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Open Materials Generation with Stochastic Interpolants
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Adapts stochastic interpolants to crystal generation (OMatG), unifying flow matching and score-based diffusion over periodic fractional coordinates, lattice vectors, and discrete species, and benchmarks CSP and de novo generation against DiffCSP, FlowMM, and MatterGen.
Problem
Generative modeling of inorganic crystal structures for materials discovery: crystal structure prediction for fixed compositions and de novo generation of stable, novel, unique structures, under periodic boundary conditions.
Approach
Extends stochastic interpolants to flat-torus (periodic) fractional coordinates via shortest-geodesic unwrapping, combines SI flows over coordinates and lattice with discrete flow matching for species, and tunes interpolant choice separately for positions and lattice to span CFM and SBDM as special cases.
Key results
- On perov-5 CSP, VP SBD (ODE) reaches 83.06% match rate versus 53.08% for DiffCSP, about 1.6x.
- On MP-20 de novo generation, Trig (ODE) reaches 52.81% stability rate and Enc-Dec (ODE) 60.04%, versus 43.43% for DiffCSP; Linear (SDE) gives the best S.U.N. rate of 22.48% vs 20.30% for MatterGen-MP.
- OMatG establishes the first CSP baseline on Alex-MP-20, with Trig (SDE) at 72.50% match on MP-20-like evaluation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use VP SBD rather than the strongest baseline | OMatG CSP · perov-5 | Match (%): 83.06 / 81.27 vs 53.63 / 51.86 | Helped |
| Use linear ODE without γ rather than FlowMM | OMatG CSP · MP-20 | Match (%): 69.83 / 63.75 vs 66.22 / 59.98 | Helped |
| Use linear ODE without γ rather than FlowMM | OMatG CSP · MPTS-52 | Match (%): 27.38 / 25.15 vs 22.29 / 20.28 | Helped |
| Use trigonometric SDE with γ rather than FlowMM | OMatG CSP · Alex-MP-20 | Match (%): 72.50 / 64.71 | Helped |
| Use encoder-decoder ODE with γ rather than MatterGen-MP | OMatG DNG · MP-20 | Combined validity (%): 84.19 vs 83.89 | Helped |
| Use trigonometric ODE with γ rather than competing methods | OMatG DNG · MP-20 | wdist (ρ): 0.0607 | Helped |
| Use encoder-decoder ODE with γ rather than competing methods | OMatG DNG · MP-20 | Stability rate (%): 60.04 vs 44.79 | Helped |
| Use linear SDE with γ rather than MatterGen-MP | OMatG DNG · MP-20 | S.U.N. rate (%): 22.48 vs 20.30 | Helped |
| Use encoder-decoder ODE with γ rather than DiffCSP | OMatG DNG · MP-20 | Average energy above hull (eV/atom): 0.1482 vs 0.1751 | Helped |
| Replace the positional interpolant with linear SDE with γ (ablation) | OMatG DNG · MP-20 | Novelty rate (%): 73.31; 66.45; 55.21; 76.25 | Mixed |
| Replace the positional interpolant with encoder-decoder ODE with γ (ablation) | OMatG DNG · MP-20 | Combined validity (%): 84.19 vs 80.66 | Helped |
| Replace the positional interpolant with VP SBD and use SDE sampling (ablation) | OMatG DNG · MP-20 | Novelty rate (%): 76.25 vs 73.31 | Helped |
Surprising findings
- Match rate and RMSE trade off: interpolants with higher match rate often have higher RMSE, and the ODE linear interpolant without latent variable has the lowest RMSE but wrong local species.
- Relative performance of ODE vs SDE sampling depends on the positional interpolant rather than being uniformly better.
Limitations
- Symmetry-constrained generation methods are not compared against.
- Unit cell representation does not enforce invariance to the choice of periodic repeat unit, limiting symmetric structure generation.
- Hyperparameter optimization was done per interpolant, making the comparison design-space dependent.
Experimental setup
Datasets: perov-5 MP-20 MPTS-52 Alex-MP-20 Alexandria Materials Project
Benchmarks: perov-5 MP-20 MPTS-52 Alex-MP-20
Metrics: match rate RMSE structural validity composition validity coverage recall coverage precision wasserstein distance density wasserstein distance nary wasserstein distance coordination number stability rate
Baselines: DiffCSP FlowMM MatterGen-MP CDVAE
Builds on: stochastic interpolants FlowMM DiffCSP Riemannian flow matching discrete flow matching
Closest papers by meaning
- Scalable Diffusion for Materials Generation (ICLR 2024 · similarity 0.91)
- Periodic Materials Generation using Text-Guided Joint Diffusion Model (ICLR 2025 · similarity 0.90)
- SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models (ICLR 2025 · similarity 0.90)
- Vector Field Oriented Diffusion Model for Crystal Material Generation (AAAI 2024 · similarity 0.89)
- WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry (ICML 2025 · similarity 0.89)
- FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributions (NeurIPS 2024 · similarity 0.89)
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