cs.LGOct 6, 2026

OxiGen: Oxidation-State-Aware Crystal Generation

Authors: Dylan John, Kim E. Jelfs, Alex M. Ganose, Eleonora Giunchiglia

Organizations: Department of Chemistry, Imperial College London · Department of Electrical and Electronic Engineering, Imperial College London

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Abstract

Generative models have the potential to accelerate inorganic materials discovery by enabling inverse design, but generating experimentally realisable crystals remains challenging. Oxidation states are widely used to assess the compositional validity of crystals and guide inorganic materials discovery. While existing generative models for crystals can generate materials with charge-neutral oxidation-state assignments, they poorly reproduce the distributions of oxidation states observed in synthesised materials. To address this limitation, we propose OxiGen, an oxidation-state-aware crystal diffusion model that explicitly represents oxidation states during generation. OxiGen enforces global charge neutrality by construction using a structured output layer with exact inference over a finite-state automaton. Empirically, OxiGen substantially improves oxidation-state fidelity, generates the highest rate of stable, unique, and novel crystals among evaluated methods, and maintains high compositional validity even under property conditioning.

Figures & tables

Figure 1: Example of OxiGen discrete diffusion sampling over a species vocabulary of {Na+,O2−}\{\mathrm{Na}^{+},\mathrm{O}^{2-}\} . The noisy crystal state Mt\boldsymbol{M}_{t} is processed by the denoiser, which predicts site-wise species probabilities pθ,i(s0,i∣Mt,t)p_{\theta,i}(s_{0,i}\mid\boldsymbol{M}_{t},t) . These are passed through the structured output layer to sample a charge-neutral assignment S^0\hat{\boldsymbol{S}}_{0} , which is used in the reverse diffusion step.
MethodDecodingCharge Neutrality (%) ↑\uparrowSite Accuracy (%) ↑\uparrowCrystal Accuracy (%) ↑\uparrow
BVAnalyzer–100.00\mathbf{100.00}88.1986.02
BERTOSArgmax92.83\mbox{\pm 0.22}97.81\mbox{\pm 0.17}90.93\mbox{\pm 0.24}
OursArgmax\underline{94.37}\mbox{\pm 0.26}\underline{98.47}\mbox{\pm 0.10}\underline{92.79}\mbox{\pm 0.18}
Viterbi\mathbf{100.00}\mbox{\pm 0.00}\mathbf{98.74}\mbox{\pm 0.09}\mathbf{96.00}\mbox{\pm 0.25}
Table 1: Oxidation-state prediction results, reported as mean ±\pm std over five independently seeded training runs; the deterministic BVAnalyzer is reported as a single value. Best values are shown in bold and second-best values are underlined .
MethodOxidation-State FidelityStability & Relaxation
Comp. Val.fOSf_{\mathrm{OS}}dOSd_{\mathrm{OS}}S.U.N.EhullE_{\mathrm{hull}}RMSD
(%) ↑\uparrow(%)↓\downarrow(%) ↑\uparrow(eV/atom) ↓\downarrow(Å) ↓\downarrow
MP-20-OS91.7353.78––––
DiffCSP78.47\mbox{\pm 2.55}35.67\mbox{\pm 1.05}0.1566\mbox{\pm 0.0037}18.24\mbox{\pm 1.38}0.2007\mbox{\pm 0.0101}0.3555\mbox{\pm 0.0427}
MatterGen81.18\mbox{\pm 0.94}37.89\mbox{\pm 1.02}0.1537\mbox{\pm 0.0039}\underline{24.54}\mbox{\pm 0.91}0.1799\mbox{\pm 0.0085}\underline{0.1747}\mbox{\pm 0.0203}
FlowMM79.87\mbox{\pm 0.20}37.34\mbox{\pm 0.65}0.1626\mbox{\pm 0.0037}13.85\mbox{\pm 0.39}0.2481\mbox{\pm 0.0104}0.6704\mbox{\pm 0.0347}
Table 2: De novo generation results, reported as mean ±\pm std over five independently seeded training runs, with 10,240 generated structures per seed. Best values are shown in bold and second-best values are underlined . MP-20-OS denotes the test set.
Figure 2: Left : Compositional validity as a function of the ICSD frequency threshold required for an oxidation state to be considered admissible. Right : Marginal oxidation-state distributions for selected elements. MP-20-OS denotes the test set in both panels.
RepresentationStructured Output LayerCharge NeutralityComp. Val.fOSf_{\mathrm{OS}}dOSd_{\mathrm{OS}}
TrainingSampling(%) ↑\uparrow(%) ↑\uparrow(%)↓\downarrow
Element✗✗–81.12\mbox{\pm 0.46}37.78\mbox{\pm 1.16}0.1589\mbox{\pm 0.0050}
Species✗✗\underline{39.08}\mbox{\pm 2.60}82.31\mbox{\pm 0.77}40.54\mbox{\pm 1.29}0.1368\mbox{\pm 0.0047}
Species✗✓\mathbf{100.00}\mbox{\pm 0.00}\underline{90.65}\mbox{\pm 0.94}\mathbf{53.01}\mbox{\pm 0.96}\underline{0.0911}\mbox{\pm 0.0028}
Species✓✓\mathbf{100.00}\mbox{\pm 0.00}\mathbf{90.70}\mbox{\pm 0.67}\underline{52.65}\mbox{\pm 0.76}\mathbf{0.0874}\mbox{\pm 0.0029}
Table 3: De novo generation ablation results, reported as mean ±\pm std over five independently seeded training runs, with 10,240 generated structures per seed. Best values are shown in bold and second-best values are underlined . The shaded row is OxiGen.
Figure 3: Left : Compositional validity at target band gaps of 1, 3, 5, and 7 eV. Right : Kernel density estimates of the predicted band-gap distributions for structures generated at each target. Results are shown for a single fine-tuning seed. Dashed vertical lines indicate the conditioning targets and the grey density shows the band-gap distribution for the MP-20-OS test set.
Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

StageTrainVal.TestTotal
MP-2027,1369,0479,04645,229
Removed
Outside vocabulary2899083462
Elemental non-metal55201085
No feasible charge-neutral assignment1,0033593271,689
Chemically implausible assignment2538381417
Appendix
Table 4: MP-20-OS filtering. Rows under removed report structures excluded at each filtering stage.
(a) Architecture
SettingBERTOSCrystaliteOS
Hidden dimension120128
Transformer layers1212
Attention heads44
MLP hidden dimension512256
Dropout0.10.1
Appendix
Table 5: Architecture and training settings for BERTOS and CrystaliteOS.
Structured Output LayerTraining TimeSampling Time
(s/epoch) ↓\downarrow(s/batch) ↓\downarrow
✗78.797\mbox{\pm 0.101}309.527\mbox{\pm 4.923}
✓98.906\mbox{\pm 0.057}329.716\mbox{\pm 4.809}
Change (%)+25.52+25.52+6.52+6.52
Appendix
Table 6: Computational overhead of the structured output layer, reported as mean ±\pm std over five epochs or five batches. Percentage changes are relative to the model without the structured output layer.
SettingValue
Hidden / atom / edge dimension512 / 512 / 512
Interaction blocks4
Cutoff7.07.0 Å
Maximum neighbours50
OptimiserAdam
Learning rate10−410^{-4}
Appendix
Table 7: Architecture, training, and sampling settings for OxiGen.
SettingValue
Property embedding dimension512
Null conditionLearned embedding
Fine-tuning modeFull-model
InitialisationUnconditional last epoch
OptimiserAdam
Learning rate5×10−65\times 10^{-6}
Appendix
Table 8: Band-gap conditional fine-tuning and sampling settings for OxiGen and MatterGen.
MethodStableUniqueNovelS.U.N.EhullE_{\mathrm{hull}}RMSD
(%) ↑\uparrow(%) ↑\uparrow(%) ↑\uparrow(%) ↑\uparrow(eV/atom) ↓\downarrow(Å) ↓\downarrow
DiffCSP43.34\mbox{\pm 1.29}95.80\mbox{\pm 0.58}71.58\mbox{\pm 1.57}18.24\mbox{\pm 1.38}0.2007\mbox{\pm 0.0101}0.3555\mbox{\pm 0.0427}
MatterGen46.11\mbox{\pm 3.17}\underline{97.74}\mbox{\pm 0.49}\mathbf{75.32}\mbox{\pm 2.72}\underline{24.54}\mbox{\pm 0.91}0.1799\mbox{\pm 0.0085}\underline{0.1747}\mbox{\pm 0.0203}
FlowMM36.04\mbox{\pm 0.83}\mathbf{97.99}\mbox{\pm 0.21}\underline{74.07}\mbox{\pm 1.01}13.85\mbox{\pm 0.39}0.2481\mbox{\pm 0.0104}0.6704\mbox{\pm 0.0347}
OMatG49.12\mbox{\pm 0.39}95.12\mbox{\pm 0.33}65.42\mbox{\pm 0.87}19.03\mbox{\pm 0.78}0.1831\mbox{\pm 0.0030}0.5244\mbox{\pm 0.0278}
Crystalite\mathbf{67.17}\mbox{\pm 2.18}93.03\mbox{\pm 0.91}52.25\mbox{\pm 2.61}22.83\mbox{\pm 0.76}\mathbf{0.1437}\mbox{\pm 0.0083}0.2496\mbox{\pm 0.0198}
Appendix
Table 9: Additional de novo generation results, reported as mean ±\pm std over five independently seeded training runs, with 10,240 generated structures per seed. Best values are shown in bold and second-best values are underlined .
MethodValidityCoverageDistribution
Comp. (%) ↑\uparrowStruct. (%) ↑\uparrowCov-R (%) ↑\uparrowCov-P (%) ↑\uparrowwdist ρ\rho ↓\downarrowwdist NelN_{\mathrm{el}} ↓\downarrow
DiffCSP87.29\mbox{\pm 1.97}99.89\mbox{\pm 0.05}99.58\mbox{\pm 0.05}99.70\mbox{\pm 0.10}0.2514\mbox{\pm 0.1340}0.5052\mbox{\pm 0.0557}
MatterGen88.71\mbox{\pm 0.64}\underline{99.97}\mbox{\pm 0.04}\mathbf{99.71}\mbox{\pm 0.08}99.69\mbox{\pm 0.07}\mathbf{0.1416}\mbox{\pm 0.0576}0.2398\mbox{\pm 0.0791}
FlowMM87.58\mbox{\pm 0.17}91.80\mbox{\pm 0.86}99.27\mbox{\pm 0.11}98.83\mbox{\pm 0.18}1.3027\mbox{\pm 0.4222}0.1200\mbox{\pm 0.0125}
OMatG89.06\mbox{\pm 0.37}99.11\mbox{\pm 0.19}99.59\mbox{\pm 0.09}\underline{99.83}\mbox{\pm 0.03}0.2672\mbox{\pm 0.0152}\mathbf{0.0549}\mbox{\pm 0.0097}
Crystalite\underline{89.12}\mbox{\pm 0.41}99.68\mbox{\pm 0.06}\underline{99.67}\mbox{\pm 0.09}\mathbf{99.87}\mbox{\pm 0.04}\underline{0.1541}\mbox{\pm 0.0266}\underline{0.1151}\mbox{\pm 0.0190}
Appendix
Table 10: Proxy metrics for de novo generation, reported as mean ±\pm std over five independently seeded training runs, with 10,240 generated structures per seed. Best values are shown in bold and second-best values are underlined .
ModelValidUniqueNovelStableMetastableS.U.N.M.S.U.N.EhullE_{\mathrm{hull}}
(%) ↑\uparrow(%) ↑\uparrow(%) ↑\uparrow(%) ↑\uparrow(%) ↑\uparrow(%) ↑\uparrow(%) ↑\uparrow(eV/atom) ↓\downarrow
Pre-Relaxed Structures
WyFormer93.493.066.40.515.70.11.90.4988
PLaID++96.077.824.212.460.71.07.60.0854
WyFormer-DFT95.295.066.43.724.80.47.80.2708
OMatG-FC97.292.828.918.457.91.712.00.0694
Appendix
Table 11: De novo generation results under the LeMat-GenBench evaluation procedure. OxiGen results are computed over 2,500 generated structures; results for all other models trained only on MP-20 are taken from the public LeMat-GenBench leaderboard. Rows are grouped according to whether the submitted structures are pre-relaxed. Best and second-best values within the pre-relaxed group are shown in bold and underlined , respectively.
MethodStableUniqueNovelS.U.N.EhullE_{\mathrm{hull}}RMSD
 (%) ↑\uparrow(%) ↑\uparrow(%) ↑\uparrow(%) ↑\uparrow(eV/atom) ↓\downarrow(Å) ↓\downarrow
Element ✗/✗47.47\mbox{\pm 2.65}\mathbf{97.48}\mbox{\pm 0.36}\mathbf{74.68}\mbox{\pm 2.03}25.21\mbox{\pm 0.60}0.1709\mbox{\pm 0.0103}0.1728\mbox{\pm 0.0098}
Species ✗/✗49.72\mbox{\pm 2.53}\underline{97.28}\mbox{\pm 0.35}\underline{73.20}\mbox{\pm 1.80}\underline{26.08}\mbox{\pm 0.92}\underline{0.1646}\mbox{\pm 0.0035}\mathbf{0.1616}\mbox{\pm 0.0102}
Species ✗/✓\mathbf{52.59}\mbox{\pm 2.25}96.45\mbox{\pm 0.64}70.68\mbox{\pm 2.31}\mathbf{26.38}\mbox{\pm 1.01}\mathbf{0.1575}\mbox{\pm 0.0080}\underline{0.1679}\mbox{\pm 0.0117}
Species ✓/✓\underline{50.35}\mbox{\pm 2.39}96.80\mbox{\pm 0.70}72.04\mbox{\pm 2.03}25.62\mbox{\pm 0.69}0.1696\mbox{\pm 0.0075}0.1853\mbox{\pm 0.0175}
Appendix
Table 12: Ablation results for stability, uniqueness, novelty, and relaxation quality. Results are reported as mean ±\pm std over five independently seeded training runs, with 10,240 generated structures per seed. The method names indicate whether structured training / structured sampling are used, respectively. Best values are shown in bold and second-best values are underlined ; the shaded row is OxiGen.
MethodCharge Neutrality (%) ↑\uparrowSite Agreement (%) ↑\uparrowCrystal Agreement (%) ↑\uparrow
Element ✗/✗–––
Species ✗/✗\underline{39.08}\mbox{\pm 2.60}74.45\mbox{\pm 1.84}33.57\mbox{\pm 2.29}
Species ✗/✓\mathbf{100.00}\mbox{\pm 0.00}\mathbf{90.69}\mbox{\pm 0.81}\mathbf{72.47}\mbox{\pm 1.40}
Species ✓/✓\mathbf{100.00}\mbox{\pm 0.00}\underline{90.45}\mbox{\pm 0.39}\underline{71.49}\mbox{\pm 1.32}
Appendix
Table 13: Ablation results for charge neutrality and oxidation-state agreement. Results are reported as mean ±\pm std over five independently seeded training runs, with 10,240 generated structures per seed. The method names indicate whether structured training / structured sampling are used, respectively. Best values are shown in bold and second-best values are underlined ; the shaded row is OxiGen.
MethodTargetRMSEStableUniqueNovelS.U.N.EhullE_{\mathrm{hull}}RMSD
(eV)(eV) ↓\downarrow(%) ↑\uparrow(%) ↑\uparrow(%) ↑\uparrow(%) ↑\uparrow(eV/atom) ↓\downarrow(Å) ↓\downarrow
MatterGen11.11649.3299.0282.4233.590.18470.1961
31.72445.9098.9383.9831.050.15300.2684
52.18549.5194.8282.3231.540.15130.3016
72.62255.3786.8284.1835.160.14560.3338
OxiGen11.13860.5596.4873.6335.840.14890.1813
Appendix
Table 14: Band-gap-conditioned generation results for target band gaps of 1, 3, 5, and 7 eV. Results are shown for a single fine-tuning seed, with 1,024 generated structures at each target.
Figure 4: Examples of stable, unique, and novel crystals generated by OxiGen.

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