Research map / Probabilistic and scientific modeling / Molecules and proteins
FlowMM: Generating Materials with Riemannian Flow Matching
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes FlowMM, a pair of Riemannian flow matching models for crystal structure prediction and de novo generation of periodic materials, achieving competitive accuracy with ~3x fewer integration steps than diffusion baselines.
Problem
Generating periodic crystal structures (predicting structures for known compositions and jointly generating composition and structure) that are thermodynamically stable, while being efficient at inference and respecting crystal symmetries.
Approach
Generalizes Riemannian Flow Matching to crystal symmetries (permutation, translation with periodic boundaries, rotation) using flat-torus geodesics with mean-subtracted tangent targets, an informative lognormal/uniform base distribution on lattice parameters, unconstrained angle transform, binary atom-type encoding, and inference-time velocity anti-annealing.
Key results
- On CSP, FlowMM reaches 61.39% match rate on MP-20 vs 51.49% for DiffCSP and 17.54% vs 12.19% on MPTS-52, with maximum match rate reached in about 50 integration steps versus 1000 for DiffCSP.
- On DNG (MP-20), FlowMM at 250 steps has S.U.N. Cost 1.05 vs 2.99 for DiffCSP and Cost 0.58 vs 1.98 for stable structures, with comparable stability rate (4.32% vs 5.06%).
- FlowMM achieves lower Wasserstein distance on N_el (0.107 vs 0.125 DiffCSP) and density, matching the MP-20 arity distribution more closely.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FlowMM instead of DiffCSP | CSP · MP-20 | Match Rate (%): 51.49 -> 61.39 | Helped |
| Use FlowMM instead of DiffCSP | CSP · MPTS-52 | Match Rate (%): 12.19 -> 17.54 | Helped |
| Use FlowMM instead of DiffCSP | CSP · Perov-5 | RMSE: 0.0760 -> 0.0992 | Hurt |
| Use FlowMM instead of DiffCSP | CSP · Carbon-24 | RMSE: 0.2759 -> 0.4122 | Hurt |
| Use FlowMM instead of DiffCSP | DNG · MP-20 | Cost (Steps/Stable): 1.98 -> 0.58 | Helped |
| Use FlowMM instead of DiffCSP | DNG · MP-20 | S.U.N. Cost (Steps/S.U.N.): 2.99 -> 1.05 | Helped |
| Use FlowMM instead of DiffCSP | DNG · MP-20 | S.U.N. Rate: 3.34 -> 2.38 | Hurt |
| Add the proposed lattice base distribution and unconstrained angle transformation (ablation) | FlowMM CSP · MP-20 | Match Rate (%): 43.21 ± 0.47 -> 56.82 ± 0.42 | Helped |
| Add the proposed lattice base distribution and unconstrained angle transformation (ablation) | FlowMM CSP · MPTS-52 | Match Rate (%): 4.04 ± 0.21 -> 12.12 ± 0.36 | Helped |
| Add velocity anti-annealing to fractional coordinates (ablation) | FlowMM CSP · MP-20 | Match Rate (%): 56.82 ± 0.42 -> 61.26 ± 0.14 | Helped |
| Add velocity anti-annealing to lattice parameters (ablation) | FlowMM CSP · MP-20 | Match Rate (%): 56.82 ± 0.42 -> 59.23 ± 0.08 | Hurt |
Surprising findings
- On Carbon-24 CSP, FlowMM's RMSE (0.4122) is worse than DiffCSP (0.2759) despite higher match rate.
- Velocity anti-annealing applied to lattice parameters hurt performance, so it was applied only to fractional coordinates.
Limitations
- Stability is evaluated with a zero-temperature DFT proxy and convex hull with epistemic uncertainty; many generated structures are not verified as novel by domain experts.
- Structure novelty and uniqueness rely on StructureMatcher, which is not a strict equivalence relation.
- Does not model periodic cell choice or supercell invariances explicitly.
Experimental setup
Datasets: MP-20 MPTS-52 Perov-5 Carbon-24
Benchmarks: MP-20 MPTS-52 Perov-5 Carbon-24
Metrics: match rate RMSE structural validity composition validity coverage recall coverage precision wasserstein distance stability rate S.U.N. rate cost (integration steps)
Baselines: CDVAE DiffCSP
Builds on: Riemannian Flow Matching Flow Matching DiffCSP CDVAE Continuous Normalizing Flow
Closest papers by meaning
- FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributions (NeurIPS 2024 · similarity 0.93)
- WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry (ICML 2025 · similarity 0.89)
- SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models (ICLR 2025 · similarity 0.89)
- LLM Meets Diffusion: A Hybrid Framework for Crystal Material Generation (NeurIPS 2025 · similarity 0.88)
- Generating Symmetric Materials using Latent Flow Matching (NeurIPS 2026 · similarity 0.88)
- Open Materials Generation with Stochastic Interpolants (ICML 2025 · similarity 0.88)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.