Framework-Conditional Open Materials Generation

Maya M. Martirossyan; Hillary Pan; Philipp Höllmer; Stefano Martiniani

cs.LGOct 29, 2026

Framework-Conditional Open Materials Generation

Authors: Maya M. Martirossyan, Hillary Pan, Philipp Höllmer, Stefano Martiniani

Organizations: NYU Langone Health · New York University

Abstract

Theoretical predictions of novel materials rely on a variety of techniques, from data-mining-based ion substitution methods to fully de novo generative models. Each approach imposes specific constraints and encounters unique challenges when extrapolating beyond the distribution of known materials to discover new ones. The foremost goal of materials generation is to produce stable, unique, and novel (S.U.N.) structures. Predicted structures that meet these criteria, however, typically result from novel chemical compositions mapped onto known structural prototypes or frameworks. We leverage this heuristic insight to present a new generative paradigm for the de novo prediction of inorganic crystalline materials constrained by their structural framework---i.e., the unit cell shapes and respective particle positions. Our method, termed OMatG-FC (Open Materials Framework-Conditional Generation), learns via a combination of discrete flow matching on the atomic species and stochastic interpolants for the volume scaling of the unit cell lattice, while fixing in-place the fractional coordinates and the unit-volume lattice vectors, dramatically reducing the dimensionality of the problem compared to unconstrained (framework-free) generation. Our method is more flexible than existing prototype-constrained methods, demonstrating capability for discovery of unseen, stable prototypes derived from known structural frameworks. We also investigate the number of unique frameworks in the MP-20 dataset, demonstrating the propensity of duplicate frameworks within the dataset and providing a framework-split version. We benchmark the performance of our model using the LeMat-GenBench suite using three ML interatomic potentials and achieve state-of-the-art S.U.N. rate below the convex hull, eschewing the need to learn atomic packings for materials discovery.

Figures & tables

Figure 1: Illustration of the generation process with different types of generative models for the same test structure: (a) crystal structure prediction (CSP) samples the species at time $t=0$ from the structure at time $t=1$ ; (b) de novo generation (DNG) evolves the lattice, species, and fractional coordinates jointly; (c) framework-conditional prediction (FCP) evolves the lattice volume scaling and atomic species only.

Figure 2: Two crystal structures—a BCC-type crystal (left) and a CsCl prototype (right)—with the same structural framework but different structural prototypes, labeled by their space groups and corresponding Wyckoff positions.

Method	Integration steps	Validity (% $\uparrow$ )			Property ( $\downarrow$ )
Method	Integration steps	Structural	Composition	Combined	wdist ( $\rho$ )	wdist ( $N$ ary)	wdist $\left(\langle CN\rangle_{S}\right)$	wdist (elem)	wdist (sg)
DiffCSP	1000	99.91	82.46	82.46	0.3133	0.3193	0.3916	1.6300	20.40
FlowMM	1000	92.26	76.87	76.86	1.0712	0.1130	0.6603	0.9255	13.02
OMatG-EncDecODE	840	97.25	84.16	84.16	0.1155	0.0553	0.1026	0.8249	24.80
OMatG-FC-LinearODE	610	100.0	87.38	87.38	0.6045	0.0719	0.1890	0.4038	4.413
OMatG-FC-LinearSDE	620	100.0	86.33	86.32	0.0860	0.0856	0.1163	0.8483	5.888

Table 1: Distribution-based metrics from de novo generation of

10\,000

structures using models trained on the

MP

-20 dataset with the structural frameworks present in the

MP

-20 test dataset. We report comparisons to other de novo generation models: DiffCSP, FlowMM, and OMatG-EncDecODE. Best scores in each category are bolded and second-best are underlined.

Method	Validity	Unique	Novelty	Stable	Metastable	S.U.N.	M.S.U.N.	$\langle E\rangle/N$	RMSD
Method	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	(eV, $\downarrow)$	( Å , $\downarrow$ )
Random enumeration [ 37 ]	70.4	70.3	61.4	0.0	0.1	0.0	0.1	2.82	1.76
Ionic substitution [ 37 , 16 ]	33.8	32.5	20.7	0.6	10.0	0.3	4.0	0.53	0.64
ADiT [ 29 ]	90.6	87.8	26.0	0.4	36.5	0.0	1.0	0.33	0.38
DiffCSP [ 19 ]	95.7	94.8	66.2	2.3	29.8	0.1	8.5	0.27	0.59
DiffCSP++ [ 31 ]	95.3	95.1	62.0	1.0	26.4	0.2	5.0	0.41	0.69

Table 2: Benchmarks for de novo generation as provided by the LeMat-GenBench software [ 49 ] on

2500

generated structures. Models are trained and evaluated on the

MP

-20 dataset. Stability is defined as having

\Delta E_{\mathrm{hull}}\leq 0

eV/atom above hull and metastability is defined as

0<\Delta E_{\mathrm{hull}}\leq 0.1

eV/atom above hull. Uniqueness and novelty results are combined with (meta)stability assessments to produce (M)SUN rates. For OMatG and OMatG-FC models, structures are subsampled from those in Tab. 1 and benchmarks are computed; for random enumeration and ionic substitution the benchmarking is described in Appendix G ; all other benchmarks from other models are reproduced from the LeMat-GenBench leaderboard. Models marked with a

\dagger

utilize pre-relaxation before assessment; comparisons are therefore made within each category (unrelaxed and relaxed). Best scores in each category are bolded and second-best are underlined.

Method	Validity	Unique	Novelty	Stable	Metastable	S.U.N.	M.S.U.N.	$\langle E\rangle/N$	RMSD
Method	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	(eV, $\downarrow)$	( Å , $\downarrow$ )
SGEquiDiff [ 34 ]	88.1	87.7	69.1	0.4	7.3	0.1	1.0	0.9145	1.1722
Crystalite [ 30 ]	86.4	85.0	45.1	4.1	38.5	0.5	6.0	0.2770	0.5036
OMatG-FC-LinearODE	92.9	87.3	64.7	2.0	30.5	0.4	8.4	0.4908	0.6431
OMatG-FC-LinearSDE	95.6	90.8	65.7	1.5	31.4	0.3	7.9	0.3521	0.6466
SGEquiDiff †	93.5	93.1	69.0	6.3	23.1	0.6	10.9	0.2688	0.3003

Table 3: Benchmarks of models trained and evaluated on the

MPTS

-52 dataset for de novo generation. LeMat-GenBench [ 49 ] is used to evaluate

2500

generated structures. The column definitions are the same as those of Tab. 2 . Models marked with a

\dagger

utilize pre-relaxation before assessment.

Figure 3: Three examples of known materials from the $MP$ -20 dataset and a S.U.N. structure sampled using OMG-FC. All four materials share the same underlying structural framework but differ by prototype. Labels denote the chemical composition, $N$ -arity, volume, and AFLOW prototype label. The sampled NdAlSiAu structure represents an unseen prototype for the model.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Optimization
Hyperparameter	Value
Optimizer	Adam
Learning rate	$1.596\times 10^{-4}$
LR scheduler	None
Batch size	128
Max epochs	1000

Appendix

Table 4: ODE sampling scheme training hyperparameters.

Optimization
Hyperparameter	Value
Optimizer	AdamW
Learning rate	$8.313\times 10^{-4}$
Weight decay	$1.935\times 10^{-5}$
LR scheduler	CosineAnnealingLR
$T_{\max}$	1000

Appendix

Table 5: SDE sampling scheme training hyperparameters.

Figure 4: (a) Uniqueness rate and kernel density estimate (using a Gaussian kernel) of the match-boundary density as a function of stol of StructureMatcher plotted for the entire $MP$ -20 dataset. (b) Examples of three structural frameworks with different compositions which ‘match’ by framework to the reference Cs 2 KPdF 6 structure, with the RMSDs and structural differences on one of the symmetry sites magnified for each.

Method	Validity	Novelty	Stable	Metastable	S.U.N.	M.S.U.N.
Method	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )
OMatG-FC-LinearODE, unrelaxed	96.2	30.2	4.8	58.1	0.2	6.7
OMatG-FC-LinearSDE, unrelaxed	96.4	32.2	4.2	55.4	0.1	6.2
OMatG-FC-LinearODE, relaxed	96.8	29.1	19.1	58.2	1.3	12.9
OMatG-FC-LinearSDE, relaxed	97.1	31.1	17.2	57.7	1.1	12.5

Appendix

Table 6: Evaluation of the OMatG-FC models with volume-scaling ablation, both before and after pre-relaxation. Benchmarks are performed on

2500

generated structures using LeMat-GenBench [ 49 ] .

Method	Validity	Stable	Metastable	S.U.N.	M.S.U.N.
Method	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )	Rate (%, $\uparrow$ )
OMatG-FC-LinearODE, unrelaxed	88.9	1.6	13.6	0.1	4.9
OMatG-FC-LinearODE, relaxed	91.3	3.8	34.9	0.7	19.1
OMatG-FC-LinearSDE, unrelaxed	89.8	1.6	17.0	0.1	6.5
OMatG-FC-LinearSDE, relaxed	91.6	3.8	36.7	0.8	19.8

Appendix

Table 7: Benchmarks for de novo generation as provided by the LeMat-GenBench software [ 49 ] on

2500

generated structures as in Tab. 2 . The OMatG-FC models in this table are trained on the framework-split

MP

-20 dataset instead of the original

MP

-20 dataset.

Split	Frameworks	Materials
Train	1,067	27,137
Validation	1,058	9,046
Test	1,058	9,046
Total	3,183	45,229

Appendix

Table 8: Number of unique frameworks and materials in each split of the framework-split

MP

-20 dataset.

Distinct (M.)S.U.N. compositions per framework	Number of frameworks
0	438
1	73
2	15
3	3
4	4
5	1

Appendix

Table 9: Distribution of distinct (M.)S.U.N. compositions across the structural frameworks identified among

2500

structures generated by OMatG-FC-LinearODE.

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OMatG-flash: An All-Atom Flow Map with Reinforce Adjoint Matching for Scalable Materials Discovery

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New York University · University of Minnesota

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The discovery of novel inorganic materials drives technological breakthroughs in critical fields such as computing and energy storage. Generative AI has promised to accelerate the materials discovery pipeline, but state-of-the-art flow and diffusion models remain bottlenecked by the cost of proposing candidate materials. To address this, we introduce OMatG-flash, an all-atom flow map for inorganic crystal structure prediction (CSP) and de novo generation (DNG). OMatG-flash is a Pareto-optimal inference engine for materials, sampling candidate materials with an order of magnitude fewer inference steps and less wall-clock time than existing flow and diffusion models while demonstrating benchmark performance on par with the state-of-the-art. To enable post-training fine-tuning we apply Reinforce Adjoint Matching to flow maps, further improving match rates and RMSE on the unconditional CSP task. OMatG-flash showcases the potential of flow maps to accelerate generation of high-quality candidate inorganic materials and demonstrates a step forward in sample throughput necessary for data-hungry materials discovery workflows.

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