# Open Materials Generation with Stochastic Interpolants

arXiv: https://arxiv.org/abs/2502.02582 · HTML: https://mlsanity.com/paper/2502.02582/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 28 of its 72 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [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)
- [Stochastic interpolants with data-dependent couplings](https://mlsanity.com/paper/2310.03725/) (2023)
- [Fine-Tuned Language Models Generate Stable Inorganic Materials as Text](https://mlsanity.com/paper/2402.04379/) (2024)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributions](https://mlsanity.com/paper/2410.23405/) (2024)
- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (2024)
- [Crystal-GFN: sampling crystals with desirable properties and constraints](https://mlsanity.com/paper/2310.04925/) (2023)
- [Large-scale machine-learning-assisted exploration of the whole materials space](https://mlsanity.com/paper/2210.00579/) (2022)
- [Optimizing Noise Schedules of Generative Models in High Dimensionss](https://mlsanity.com/paper/2501.00988/) (2025)

## Built on by (most cited first, 28 of 28)

- [FlowMol3: Flow Matching for 3D De Novo Small-Molecule Generation](https://mlsanity.com/paper/2508.12629/) (2025)
- [Space Group Equivariant Crystal Diffusion](https://mlsanity.com/paper/2505.10994/) (2025)
- [All that structure matches does not glitter](https://mlsanity.com/paper/2509.12178/) (2025)
- [Open Materials Generation with Inference-Time Reinforcement Learning](https://mlsanity.com/paper/2602.00424/) (2026)
- [MADE: Benchmark Environments for Closed-Loop Materials Discovery](https://mlsanity.com/paper/2601.20996/) (2026)
- [Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modeling](https://mlsanity.com/paper/2602.20210/) (2026)
- [Continuous SUN (Stable, Unique, and Novel) Metric for Generative Modeling of Inorganic Crystals](https://mlsanity.com/paper/2510.12405/) (2025)
- [Guided Diffusion for the Discovery of New Superconductors](https://mlsanity.com/paper/2509.25186/) (2025)
- [MolCrystalFlow: Molecular Crystal Structure Prediction via Flow Matching](https://mlsanity.com/paper/2602.16020/) (2026)
- [Zatom-1: Towards a Multimodal Foundation Model for 3D Molecules and Materials](https://mlsanity.com/paper/2602.22251/) (2026)
- [Fast Organic Crystal Structure Prediction with Unit Cell Flow Matching](https://mlsanity.com/paper/2606.03199/) (2026)
- [Introducing physics-informed generative models for targeting structural novelty in the exploration of chemical space](https://mlsanity.com/paper/2510.23181/) (2025)
- [SLayerGen: a Crystal Generative Model for all Space and Layer Groups](https://mlsanity.com/paper/2605.08262/) (2026)
- [Three Forms of Stochastic Injection for Improved Distribution-to-Distribution Generative Modeling](https://mlsanity.com/paper/2510.06634/) (2025)
- [Discovering Crystal Structure Prediction Algorithms with an AI Co-Scientist](https://mlsanity.com/paper/2606.22866/) (2026)
- [CrystalGRPO: Target-Aligned and Coverage-Preserving Reinforcement Learning for Flow-Based Crystal Structure Prediction](https://mlsanity.com/paper/2608.06582/) (2026)
- [OMatG-flash: An All-Atom Flow Map with Reinforce Adjoint Matching for Scalable Materials Discovery](https://mlsanity.com/paper/2609.26402/) (2026)
- [Stochastic Interpolants in Hilbert Spaces](https://mlsanity.com/paper/2602.01988/) (2026)
- [Atomistic Language Models Understand and Generate Materials](https://mlsanity.com/paper/2606.21395/) (2026)
- [SVGym (SciVerseGym): An Environment for Reinforcement Learning and Bayesian Optimization in Crystal Discovery](https://mlsanity.com/paper/2606.22425/) (2026)
- [Packora: Systematic Design for Generative Molecular Crystal Structure Prediction](https://mlsanity.com/paper/2608.26962/) (2026)
- [El Agente Potente: High-Throughput Agentic Atomistic Simulations](https://mlsanity.com/paper/2609.14840/) (2026)
- [Deep Generative Crystal Structure Prediction: A Benchmark Study and a Controlled Test of Prototype Dependence](https://mlsanity.com/paper/2609.26502/) (2026)
- [Let CSP Be Your ANCHOR: Adaptive Crystal Search over Frozen Structure Priors](https://mlsanity.com/paper/2609.33407/) (2026)
- [GLASS: Global Latent Aggregation with Slot-based Set Decoding for Scalable All-Atom Crystal Generation](https://mlsanity.com/paper/2609.37158/) (2026)
- [Riemannian Flow Models with Reinforcement Learning for Molecular Crystal Structure Prediction](https://mlsanity.com/paper/2609.39773/) (2026)
- [EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations](https://mlsanity.com/paper/2610.01315/) (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)

The discovery of new materials is essential for enabling technological advancements. Computational approaches for predicting novel materials must effectively learn the manifold of stable crystal structures within an infinite design space. We introduce Open Materials Generation (OMatG), a unifying framework for the generative design and discovery of inorganic crystalline materials. OMatG employs stochastic interpolants (SI) to bridge an arbitrary base distribution to the target distribution of inorganic crystals via a broad class of tunable stochastic processes, encompassing both diffusion models and flow matching as special cases. In this work, we adapt the SI framework by integrating an equivariant graph representation of crystal structures and extending it to account for periodic boundary conditions in unit cell representations. Additionally, we couple the SI flow over spatial coordinates and lattice vectors with discrete flow matching for atomic species. We benchmark OMatG's performance on two tasks: Crystal Structure Prediction (CSP) for specified compositions, and 'de novo' generation (DNG) aimed at discovering stable, novel, and unique structures. In our ground-up implementation of OMatG, we refine and extend both CSP and DNG metrics compared to previous works. OMatG establishes a new state of the art in generative modeling for materials discovery, outperforming purely flow-based and diffusion-based implementations. These results underscore the importance of designing flexible deep learning frameworks to accelerate progress in materials science. The OMatG code is available at https://github.com/FERMat-ML/OMatG.