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Kinetic Langevin Diffusion for Crystalline Materials Generation
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Proposes KLDiff, a diffusion model for crystal generation that couples torus-valued fractional coordinates with auxiliary Euclidean velocities (generalized Torus Diffusion Model), and evaluates on crystal structure prediction and de novo generation.
Problem
Diffusion models for crystalline materials must respect periodic translation symmetry while modeling fractional atomic coordinates that lie on a hypertorus; existing approaches either use Riemannian diffusion on the torus or fractional-coordinate wrapped-normal noising, which creates a mismatch betw
Approach
Generalize the Torus Diffusion Model to symmetric crystal distributions by coupling fractional coordinates (as SO(2) rotations) with Euclidean velocity variables, so diffusion acts only in flat space; use zero initial velocities, a simplified score parameterization, and mean-free velocity fields to respect translation invariance.
Key results
- On MPTS-52 @20, KLDiff-epsilon (PC) reaches 39.81% match rate vs. 34.02% for DiffCSP (PC) and 34.05% for FlowMM.
- On MP-20 de novo generation, KLDiff-x0 with discrete diffusion reaches 59.21% stable and 0.283 RMSD, outperforming DiffCSP* (41.25% stable, 0.413 RMSD).
- KLDiff is competitive with MatterGen-MP on stability metrics but has slightly higher RMSD and lower S.U.N. (18.52 vs 25.76).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use KLDiff for crystal structure prediction instead of the compared baselines | KLDiff · MP-20 CSP @1 | MR (%): 61.39 -> 65.83 | Helped |
| Use KLDiff for crystal structure prediction instead of the compared baselines | KLDiff · MPTS-52 CSP @1 | RMSE: 0.1169 -> 0.1276 | Hurt |
| Use KLDiff for crystal structure prediction instead of the compared baselines | KLDiff · MPTS-52 CSP @20 | MR (%): 34.05 -> 39.81 | Helped |
| Use KLDiff for crystal structure prediction instead of the compared baselines | KLDiff · Perov-5 CSP @20 | RMSE: 0.0128 -> 0.0152 | Hurt |
| Use analog-bit or discrete atom-type diffusion rather than one-hot continuous diffusion (ablation) | KLDiff-x₀ · MP-20 DNG | Stable (%): 38.62 -> 49.84; 59.21 | Helped |
| Use discrete atom-type diffusion rather than one-hot continuous diffusion (ablation) | KLDiff-x₀ · MP-20 DNG | Average above hull (eV/atom): 0.269 -> 0.155 | Helped |
| Use discrete atom-type diffusion rather than one-hot continuous diffusion (ablation) | KLDiff-x₀ · MP-20 DNG | RMSD (Å): 0.371 -> 0.283 | Helped |
| Use analog-bit or discrete atom-type diffusion rather than one-hot continuous diffusion (ablation) | KLDiff-x₀ · MP-20 DNG | S.U.N. (%): 16.67 -> 17.91; 18.52 | Mixed |
| Use the PC sampler instead of EM on the larger CSP datasets (ablation) | KLDiff · MP-20 and MPTS-52 CSP | MR (%) | Helped |
| Use the PC sampler instead of EM on Perov-5 CSP (ablation) | KLDiff · Perov-5 CSP | sample quality | No clear effect |
| Use zero initial velocities instead of nonzero initial velocity variance (ablation) | KLDiff · CSP validation | MR | Helped |
| Use the simplified score parameterization instead of direct score parameterization (ablation) | KLDiff with zero initial velocities · CSP validation | MR | Helped |
Surprising findings
- KLDiff's zero initial velocity choice and simplified score parameterization improve convergence and final performance over the direct parameterization.
Limitations
- Results on de novo generation are validated only with machine-learning interatomic potentials, not DFT.
- Slightly higher RMSD and lower S.U.N. than MatterGen-MP on MP-20 de novo generation.
- Noise on velocities is limited to one alternative process; the mean-preservation mismatch is only mitigated empirically at moderate noise levels.
Experimental setup
Datasets: Perov-5 MP-20 MPTS-52 Carbon-24 Materials Project
Benchmarks: Perov-5 MP-20 MPTS-52 Carbon-24 MP-20 de novo generation
Metrics: match rate RMSE RMSD energy above hull stability S.U.N.
Baselines: CDVAE DiffCSP EquiCSP FlowMM MatterGen-MP
Builds on: Torus Diffusion Model DiffCSP Riemannian diffusion models MatterGen
Closest papers by meaning
- SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models (ICLR 2025 · similarity 0.92)
- WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry (ICML 2025 · similarity 0.91)
- Vector Field Oriented Diffusion Model for Crystal Material Generation (AAAI 2024 · similarity 0.91)
- Periodic Materials Generation using Text-Guided Joint Diffusion Model (ICLR 2025 · similarity 0.90)
- LLM Meets Diffusion: A Hybrid Framework for Crystal Material Generation (NeurIPS 2025 · similarity 0.90)
- Scalable Diffusion for Materials Generation (ICLR 2024 · similarity 0.90)
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