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Generating Symmetric Materials using Latent Flow Matching

NeurIPS 2026 · Image generation › Autoregressive and latent generation · approach: Equivariant diffusion for 3D molecules · 0 citations (OpenAlex)

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Proposes SymADiT, a symmetry-aware latent flow matching model for crystal generation that represents materials via Wyckoff-position asymmetric units with a simple Transformer autoencoder and DiT denoiser.

Problem

Symmetry-agnostic crystal generators produce structures almost entirely in P1 (pure translational symmetry), unlike real materials where most crystals have substantial symmetry, and they encode redundant structural detail.

Approach

Encode crystals as asymmetric units of symmetry orbits (Wyckoff positions, space group, free fractional coordinates and free lattice parameters), train a Transformer autoencoder with symmetry-enforcing decoding, and run flow matching in the latent space of ADiT, conditioned on space group via classifier-free guidance.

Key results

• On MP20, SymADiT reaches 96.50% structural validity, 0.07 JSD_G-free space group distribution gap (JSD_Wy 0.04), and 1.67% P1 versus >98% P1 for ADiT and CrystalDiT.
• SymADiT achieves 12 stable and 30 metastable out of 100 DFT-evaluated structures on MP20, the best among symmetry-aware methods (SGEquiDiff 6/17, SymmCD 8/14, DiffCSP++ 8/16).
• SymADiT uses about 4.74 tokens per sample on MP20 versus 10.30 for ADiT, with a 130M-parameter DiT.

Surprising findings

• Space group conditioning is needed for validity; without it, latent flow matching yields high novelty but low structural validity.
• Symmetry-aware SymADiT has lower uniqueness and novelty (87.42% U|N) than several symmetry-agnostic DiT baselines, lowering M/S.U.N. rates relative to them.

Limitations

• Only 100 DFT evaluations per model, adding unknown variance to M/S.U.N. rates.
• Lower uniqueness and novelty than several symmetry-agnostic DiT baselines.
• No guidance on synthesizability of generated materials; only crystals, not molecules, evaluated.

Experimental setup

Datasets: MP20 MPTS52

Benchmarks: MP20 MPTS52 MP20+MPTS52

Metrics: structural validity compositional validity uniqueness novelty S.U.N. rate M.S.U.N. rate P1 fraction JSD space group JSD Wyckoff Wasserstein distance atom count

Baselines: SGEquiDiff SymmCD DiffCSP++ ADiT CrystalDiT MatterGen FlowMM DiffCSP

Builds on: ADiT flow matching Diffusion Transformer self-conditioning classifier-free guidance

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)
• Wyckoff Transformer: Generation of Symmetric Crystals (ICML 2025 · similarity 0.91)
• Kinetic Langevin Diffusion for Crystalline Materials Generation (ICML 2025 · similarity 0.89)
• All-atom Diffusion Transformers: Unified generative modelling of molecules and materials (ICML 2025 · similarity 0.89)
• FlowMM: Generating Materials with Riemannian Flow Matching (ICML 2024 · similarity 0.88)