with the recent FastCSP model (Gharakhanyan et al., 2025) applied to organic CSP.
Generative models for inorganic erystal structure prediction. Generative models have emerged as a promising new paradigm for crystal structure prediction, focusing mainly on conformer search in molecular structures well inorganic, periodic crystals. For inorganic crystal structures,
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which consist of periodic unit cell of atoms, generative models first applied for unconditional de-novo generation of new crystals (Xie et al., 2022) and later used for structure generation conditioned crystal composition (Jiao al., 2023: 2024; Miller et al., 2024; Levy et al., 2025). The use of generative models has spanned multiple modeling methods, including diffusion models with equivariant models (Jiao al., 2023; 2024), symmetry-aware diffusion models (Levy al., 2025), and now-matching models on specialized manifolds (Miller et al., 2024), Recent work have also applied large-language models crystal generation and structure prediction with more varied success compared to other methods (Antunes et al., 2024; Ding et al., 2025).
H ADDITIONAL CHEMICAL ANALYSIS
Figure 16: OXTAL learns small local neighborhoods from S crops and generalizes infer large and periodic structures. Example of ANTCEN with over 2400 tokens (RMSD = 1.9A).
BALNAD RMSD
PERTCQ01 RMEDgF1.78.
Figure 17:
Examples of OXTAL generated co-crystal structures (color) compared against experi-
mental structures (gray).
(b)
(c)
XAFPAY RMABD 050
GUFJOG RMSDy0024
MELFIT01 RMSD,-1.06. 1000
INDMET01 204SD--1.111
INDMET07 HMSD
PDB: 1056 RM80,-0.53 A
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, utilized the
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semi-empirical GFN2-xTB method computational proxy. GFN2-XTB was selected for its bal- ance of computational speed and accuracy in capturing non-covalent interactions. This analysis should be interpreted as consistency check gross energetic behaviour rather than quantita- tive ranking of polymorph stability.
We retrieved 1,500 physics-based structure predictions submitted to the CSP blind tests to baseline. Both the physics-basee based submissions and the experimental ground truth were expanded into 2x2x2 supercells to match the approximate atom count the OXTAL generations (30 molecules). For OXTAL samples, hydrogens were added using the CCDC API.
We performed single-point energy (SPE) calculations all structures. The energy difference is relative to the experimental structure and standardized by number of molecules. It is important note that the DFT baseline consists of structures that underwent varying degrees of geometry optimization, whereas OXTAL samples were evaluated as raw generative outputs with no geometry optimization, including the hydrogen atoms.
The results show that first, OXTAL samples do not contain energetically catastrophic motifs. Second, despite lacking relaxation, the generative samples exhibit narrow energy distribution comparable to the stable basin of the DFT samples. This confirms that the generative model implicitly learns to avoid severe steric clashes and produces metastable packing configurations.
10000
10000
Experimental
Experimental
1000
1000
100
100
AE (kcal/mol)
AE (kcal/mol)
80
80
40
20
6ooo0ooo0o
-20
-20
DFT
OXtal
DFT
OXtal
(a) OBEQOD (XVII in CSP5)
(b) NACIAF (XXII in CSP6)
Figure 19: GFN2-XTB single point energy analysis of ground truth crystal structures, 1,500 subsam- pled physics-based based samples from the blind test submissions, and OXTAL samples.
H.2 DIVERSITY OF GENERATED SAMPLES
In Figure 20, provide a qualitative visualization of some example packings generated by OX- TAL. We see that although several samples lie in the same orientation, some generated samples also present more complex herringbone packing. This is evident in the XATJOT co-crystal, which does not collapse the two different molecular components into the same orientation. These results suggest that TATA may prefer planar packings, which are more prevalent in the training dataset. However, this may be mitigated with additional tuning on noise scheduler parameters.
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KONTIQ
OBEQET
OBEQIX
OBEQOD
OBEQUJ
XATJOT
RARA RARA
M tH
Figure 20: Example set of structures generated by OXTAL for various crystals (labeled by CSD ID).
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I DETAILED DFT BASELINES FROM CSP BLIND TESTS
Table 8: Results per crystal of submitted methods for CSP blind test
Madel
%g
Colp
Pacs
Pace!
Rocs
Rece?
Soko?
Target XVI (OBBIQUI)
Group Anumus
Croup Boszigger
Group
Group Desingi
0.250
0,000
0.500
Moleev
0,000
0U000
0564
Group
105
0,000
01210
Group Nikylov
0,000
01000
Group Crcad:
292
0,000
0.259
1000
Group Price
150
0,000
0.357
1000
Group Scheraga
61
0,000
0
1000
Crrup wasEja.
1E7
0.000
0.399
1.000
Group Veaus
61
0.033
0.049
0.475
Target XVII (OBBQOD))
Group Ammmus
0.167
Group Revnrigerr
Group
Group Desingu
Group
0.000
0.200
0.000
0.855
Grendi
0,000
0.051
0551
Group
0,000
0.122
Group Scherupa
74
0,000
0.199
0.966
Group vanElikk
132
0,000
0.129
Y
0.922
Group Veausi
71
0,563
0.014
0.211
Target XVIII (OHEQQTT)
Group Ammus
0.000
0.000
8.600
Group Boerrgger
2001
0.000
0.005
01448
Group Dry
438
0.000
(1030
Grrup Desngg
0.000
0018
Grrup
0.000
Group
Group
0.000
0.012
250
0.000
0.008
Schergga
0.000
0.014
Group vunlijok
0.000
Group Venus
100
0.000
0.000
0.040
Target XIX (XATIOT)
Group Boerigger
583
0.000
0.355
10000)
Grrup Day
103
0.000
01252
1.000
Grrup Daangj
202
0.000
0.262
1.000
Group Hofmazn
R03
0,000
0.155
1.000
Group Kendrick
330
0,000
0.326
1.000)
Group Malees
0,000
0227
Group
0.000
0144
Group
Group Schergga
Group witbbjck
0.050
Group Ammus
11
0.000
0.000
0.000
Group Boerngger
8005
0.000
0.000
0014
Group Day
53
0.000
0.0%
0.355
Group Hulnuan
103
0.971
0.000
0.000
Group Kendrick
TE7
0.000
0.205
01248
Group Moller
8
0.000
(1900
0000
Crrup Owardi
196
0.000
0.006
8006
Group Piiee
103
0,000
0.839
0.243
Group vastbide
121
0,000
0U000
0.07
Group Venuri
100
0.020
(U000
00000
Targst (KONTIQ)
Group Boerrigter
Group
0.945
0.911
Kendräk
0.000
0.950
0.901
Group Malery
01000
(1256)
(1268)
Group Orandi
904
01000
(1938
01941
Group Prizz
449
0.002
0197%
0.950
Group weFiick
132
0.000
0.955
0.955
Group Venuri
294
0.000
01558
0055
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Table 9: Results per crystal of submitted methods for CSP blind test
Taagst XXL (NACCAR)
Gouplhi Chalka
0.301
1.000
Gsage0 Cot
100
(U39)
01230
1.000
Oongll Doubdaekke
0.30
01.20
Goople satiijk
BaciMaluur
0.595
Goagdh wandeataaoo-ppeeeee
200
0030
0.201
1.000
Googde Guta-Omnaa
0230
0.290
Goeplt Hedruss
0.301
0.300
100
Googl2 Manos
600
10225
0222
0.33
Googs14 Nearar Sendack--aaaeee
02301
Ooeglt Arjess Parviide
0.301
0.300
160
0.00
0.911
100
Goopue SpalevicsPPiice
0.311
Osagol dioren Sealovice
0.900
01130
Oonqg2 Boce Hofeuze
0.000
0.30
1.000
Googeh Brandintury Erteras
Tappe X0HH (UAFIWY)
Goagdi Chala-Sagh
0.300
0.331
0.000
Google Cale
Ghagd0 mallick
160
(090)
02281
0.080
Goagdi Cappr
0.30
0.231
0.000
Goegle
01301
Cheque Hedraes
160
0.301
01001
8000
Gosql1 Neasar Sernaat--Snnni--Leeee
(230)
0.233
Goeplt Aujican Parviidde
0.301
11:00
0.30
03381
0.119
Bocao Hofenan
(130)
01431
0.364
OrageS Tusiheiiio
0.990
0.791
0.250
(XAFQON))
Googgó
(1391
0.983
Osagee Elking Mekae
0.90)
0.359
11.00
Ussqui Hi Hidress
0.00
0.900
Google Nouram
01100
1.000
03880
Uongg2 Bi aaaiittau Orkannd
(1361
0.995
0.003
Goog2t
11991
Taget X0VV (KAFQAZI0)
Goagd2 Calk
0.000
0.201
1.000
Goegth
11:01
Cheglht sulf
160
0156)
1000
Elkag Porkebr
Choggh waddiallad Capper
(1301
Giaegee Faeli
01901
01300
Chepui Hefrwes
160
(1900
01000
180
Googli Miluand
Osagls Aupinas Praxciiie
01900
(1290
100
01000
03300
080
Googe2: Booms Hofrane
GraggS Toacherio
(199)
(1.01
1.000
Googth Charka Singh
Cragl0 Day
(.90)
08155
01000
Gongd0 nadidd
0.00
0.20
0.000
Grople RactMobuu
(hoep)3 Moluein
160
(1991
0100)
0100
Gongst Acjasa--Paaaiiio
(130)
0223)
Chegth Booon Hofruce
15
(1:00)
0100)
0100
Gosgch Braniirhapp Urtezac
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Published as a conference paper at ICLR 2026
Table 10: Results per crystal of submitted methods for CSP blind test 7.
Bece
Tirgs X0V11 (CFO-61)
Gro dla BEEA
1239
0500
000-1
0.066
1380
0U83
1483
01065
Dosutt Mati
(19)
0100
(599
0000
UneeS Pec
1580
0033
Groegh 21 Kaacknkk Milsbweee:
0300
0007
01800
Tano
1700
1589
0342
Diverht han
199)
1000
0985
0180
Gose Scuuaikke
1590
1200
0400
N
0.00
0ige 5315 (PASUP))
Pa
15:1
1539
0030
Divegt No
1030
0700
03311
1199
306
0200
0.00
0.80
Cover www.ll--taem---eee
1531
0440
1676
1380
1d0n
0000
1903
1539
0380
Goo 54 him
1385
0000
0053
0399
1231
0460
0135
0373
aldi
1689
0380
(ives1 Thee
801
000
0691
01:13
Goved (il-aaaaeadddd
(600
0000
1000
Uneel Mhorm
(60)
0181
1600
0080
Diwwy'
1650
0181
0681
0095
(69)
0380
1056
(141
0190
1180
Goapth Openleee
1000
Gie di Cluas Cado
(600
0000
0096
0386
(60)
0380
1601
0300
Diw
1401
0181
Tayr VEXI-25HF
1559
0760
1581
0763
(28)
0060
1056
0199
Uneer12 Mbee
(19)
0181
Doaul
0000
150)
0000
Divertl Ner
(10)
0100
1067
Gom SSuaied Milllarnnn
(50)
0200
0600
0003
Tapei
Goaptt Daacka
150)
0,50
1981
0181
300
0000
0001
0100
Govest Mili---
(50)
0000
0136
1396
1500
0000
1000
(000
1655
0.80
128)
0000
0613
0.23
119)
0180
1050
1581
0.00
(10)
0100
000
1161
Goadd Sk.
(58)
0000
0663
0.60
(18)
016)
1001
0201
36

---

Published as a conference paper at ICLR 2026
Table 11: Summary of computational resources used by some of the participants as reported in the 5th CSP blind test. CPU hours are approximately normalized 3.0 GHz. OXTAL times are reported as elapsed wall time in hours on L40S GPU and 6 CPUs.
Group
XVI XVII
XVIII
XIX
XX
XXI
Total
Boerrigter
90
100
350
650
2,105
600
3,800
Day, Cruz-Cabeza
110
1,941
21,051
6,097
54,090
22,197
91,400
Desiraju, Thakur, Tiwari, Pal
114
2,303
324
114
1,431
4,600
Hofmann
2
7
12
694
670
187
1,600
Neumann, Leusen, Kendrick, van de Streek
115,000
Price et al.
200
5,000
14,000
3,000
120,000
52,800
195,000
Van Eijck
27
9,500
Della Valle, Venuti
3,200
Maleev, Zhitkov
7,500
Misquitta, Pickard & Needs Scheraga, Amautova
162,000
150
150
610
720
1,300
OXTAL
0.024
0.011
0.012
0.013
0.029
0.011
0.100
Table 12: Summary of the computational resources used by each submission terms of raw CPU hours reported in the 6th CSP blind test. OXTAL times are reported elapsed wall time in hours on L40S GPU and 6 CPUs. Note that Group 22 re-ranks structures submitted by Group 10, and Groups 23, 24, and 25 re-rank structures submitted by Group 18.
Group
XXII
XXIII
XXIV
XXV
XXVI
Total
01 O1-Chadha & Singh 02-Cole et al.
350
450
600
1,400
6
538
46
246
836
03-Day et al.
12,714
394,948
15,241
121,701
179,897
724,501
(4-Dzyabchenko
144
3,648
3,360
7,152
05-van Eijek
130
2,810
1,400
8,060
7,630
20,030
06-Elking & Fusti-Molnar
418,540
242,000
235,400
135,000
190,000
1,220,940
07- den Ende, Cuppen et al.
9,741
7,777
6,388
23,906
08- 08-Facelli et al.
268,012
38,500
11,500
39,000
357,012
09-Obata Goto
19,200
346,000
325,000
690,200
10-Hofmann & Kuleshova 11-Lx, Wang, Ma
10
630
623
202
255
1,720
325,000
325,000
12-Maron et al.
30,000,000
30,000,000
13-Mohamed
26
106
81
61
274
14-Neumann, Kendrick, Leusen
32,160
146, 120
103,700
84,680
356,844
723,504
15- Pantelldess Adjiman et al.
333
87,000
37,535
272,500
397,368
(6-Pickard al.
380,000
380,000
17-Podeszwa et al.
72,220
72,220
18-Price al.
26,000
84,000
63,000
169,000
327,000
669,000
19- P-SSzllewizz et al.
66,000
66,000
20- Tuckerman, Szalewicz al.
81,000
81,000
21-Zhu, Oganov, Masunov
4,000
275,000
279,800
30,000
180,000
768,800
22-Bocss
80,000
80,000
80,000
80,000
80,000
400,000
23- Brandenburg & Grimme
13,665
8,661
3,509
34,824
10,135
70,794
244--zzlewizz et al.
15,000
15,000
25- Tkatchenko et al.
100,000
2,100,000
500,000
500,000
3,200,000
OXTAL
0.012
0.019
0.011
0.030
0.042
0.114
37

---

Published as a conference paper at ICLR 2026
Table 13: CPU core hours per target molecule for each prediction method reported in the 7th CSP blind test. OXTAL times are reported as elapsed wall time in hours on L40S GPU and 6 CPUs.
Group
XXVII XXVIII
XXIX
XXX
XXXI
XXXII
XXXIII
Total
Ol-Adjiman-Pantie Pantelides
652,495
840,000
1,597,000
412,000
3,501,495
03-DBeese
1,600,000
1,500,000
3,600,000
6,700,000
05-GDay
768,766
33,000
2,900,000
510,563
846,698
228,957
5,287,984
BEijek
1,350
1,310
2,900
4,980
29,930
08-DW DD-DWMMoofman
3,200
10
4,000
1,840
9,050
10-XtalPi
772,500
1,242,500
1,146,588
644.927
381,672
644,927
612,500
5,445.614
643,882
643,882
12: 12-1Juse
20,000
80,000
20,000
120,000
13-DKhakimev
350
1,500
500
2,350
16-Marom-lsayer
1,700,000
2, 2,128,000
630,000
4,458,000
17-Matsui
95.819
95,819
18 SMuhamed
1,050
36,864
632
1,561
40,107
19. OpenTyye
60.000
1,920,000
20-MNeumann
1,022,976
283,538
755,712
1,769,472
1,028,064
3,935.232
728.064
9,523,058
31-Obata-Goto
333.586
92.890
580,436
1.889.649
477.210
3.373,771
22-AOganov
20,000
2,000
15,000
180,000
20,000
25,000
25,000
287,000
23-CIPickard
10,000
10,000
24-S 24-SLPrice
450,290
89,666
76,541
100,000
49,177
244,520
123,427
1,133,621
CShang
55,150
29,691
4,784
6,476
76,161
34,648
206,910
26- KSrleewicz
28,332
28,332
27-
1,280,566
60,457
242,424
213.722
1,663,940
150,650
3,611,759
QiZuu
15,280
OXTAL
0.060
0.026
0.011
0.056
0.015
0.050
0.017
0.235
38


Reviews:
[{"review_id": "lvB0thUy14", "reviewer": "Reviewer_zXpA", "summary": "This paper introduces OXTAL, a large-scale, all-atom diffusion model designed to tackle the problem of organic crystal structure prediction (CSP). The model aims to predict the complete 3D crystal structure—encompassing both the molecule's internal conformation and its periodic packing arrangement—conditioned only on the 2D molecular graphs.", "questions": "1. Could you provide an ablation study comparing OXTAL's non-equivariant Pairformer trunk against a state-of-the-art equivariant trunk (e.g., an equivariant transformer or GNN) trained with the same $S^4$ cropping method?\n\n\n2. Can you provide a baseline comparison showing the benefit of the $S^4$ \"lattice-free\" scheme?\n\n3. How sensitive is the model's performance to the choice of the shell radius?\n\n4. Could you please elaborate on how the model handles co-crystals and solvates with specific stoichiometries? How is the model conditioned at inference time to produce, given that the input is just the SMILES strings?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The idea of the lattice-free approach is interesting. Instead of \"generate a valid unit cell,\" it becomes \"generate a locally consistent, periodic atomic environment\". This is a fundamental and elegant simplification that is physically motivated by the local-to-global nature of crystallization.\n\n2. The decision to abandon explicit equivariance in favor of a massive model, massive data, and simple data augmentation is a bold and counterintuitive claim compared to most current research literature in geometric ML for this application.\n\n3. The cost-performance plot in Figure 7 is an amazing result. It demonstrates that the proposed OXTAL provides a solution that is orders of magnitude cheaper than the baseline models.", "weaknesses": "1. The paper's most important claim is that abandoning explicit equivariance is an interesting idea. This is a central, non-obvious claim. However, there is no ablation study to back this up. The ablation study regarding other components in the $S^4$ is also missing.\n\n\n2. Some baseline models are missing in the experiments, including MatterGen[1] and ADiT[2]. It is important to compare the proposed method with the latest methods in this evolving field.\n\n\n3. Algorithm 1 introduces several new hyperparameters, including the shell radius, which is particularly critical. The paper provides no sensitivity analysis for these choices.\n\n\n\n[1] Claudio Zeni, Robert Pinsler, Daniel Zugner, Andrew Fowler, Matthew Horton, Xiang Fu, Zilong Wang, Aliaksandra Shysheya, Jonathan Crabbe, Shoko Ueda, et al. A generative model for inorganic materials design. Nature, 639(8055):624–632, 2025. \n\n\n[2] Chaitanya K. Joshi and Xiang Fu and Yi-Lun Liao and Vahe Gharakhanyan and Benjamin Kurt Miller and Anuroop Sriram and Zachary W. Ulissi. All-atom Diffusion Transformers: Unified generative modelling of molecules and materials. International Conference on Machine Learning, 2025.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "BWYO1Kvwtb", "reviewer": "Reviewer_5p8A", "summary": "This paper presents OXTAL, a large-scale diffusion model for organic crystal structure prediction (CSP). The model uniquely abandons explicit equivariant architectures, instead training a non-equivariant transformer on a massive 600K-structure dataset. It introduces \"Stoichiometric Stochastic Shell Sampling\" (S⁴) to train on local, non-periodic atomic blocks, aiming to learn both intramolecular conformation and intermolecular packing. The method reports state-of-the-art results among machine learning baselines and achieves performance competitive with DFT methods at orders-of-magnitude lower inference cost.", "questions": "1. Learned Representations (Fig. 4): In Figure 4, the generated molecules appear to have an identical orientation, suggesting the model may have only learned a packing arrangement rather than diverse, atomic-resolution geometries. Is this a common failure mode, and what does it imply about the model's learned representations?\n\n2. Robustness to Input: How robust is OXTAL's performance to the quality of the initial GFN2-xTB conformer? What happens if the input is a high-energy or physically unrealistic conformer?\n\n3. Choice of Architecture: Given that the S⁴ method trains on local atomic blocks, why was an explicitly SE(3)-equivariant denoiser (e.g., based on Equiformer or E(3)-GNNs) not used?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 4, "contribution": 3, "strengths": "1. Performance and Efficiency: The model demonstrates impressive results, significantly outperforming existing ML baselines and achieving a massive reduction in computational cost compared to traditional DFT-based CSP workflows.\n\n2. Scalability and Data: The work successfully scales a generative model to an exceptionally large and diverse dataset (600K CSD structures), a non-trivial data engineering and modeling achievement.\n\n3. Clarity and Presentation: The figures and tables are clear, informative, and visually compelling.", "weaknesses": "1. Input Conformer Dependency: The model relies on a pre-optimized GFN2-xTB 3D conformer as input. This introduces a significant confounding variable and undermines the claim of learning a \"joint distribution\" ab initio; it appears to be refining a pre-calculated conformer rather than generating one from scratch.\n\n2. Weak Theoretical Justification (Prop. 1): Proposition 1 merely describes a standard geometric surface-to-volume scaling law $O(T^{-1/3})$. It provides no evidence that the model learns true long-range periodicity or order from the local S⁴ crops.\n\n3. Lack of Ablation Studies: The paper is missing crucial ablation studies. The individual contributions of the S⁴ sampling scheme, the non-equivariant architecture, and the large dataset are not decoupled, making it difficult to assess the true sources of the performance gain.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "XBg002TBHx", "reviewer": "Reviewer_Q6b1", "summary": "This paper presents OXtal, an all-atom diffusion model for molecular crystal structure prediction (CSP). The method directly learns the conditional joint distribution of intramolecular conformations and periodic crystal packing from input 2D chemical graphs. A key novelty is the introduction of the Stoichiometric Stochastic Shell Sampling ($S^4$) scheme, which avoids explicit lattice parameterization while capturing long-range interactions. Extensive experiments show that OXtal substantially improves over prior machine-learning CSP methods and even partially surpasses DFT-based methods on CCDC CSP blind tests.", "questions": "In addition to the above weaknesses specific to $S^4$, the reviewer has the following additional questions:\n\n1. In the case where $n_S>1$, how are the evaluation metrics chosen? For instance, are they the average over all samples, or the best among them, or some other criterion?\n2. In the CSP Blind Test 5 benchmark, the OXtal method outperforms prior DFT-based methods on most metrics, yet on the Sol_C subset there remains a noticeable gap. What are the suspected causes of the lower performance on Sol_C? Can the authors identify any corner-cases that the model struggles with and that would guide future improvements?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "1. To the best of the reviewer's knowledge, this is the first work to apply a full all-atom diffusion framework to molecular crystal structure prediction, which is a significant leap compared to previous approaches.\n\n2. The empirical results are impressive, especially in realistic CCDC CSP blind tests, suggesting both effectiveness and efficiency of the proposed framework.\n\n3. The $S^4$ representation is a novel idea for trading off explicit lattice parametrisation by sampling shells around stoichiometric units, which may offer a scalable solution for large-scale training of molecule CSP models.", "weaknesses": "While the proposed $S^4$ representation enables training on the proposed all-atom backbone model and the diffusion framework, there remain several issues and open questions that should be addressed or clarified, which are listed as follows:\n\n1. The number of conformations inside each $S^4$ unit is not deterministic for one molecule crystal. In generation time, how many conformers one should generate per $S^4$ unit? Does this number affect downstream results?\n2. Within each $S^4$ unit, the consistency of generated conformations is unclear. If conformations vary slightly or even significantly, how does one pick a representative conformer to compute RMSD or other evaluation metrics?\n3. Although the selection of the lattice matrix is not unique, is it possible to recover one $S^4$ unit into a valid $(L,B)$ pair, i.e. an arbitrary unit cell? If so, can the detailed algorithm be provided?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "a5oJObtFFm", "reviewer": "Reviewer_cVf8", "summary": "The paper introduces OXTAL, an all-atom diffusion model for molecular crystal structure prediction (CSP).\nTrained on ∼600k crystals from the Cambridge Structural Database (CSD), OXTAL learns the joint distribution of molecular conformations and periodic packings using a new S4 (Stoichiometric Stochastic Shell Sampling) scheme.\nIt achieves strong performance on CCDC blind tests with competitive lattice recovery compared to DFT-based CSP at vastly lower cost.", "questions": "- Could the authors clarify why the training code cannot be released if it only depends on the data interface, not the CSD files themselves?\n- How does OXTAL perform on public datasets (e.g., COD) or inorganic datasets to demonstrate cross-domain generalization?\n- What is the impact of using non-equivariant Transformer architecture compared to SE(3)-equivariant baselines such as GemNet-OC or EquiformerV2 in this setting?\n- Could a smaller-scale variant of OXTAL (e.g., <100 M parameters) achieve comparable results with fewer GPU resources?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "This is among the most technically compelling works to date on molecular crystal structure prediction, and, to the best of my knowledge, the first diffusion-based framework that addresses molecular crystals comprehensively.\n- Innovative lattice-free diffusion formulation (S4).\n- Extensive benchmarks and realistic evaluation metrics (RMSD₁, RMSD₁₅, Smooth-LDDT).\n- Strong empirical results and clear scientific motivation.", "weaknesses": "- The training dataset (CSD) is under commercial license, and the authors will not release the training code. This prevents full replication of results.\n- The reason given (“CSD redistribution restrictions”) does not strictly apply to code; code could be released with dummy data-loading interfaces.\n- The paper does not evaluate OXTAL on public molecular crystal datasets (e.g., COD, MP-organic subsets), so it is unclear whether the method generalizes beyond CSD.\n- The paper could include more quantitative analysis on the impact of shell radius or token size in S4 on model accuracy.\n- Minor language and formatting issues:\n  * “do we 2 rounds of recycling” → should be “we do 2 rounds of recycling.”\n  * “orders-of-magnitude lower inference cost” → better phrased as “several orders of magnitude lower.”\n  * Variables  L and  d in Eqs. (21–27) are undefined in the main text.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)