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Equivariant Diffusion for Crystal Structure Prediction
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Proposes EquiCSP, an equivariant diffusion model for crystal structure prediction that enforces lattice permutation equivariance via loss penalties and a Periodic CoM-free Noising scheme for periodic translation invariance.
Problem
Crystal structure prediction requires generative models that respect crystal symmetries, but existing diffusion models (e.g., DiffCSP) do not guarantee lattice permutation equivariance or periodic translation equivariance of the diffusion process.
Approach
Adds permutation-equivariance penalty losses for lattice parameters and fractional coordinates, and a periodic center-of-mass-free noising (via a circular mean-angle map plus von Mises score approximation) so that the fractional-coordinate score is periodic-translation invariant, built on DiffCSP.
Key results
- On MP-20, EquiCSP reaches 57.59% match rate and 0.0510 RMSE vs. DiffCSP's 51.49% and 0.0631.
- On MPTS-52, EquiCSP reaches 14.85% match rate and 0.1169 RMSE vs. DiffCSP's 12.19% and 0.1786.
- Ablation on MP-20: removing the periodic CoM-free noising drops match rate from 57.59% to 52.31%; removing the permutation loss drops it to 55.42%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use EquiCSP instead of DiffCSP | Crystal structure prediction · Perov-5 | Match rate: 52.02 -> 52.02 | No clear effect |
| Use EquiCSP instead of DiffCSP | Crystal structure prediction · MP-20 | Match rate: 51.49 -> 57.59 | Helped |
| Use EquiCSP instead of DiffCSP | Crystal structure prediction · MPTS-52 | Match rate: 12.19 -> 14.85 | Helped |
| Add lattice permutation loss (ablation) | EquiCSP · MP-20 | Match rate: 55.42 -> 57.59 | Helped |
| Use permutation loss instead of Frame Average (ablation) | EquiCSP · MP-20 | Match rate: 55.92 -> 57.59 | Helped |
| Add periodic CoM-free noising (ablation) | EquiCSP · MP-20 | Match rate: 52.31 -> 57.59 | Helped |
| Add Von Mises and probabilistic modeling components (ablation) | EquiCSP · MP-20 | Match rate: 54.77 -> 57.59 | Helped |
| Add probabilistic modeling component (ablation) | EquiCSP with Von Mises · MP-20 | Match rate: 57.03 -> 57.59 | Helped |
| Add Von Mises component (ablation) | EquiCSP with probabilistic model · MP-20 | Match rate: 56.32 -> 57.59 | Helped |
Surprising findings
- Frame Averaging, an architectural hard-constraint for the same equivariance, performed worse (55.92%) than the proposed soft permutation loss while being much more computationally expensive.
Limitations
- Von Mises approximation of the marginal distribution of the CoM-free noise is a simplification, not an exact density.
- Permutation equivariance is enforced only softly via loss penalties, so exact invariance is not guaranteed.
Experimental setup
Datasets: Perov-5 MP-20 MPTS-52
Benchmarks: Perov-5 MP-20 MPTS-52
Metrics: match rate RMSE
Baselines: RS BO PSO P-cG-SchNet CDVAE DiffCSP Frame Average
Builds on: DiffCSP DDPM wrapped normal score matching frame averaging
Closest papers by meaning
- Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation (ICLR 2024 · similarity 0.91)
- Vector Field Oriented Diffusion Model for Crystal Material Generation (AAAI 2024 · similarity 0.90)
- WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry (ICML 2025 · similarity 0.90)
- Equivariant Neural Diffusion for Molecule Generation (NeurIPS 2024 · similarity 0.90)
- Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusion (NeurIPS 2025 · similarity 0.88)
- Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignment (ICML 2025 · similarity 0.88)
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