journal article·2026-09-01Open access

Transport novelty distance: a distributional metric for evaluating material generative models

Paul Hagemann, Simon Müller, Janine George, Philipp Benner

Journal of Physics: Materials· Volume 9· Issue 3

Abstract

Abstract Recent advances in generative machine learning have opened new possibilities for the discovery and design of novel materials. However, as these models become more sophisticated, the need for rigorous and meaningful evaluation metrics has grown. Existing evaluation approaches often fail to capture both the quality and novelty of generated structures, limiting our ability to assess true generative performance. In this paper, we introduce the Transport Novelty Distance (TNovD) to judge generative models used for materials discovery jointly by the quality and novelty of the generated materials. Based on ideas from optimal transport theory, TNovD uses a coupling between the features of the training and generated sets, which is used to penalize quality and memorization independently. The two regimes are defined by thresholding the pairwise distances of trained and generated features. The features are generated from crystal structures using a graph neural network that is trained to distinguish between materials, their augmented counterparts, and differently sized supercells using contrastive learning. We evaluate our proposed metric on typical toy experiments relevant for crystal structure prediction, including memorization, noise injection and lattice deformations. Additionally, we validate the TNovD on the MP20 validation set and the WBM substitution dataset, demonstrating that it is capable of detecting both memorized structures and unrealistic material representations that are outside of the training data distribution. We also benchmark the performance of several popular material generative models. While introduced for materials, our TNovD framework is domain-agnostic and can be adapted for other areas, such as images and molecules.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Machine Learning in Materials Science · Generative Adversarial Networks and Image Synthesis · Advanced Electron Microscopy Techniques and Applications

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Bundesanstalt für Materialforschung und -prüfung (BAM)

Friedrich-Schiller-Universität Jena

Funding

European Union · ERC Grant MultiBonds

References (64)

Show source-provided references
1. Generative models for crystalline materials
2. All-atom diffusion transformers: unified generative modelling of molecules and materials
3. Crystal diffusion variational autoencoder for periodic material generation
4. A generative model for inorganic materials design10.1038/s41586-025-08628-5 ↗
5. Crystal structure prediction by joint equivariant diffusion10.52202/075280-0767 ↗
6. GANs trained by a two time-scale update rule converge to a local nash equilibrium
7. Fréchet chemnet distance: a metric for generative models for molecules in drug discovery10.1021/acs.jcim.8b00234 ↗
8. Vector field oriented diffusion model for crystal material generation10.1609/aaai.v38i20.30224 ↗
9. Learning crystallographic disorder: bridging prediction and experiment in materials discovery10.1002/adma.202514226 ↗
10. Continued challenges in high-throughput materials predictions: Mattergen predicts compounds from the training dataset10.1039/d6mh00268d ↗
11. Beware of diffusion models for synthesizing medical images-a comparison with GANs in terms of memorizing brain MRI and chest x-ray images10.1088/2632-2153/ad9a3a ↗
12. Score-based generative modeling through stochastic differential equations
13. Villani · Optim. Transp.–Old New · 2008 · 338 · xxii+973. 0110.1007/978-3-540-71050-9 ↗
14. Di Marino · 2017 · pp 204
15. E(n) equivariant graph neural networks
16. Representation learning with contrastive predictive coding
17. Continuous uniqueness and novelty metrics for generative modeling of inorganic crystals
18. Commentary: the materials project: a materials genome approach to accelerating materials innovation10.1063/1.4812323 ↗
19. Predicting stable crystalline compounds using chemical similarity10.1038/s41524-020-00481-6 ↗
20. LeMat-GenBench: bridging the gap between crystal generation and materials discovery
21. matbench-genmetrics: a Python library for benchmarking crystal structure generative models using time-based splits of materials project structures10.21105/joss.05618 ↗
22. Establishing baselines for generative discovery of inorganic crystals10.1039/D5MH00010F ↗
23. The earth mover’s distance as a metric for the space of inorganic compositions10.1021/acs.chemmater.0c03381 ↗
24. Element similarity in high-dimensional materials representations10.1039/D3DD00121K ↗
25. WyckoffDiff–a generative diffusion model for crystal symmetry
26. Exposing flaws of generative model evaluation metrics and their unfair treatment of diffusion models
27. Understanding and mitigating memorization in generative models via sharpness of probability landscapes
28. Score-based generative models detect manifolds10.52202/068431-2598 ↗
29. An interpretable evaluation of entropy-based novelty of generative models
30. Feature likelihood score: evaluating the generalization of generative models using samples
31. Density estimation using real NVP
32. Computational optimal transport: with applications to data science10.1561/2200000073 ↗
33. Improving and generalizing flow-based generative models with minibatch optimal transport
34. OT-Flow: fast and accurate continuous normalizing flows via optimal transport
35. The graph neural network model10.1109/TNN.2008.2005605 ↗
36. Semi-supervised classification with graph convolutional networks
37. A gentle introduction to graph neural networks10.23915/distill.00033 ↗
38. Neural message passing for quantum chemistry
39. Graph contrastive learning for materials
40. CSI: Novelty detection via contrastive learning on distributionally shifted instances
41. The crystallographic information file (CIF): a new standard archive file for crystallography10.1107/S010876739101067X ↗
42. Romain Tavenard, Alexander Tong and Titouan Vayer. POT: Python optimal transport
43. Python Materials Genomics (pymatgen): a robust, open-source python library for materials analysis10.1016/j.commatsci.2012.10.028 ↗
44. Pytorch: an imperative style, high-performance deep learning library
45. Fast graph representation learning with PyTorch Geometric
46. PyG 2.0: Scalable learning on real world graphs
47. Closed-form diffusion models
48. Diffusion models and the manifold hypothesis: log-domain smoothing is geometry adaptive
49. Colocalization for super-resolution microscopy via optimal transport10.1038/s43588-021-00050-x ↗
50. On the edge of memorization in diffusion models
51. Provable separations between memorization and generalization in diffusion models
52. Diffusion probabilistic models generalize when they fail to memorize
53. Schnet: a continuous-filter convolutional neural network for modeling quantum interactions
54. Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties10.1103/PhysRevLett.120.145301 ↗
55. A simple framework for contrastive learning of visual representations
56. Facenet: a unified embedding for face recognition and clustering
57. Artificial intelligence driving materials discovery? Perspective on the article: scaling deep learning for materials discovery10.1021/acs.chemmater.4c00643 ↗
58. Space group constrained crystal generation
59. Exploration of crystal chemical space using text-guided generative artificial intelligence10.1038/s41467-025-59636-y ↗
60. A foundation model for atomistic materials chemistry10.1063/5.0297006 ↗
61. LeMat-GenBench: a unified evaluation framework for crystal generative models
62. Closing the synthesis gap in computational materials design10.1038/s44160-026-01027-2 ↗
63. Syncotrain: a dual classifier pu-learning framework for synthesizability prediction10.1039/D4DD00394B ↗
64. Hagemann P Müller S 2026 Transport Novelty Distance (TNovD) (available at: https://github.com/BAMeScience/TransportNoveltyDistance )