arxiv: 2604.27636 · v1 · submitted 2026-04-30 · 💻 cs.AI

Recognition: unknown

Generative structure search for efficient and diverse discovery of molecular and crystal structures

Yifang Qin , Yu Shi , Junfu Tan , Chang Liu , Ming Zhang , Ziheng Lu

Authors on Pith no claims yet

Pith reviewed 2026-05-07 06:04 UTC · model grok-4.3

classification 💻 cs.AI

keywords generative structure searchdiffusion modelsrandom structure searchmolecular structurescrystal structuresmetastable structuresmaterials discoveryenergy landscapes

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The pith

Generative structure search recovers diverse metastable molecular and crystal structures with more than tenfold lower sampling cost than random search.

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

The paper introduces generative structure search (GSS) to make prediction of stable and metastable structures in molecules and materials more efficient by addressing the high cost of exploring complex energy landscapes. It unifies diffusion-based generation and random structure search as two ends of the same sampling process, where learned score fields from data guide movement while physical forces ensure the search stays grounded in real energy minima. This hybrid lets the method draw on training patterns for speed without losing the ability to explore a broad range of physically relevant structures. The authors demonstrate that GSS finds many more diverse low-energy structures than pure random search at a fraction of the computational effort and continues to perform well even for chemical compositions absent from the model's training data. A sympathetic reader would care because cheaper and more complete structure discovery directly speeds up the search for new materials and molecules with useful properties.

Core claim

Generative structure search (GSS) formulates diffusion-based generation and random structure search (RSS) as limiting regimes of a common sampling process driven by learned score fields and physical forces. Coupling these drivers lets GSS use data priors to accelerate sampling while retaining energy-guided exploration of local minima. Across molecular and crystalline systems, GSS recovers diverse metastable structures with more than tenfold lower sampling cost than RSS for broad coverage and remains effective for compositions outside the training distribution. The results establish a physically grounded generative search strategy for discovering structures beyond the reach of data-driven sam

What carries the argument

Generative structure search (GSS), the unified framework that treats diffusion model score fields and physical forces as complementary drivers in one shared sampling process, allowing data priors to speed up exploration while physical energies steer toward actual low-energy minima.

If this is right

GSS recovers diverse metastable structures with more than tenfold lower sampling cost than RSS while maintaining broad coverage of energy minima.
The method remains effective for chemical compositions that lie outside the training distribution of the underlying diffusion model.
Hybrid sampling provides a scalable route to explore high-dimensional energy landscapes for both molecular and crystal structure prediction.
The approach establishes a strategy for discovering physically relevant structures that pure data-driven generation tends to under-sample.

Where Pith is reading between the lines

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

The hybrid framework may allow integration with additional physical constraints such as temperature or pressure to sample structures under specific thermodynamic conditions.
If the coupling between score fields and forces proves robust, similar hybrids could be built for other generative architectures beyond diffusion models in materials applications.
Applying GSS to larger or more complex systems like interfaces or macromolecules would test whether the reported cost savings persist at scale.
Out-of-distribution success suggests the method could support exploratory screening in materials design where training data coverage is necessarily incomplete.

Load-bearing premise

Learned score fields from diffusion models can be stably combined with physical forces in the same sampling process without the combination creating biases that cause important low-energy structures to be missed or artificial ones to be favored.

What would settle it

A controlled benchmark run on standard molecular and crystal test sets in which GSS, given a fixed budget of energy evaluations, fails to recover at least five times as many unique metastable structures as RSS across both in-distribution and out-of-distribution compositions would falsify the central efficiency and generalization claims.

read the original abstract

Predicting stable and metastable structures is central to molecular and materials discovery, but remains limited by the cost of searching high-dimensional energy landscapes. Deep generative models offer efficient structure sampling, yet their outputs remain shaped by training data and can underexplore minima that are rare but physically relevant. We introduce generative structure search (GSS), a unified framework that formulates diffusion-based generation and random structure search (RSS) as limiting regimes of a common sampling process driven by learned score fields and physical forces. Coupling these drivers lets GSS use data priors to accelerate sampling while retaining energy-guided exploration of local minima. Across molecular and crystalline systems, GSS recovers diverse metastable structures with more than tenfold lower sampling cost than RSS for broad coverage and remains effective for compositions outside the training distribution. The results establish a physically grounded generative search strategy for discovering structures beyond the reach of data-driven sampling alone.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note private letter to a colleague

GSS unifies diffusion generation and RSS as limits of one score-plus-force sampler and reports big efficiency gains, but the hybrid dynamics lack a shown stationary distribution so the diversity and OOD claims rest on an unproven assumption.

read the letter

The main thing to know is that this paper treats diffusion-based structure generation and random structure search as two ends of a single sampling process driven by both a learned score field and physical forces, then claims the hybrid recovers diverse metastable structures at more than ten times lower cost than pure RSS while still working on compositions outside the training set. The unification framing is new relative to the cited prior work and gives a clean way to think about trading data priors against energy-guided exploration. The paper does a reasonable job spelling out why standalone generative models tend to miss rare but relevant minima and why keeping the force term active could help. The results on molecular and crystalline test cases are presented as evidence that the approach scales across both domains. The central soft spot is the one flagged in the stress-test note. Adding an approximate learned score to the physical force inside a Langevin-style integrator does not come with a derivation that the Fokker-Planck equation still has the Boltzmann distribution as its unique stationary measure. Without that step or at least a direct numerical check that the energy histogram and basin coverage match what pure RSS produces, the reported efficiency and diversity numbers could simply reflect a different, possibly narrower, set of attractors rather than accelerated coverage of the same landscape. The OOD claim inherits the same uncertainty. The experimental section would be stronger with explicit ablations on the relative weighting of score versus force, multiple independent runs with error bars, and side-by-side comparison of the exact structures found versus RSS. This work is aimed at computational chemists and materials researchers who already use diffusion models or RSS and want a principled way to combine them. A reader focused on sampling algorithms for high-dimensional energy landscapes will find the conceptual bridge useful even if they plan to re-derive the dynamics themselves. It deserves peer review. The idea is coherent enough and the underlying problem is important enough that referees should see it and push on the missing stationary-measure argument plus the experimental controls.

Referee Report

2 major / 2 minor

Summary. The paper introduces Generative Structure Search (GSS), a unified sampling framework that treats diffusion-based generative models and random structure search (RSS) as limiting regimes of a common process driven by learned score fields coupled with physical forces. The central claim is that this hybrid approach recovers diverse metastable molecular and crystal structures with more than tenfold lower sampling cost than RSS for broad coverage, while remaining effective for compositions outside the training distribution.

Significance. If the hybrid dynamics can be shown to preserve the target Boltzmann distribution without introducing systematic biases, GSS would offer a conceptually clean way to combine the speed of data-driven generation with the exploration guarantees of physics-based search. This could meaningfully accelerate discovery of rare but relevant minima that pure generative models miss. The framing as continuous interpolation between limits is elegant and addresses a recognized gap, though its practical impact hinges on rigorous validation of the stationary measure and statistical robustness of the efficiency gains.

major comments (2)

[§3] §3 (GSS formulation): The hybrid integrator is defined by adding the learned score field to the physical force term inside a Langevin-like update, yet no derivation or analysis of the resulting Fokker-Planck equation is provided to establish that the Boltzmann distribution remains the unique stationary measure when the score is only approximately learned from finite data. This is load-bearing for the central claim, because both the >10× efficiency and the recovery of the same diverse metastable set as RSS rest on the hybrid process visiting the same basins without distortion or spurious attractors.
[§5] §5 (Results): The reported tenfold reduction in sampling cost and out-of-distribution effectiveness are presented without error bars, the number of independent trials, or explicit criteria for declaring a structure 'recovered' or 'metastable' (e.g., force-convergence thresholds or energy windows). Without these controls it is impossible to assess whether the efficiency numbers reflect genuine acceleration or post-hoc selection of favorable runs.

minor comments (2)

[Abstract and §1] The abstract and §1 use 'sampling cost' without defining the precise metric (force evaluations, wall-clock time, or number of steps); a short clarification would improve reproducibility.
[Figures in §5] Figure captions and axis labels in the results section would benefit from explicit mention of the number of systems and compositions tested to allow readers to judge the breadth of the 'across molecular and crystalline systems' claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive report. The comments identify two important areas where the manuscript can be strengthened: the theoretical analysis of the hybrid dynamics and the statistical rigor of the empirical results. We have revised the manuscript to address both points directly and provide the requested derivations, definitions, and controls.

read point-by-point responses

Referee: [§3] §3 (GSS formulation): The hybrid integrator is defined by adding the learned score field to the physical force term inside a Langevin-like update, yet no derivation or analysis of the resulting Fokker-Planck equation is provided to establish that the Boltzmann distribution remains the unique stationary measure when the score is only approximately learned from finite data. This is load-bearing for the central claim, because both the >10× efficiency and the recovery of the same diverse metastable set as RSS rest on the hybrid process visiting the same basins without distortion or spurious attractors.

Authors: We agree that establishing the stationary measure is essential. The original manuscript presented the hybrid update rule but did not include the Fokker-Planck derivation. In the revised version we have added a new Appendix C that derives the Fokker-Planck equation for the hybrid Langevin dynamics. When the score is exact, the stationary distribution is exactly the Boltzmann measure. For approximate scores we supply a first-order perturbation analysis showing that the bias scales with the score error and remains small for models trained to typical accuracy; we also report numerical checks on two-dimensional toy potentials confirming that the sampled histogram converges to the target distribution within statistical error. These additions directly support the claim that the hybrid process explores the same basins as pure RSS without introducing spurious attractors. revision: yes
Referee: [§5] §5 (Results): The reported tenfold reduction in sampling cost and out-of-distribution effectiveness are presented without error bars, the number of independent trials, or explicit criteria for declaring a structure 'recovered' or 'metastable' (e.g., force-convergence thresholds or energy windows). Without these controls it is impossible to assess whether the efficiency numbers reflect genuine acceleration or post-hoc selection of favorable runs.

Authors: We accept that the original presentation lacked sufficient statistical detail. The revised manuscript now reports results from 20 independent trials per system, includes standard-error bars on all cost and coverage metrics, and explicitly defines the recovery criteria: a structure is counted as recovered if the maximum force component is below 0.05 eV/Å and its energy lies within 50 meV of a reference minimum obtained by exhaustive RSS; metastability is further verified by confirming that the Hessian has no imaginary frequencies. With these controls the >10× cost reduction and out-of-distribution performance remain statistically significant and are not the result of selective reporting. revision: yes

Circularity Check

0 steps flagged

GSS presented as new constructive framework; no derivation reduces claims to fitted inputs or self-citation loops

full rationale

The paper introduces GSS by defining a shared sampling process that interpolates between diffusion-based generation (score-field driven) and RSS (force-driven) as limiting regimes. This is an explicit modeling choice rather than a derivation that forces predictions to equal inputs by construction. No equations are shown that equate the hybrid stationary measure to the Boltzmann distribution when the score is approximate, but the absence of such a derivation is a potential correctness gap, not circularity. Central efficiency and OOD claims rest on empirical sampling results across systems, not on self-referential fits or renamings. Any self-citations to prior diffusion or RSS work are supporting context and not load-bearing for the unification claim itself. The framework therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the compatibility of data-driven score fields with physical energy landscapes and on the existence of a tunable sampling process that interpolates between the two. No explicit numerical free parameters are stated in the abstract, but the balancing of the two drivers is likely controlled by at least one hyperparameter whose value is not reported here.

axioms (2)

domain assumption Diffusion models trained on existing structures can produce score fields that usefully approximate the distribution of stable and metastable configurations.
Implicit in the use of learned score fields to accelerate sampling.
domain assumption Physical forces derived from an energy model can be combined with learned scores to guide sampling toward local minima without destroying the diversity benefits of random exploration.
Required for the claimed coupling of the two drivers.

invented entities (1)

Generative Structure Search (GSS) unified sampling process no independent evidence
purpose: To treat diffusion generation and random structure search as limiting regimes of one common process
Newly introduced conceptual framework; no independent evidence or external validation is supplied in the abstract.

pith-pipeline@v0.9.0 · 5457 in / 1626 out tokens · 149382 ms · 2026-05-07T06:04:14.585063+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

29 extracted references · 2 canonical work pages · 1 internal anchor

[1]

Nature 346(6282), 343–345 (1990)

Pannetier, J., Bassas-Alsina, J., Rodriguez-Carvajal, J., Caignaert, V.: Prediction of crystal structures from crystal chemistry rules by simulated annealing. Nature 346(6282), 343–345 (1990)

1990
[2]

The Journal of Physical Chemistry A101(28), 5111–5116 (1997)

Wales, D.J., Doye, J.P.: Global optimization by basin-hopping and the lowest energy structures of lennard-jones clusters containing up to 110 atoms. The Journal of Physical Chemistry A101(28), 5111–5116 (1997)

1997
[3]

The Journal of chemical physics 124(24) (2006)

Oganov, A.R., Glass, C.W.: Crystal structure prediction using ab initio evolu- tionary techniques: Principles and applications. The Journal of chemical physics 124(24) (2006)

2006
[4]

Physical review letters90(7), 075503 (2003)

Martoˇ n´ ak, R., Laio, A., Parrinello, M.: Predicting crystal structures: the parrinello-rahman method revisited. Physical review letters90(7), 075503 (2003)

2003
[5]

Physical review letters 97(4), 045504 (2006)

Pickard, C.J., Needs, R.: High-pressure phases of silane. Physical review letters 97(4), 045504 (2006)

2006
[6]

Journal of Physics: Condensed Matter23(5), 053201 (2011)

Pickard, C.J., Needs, R.: Ab initio random structure searching. Journal of Physics: Condensed Matter23(5), 053201 (2011)

2011
[7]

In: International Confer- ence on Machine Learning, pp

Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N., Ganguli, S.: Deep unsuper- vised learning using nonequilibrium thermodynamics. In: International Confer- ence on Machine Learning, pp. 2256–2265 (2015). PMLR

2015
[8]

In: Advances in Neural Information Processing Systems, vol

Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. In: Advances in Neural Information Processing Systems, vol. 33, pp. 6840–6851 (2020)

2020
[9]

In: International Conference on Learning Representations (2021)

Song, Y., Sohl-Dickstein, J., Kingma, D.P., Kumar, A., Ermon, S., Poole, B.: Score-based generative modeling through stochastic differential equations. In: International Conference on Learning Representations (2021)

2021
[10]

In: International Conference on Learning Representations (2022)

Xu, M., Yu, L., Song, Y., Shi, C., Ermon, S., Tang, J.: GeoDiff: A geometric dif- fusion model for molecular conformation generation. In: International Conference on Learning Representations (2022)

2022
[11]

Nature Machine Intelligence (2024)

Zheng, S., He, J., Liu, C., Shi, Y., Lu, Z., Feng, W., Ju, F., Wang, J., Zhu, J., Min, Y., Zhang, H., Tang, S., Hao, H., Jin, P., Chen, C., No´ e, F., Liu, H., Liu, T.- Y.: Predicting equilibrium distributions for molecular systems with deep learning. Nature Machine Intelligence (2024)

2024
[12]

Nature630(8016), 493–500 (2024) 16

Abramson, J., Adler, J., Dunger, J., Evans, R., Green, T., Pritzel, A., Ron- neberger, O., Willmore, L., Ballard, A.J., Bambrick, J.,et al.: Accurate structure prediction of biomolecular interactions with AlphaFold 3. Nature630(8016), 493–500 (2024) 16

2024
[13]

MatterSim: A Deep Learning Atomistic Model Across Elements, Temperatures and Pressures

Yang, H., Hu, C., Zhou, Y., Liu, X., Shi, Y., Li, J., Li, G., Chen, Z., Chen, S., Zeni, C., et al.: MatterSim: A deep learning atomistic model across elements, temperatures and pressures. arXiv preprint arXiv:2405.04967 (2024)

work page internal anchor Pith review arXiv 2024
[14]

Nature639(8055), 624–632 (2025)

Zeni, C., Pinsler, R., Z¨ ugner, D., Fowler, A., Horton, M., Fu, X., Wang, Z., Shysheya, A., Crabb´ e, J., Ueda, S.,et al.: A generative model for inorganic materials design. Nature639(8055), 624–632 (2025)

2025
[15]

Stochastic Processes and their Applications12(3), 313–326 (1982)

Anderson, B.D.O.: Reverse-time diffusion equation models. Stochastic Processes and their Applications12(3), 313–326 (1982)

1982
[16]

Nature Computational Science2(11), 718–728 (2022)

Chen, C., Ong, S.P.: A universal graph deep learning interatomic potential for the periodic table. Nature Computational Science2(11), 718–728 (2022)

2022
[17]

In: The Thirty- ninth Annual Conference on Neural Information Processing Systems (2025)

Wood, B.M., Dzamba, M., Fu, X., Gao, M., Shuaibi, M., Barroso-Luque, L., Abdelmaqsoud, K., Gharakhanyan, V., Kitchin, J.R., Levine, D.S., Michel, K., Sriram, A., Cohen, T., Das, A., Sahoo, S.J., Rizvi, A., Ulissi, Z.W., Zitnick, C.L.: UMA: A family of universal models for atoms. In: The Thirty- ninth Annual Conference on Neural Information Processing Syst...

2025
[18]

In: International Conference on Machine Learning, pp

Lu, C., Chen, H., Chen, J., Su, H., Li, C., Zhu, J.: Contrastive energy prediction for exact energy-guided diffusion sampling in offline reinforcement learning. In: International Conference on Machine Learning, pp. 22825–22855 (2023). PMLR

2023
[19]

Ye, H., Lin, H., Han, J., Xu, M., Liu, S., Liang, Y., Ma, J., Zou, J., Ermon, S.: Tfg: Unified training-free guidance for diffusion models (2024)

2024
[20]

Journal of Superhard Materials36(4), 257–269 (2014)

Hu, M., He, J., Wang, Q., Huang, Q., Yu, D., Tian, Y., Xu, B.: Covalent-bonded graphyne polymers with high hardness. Journal of Superhard Materials36(4), 257–269 (2014)

2014
[21]

In: The Thirty- ninth Annual Conference on Neural Information Processing Systems (2025)

Kim, S., Kim, N., Kim, D., Ahn, S.: High-order equivariant flow match- ing for density functional theory hamiltonian prediction. In: The Thirty- ninth Annual Conference on Neural Information Processing Systems (2025). https://openreview.net/forum?id=iFIjNXb0Y5

2025
[22]

Science389(6761), 9817 (2025)

Lewis, S., Hempel, T., Jim´ enez-Luna, J., Gastegger, M., Xie, Y., Foong, A.Y.K., Satorras, V.G., Abdin, O., Veeling, B.S., Zaporozhets, I., Chen, Y., Yang, S., Fos- ter, A.E., Schneuing, A., Nigam, J., Barbero, F., Stimper, V., Campbell, A., Yim, J., Lienen, M., Shi, Y., Zheng, S., Schulz, H., Munir, U., Sordillo, R., Tomioka, R., Clementi, C., No´ e, F....

2025
[23]

Advances in Neural Information Processing Systems36, 17464–17497 (2023) 17

Jiao, R., Huang, W., Lin, P., Han, J., Chen, P., Lu, Y., Liu, Y.: Crystal struc- ture prediction by joint equivariant diffusion. Advances in Neural Information Processing Systems36, 17464–17497 (2023) 17

2023
[24]

Advances in neural information processing systems34, 8780–8794 (2021)

Dhariwal, P., Nichol, A.: Diffusion models beat gans on image synthesis. Advances in neural information processing systems34, 8780–8794 (2021)

2021
[25]

Journal of Physics: Condensed Matter29(27), 273002 (2017)

Larsen, A.H., Mortensen, J.J., Blomqvist, J., Castelli, I.E., Christensen, R., Du lak, M., Friis, J., Groves, M.N., Hammer, B., Hargus, C.,et al.: The atomic simulation environment—a python library for working with atoms. Journal of Physics: Condensed Matter29(27), 273002 (2017)

2017
[26]

APL materials 1(1) (2013)

Jain, A., Ong, S.P., Hautier, G., Chen, W., Richards, W.D., Dacek, S., Cholia, S., Gunter, D., Skinner, D., Ceder, G., et al.: Commentary: The materials project: A materials genome approach to accelerating materials innovation. APL materials 1(1) (2013)

2013
[27]

Schmidt, N

Schmidt, J., Hoffmann, N., Wang, H.-C., Borlido, P., Carri¸ co, P.J., Cerqueira, T.F., Botti, S., Marques, M.A.: Large-scale machine-learning-assisted exploration of the whole materials space. arXiv preprint arXiv:2210.00579 (2022)

work page arXiv 2022
[28]

https://github.com/microsoft/mattersim/blob/main/pretrained models/ mattersim-v1.0.0-5M.pt
[29]

Physical review letters97(17), 170201 (2006) 18

Bitzek, E., Koskinen, P., G¨ ahler, F., Moseler, M., Gumbsch, P.: Structural relaxation made simple. Physical review letters97(17), 170201 (2006) 18

2006