# Continuous SUN (Stable, Unique, and Novel) Metric for Generative Modeling of Inorganic Crystals

arXiv: https://arxiv.org/abs/2510.12405 · HTML: https://mlsanity.com/paper/2510.12405/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 52 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Builds on (most cited first, 19 of 19)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Tackling Climate Change with Machine Learning](https://mlsanity.com/paper/1906.05433/) (2019)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [All-atom Diffusion Transformers: Unified generative modelling of molecules and materials](https://mlsanity.com/paper/2503.03965/) (2025)
- [An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties](https://mlsanity.com/paper/2005.07609/) (2020)
- [FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributions](https://mlsanity.com/paper/2410.23405/) (2024)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [Physics Guided Deep Learning for Generative Design of Crystal Materials with Symmetry Constraints](https://mlsanity.com/paper/2203.14352/) (2022)
- [Open Materials Generation with Stochastic Interpolants](https://mlsanity.com/paper/2502.02582/) (2025)
- [Wyckoff Transformer: Generation of Symmetric Crystals](https://mlsanity.com/paper/2503.02407/) (2025)
- [PLaID++: A Preference Aligned Language Model for Targeted Inorganic Materials Design](https://mlsanity.com/paper/2509.07150/) (2025)
- [Invariant Tokenization of Crystalline Materials for Language Model Enabled Generation](https://mlsanity.com/paper/2503.00152/) (2025)
- [Materials Generation in the Era of Artificial Intelligence: A Comprehensive Survey](https://mlsanity.com/paper/2505.16379/) (2025)
- [Kinetic Langevin Diffusion for Crystalline Materials Generation](https://mlsanity.com/paper/2507.03602/) (2025)
- [Artificial Intelligence and Generative Models for Materials Discovery -- A Review](https://mlsanity.com/paper/2508.03278/) (2025)
- [AI-driven materials design: a mini-review](https://mlsanity.com/paper/2502.02905/) (2025)

## Built on by (most cited first, 6 of 6)

- [Mofasa: A Step Change in Metal-Organic Framework Generation](https://mlsanity.com/paper/2512.01756/) (2025)
- [Generative Models for Crystalline Materials](https://mlsanity.com/paper/2511.22652/) (2025)
- [Substitution-Based Analysis of Structural Novelty for Generative Models of Materials](https://mlsanity.com/paper/2606.23166/) (2026)
- [Representations from Pretrained Machine-Learning Interatomic Potentials as Coarse Coordinates for Material Generation and Evaluation](https://mlsanity.com/paper/2607.28776/) (2026)
- [Let CSP Be Your ANCHOR: Adaptive Crystal Search over Frozen Structure Priors](https://mlsanity.com/paper/2609.33407/) (2026)
- [Reinforcement Learning on the Discrete Composition Channel of a Crystal Generator: Validated Gains and Reward Hacking](https://mlsanity.com/paper/2610.03880/) (2026)

## Abstract (arXiv)

To address pressing scientific challenges such as climate change, increasingly sophisticated generative models are being developed to efficiently sample the large chemical space of potential functional materials. The proliferation of these models has necessitated the establishment of rigorous evaluation metrics. While uniqueness (U), novelty (N), and stability (S) of samples serve as standard metrics, their current formulations show several limitations. U and N rely on binary comparisons of crystals, rendering them dependent on heuristic thresholds, incapable of quantifying the degree of similarity, sensitive to atomic coordinate perturbations, and not invariant to sample permutation. Similarly, the binary assessment of S risks a premature exclusion of marginally unstable yet potentially novel candidates. These limitations are addressed by making the aforementioned metrics continuous. Furthermore, we integrate them into a unified metric ``continuous SUN" (cSUN), which offers a smoother score distribution and greater tunability than the conventional binary SUN metric. Experimental results demonstrate that our continuous metrics provide granular insights into sample distributions and facilitate the identification of the most promising candidates. Finally, the use of cSUN as a reward signal in reinforcement learning is explored, showing that its adjustable weighting scheme effectively mitigates reward hacking and avoids local minima.