GLASS: Global Latent Aggregation with Slot-based Set Decoding for Scalable All-Atom Crystal Generation

Generative models for crystals enable the discovery of novel structures, but scaling all-atom generation to larger systems such as metal--organic frameworks remains challenging. We connect this difficulty to the correspondence problem of particle-space generation. Even on a single fixed target set, index-free permutation-equivariant particle flows require substantially more training for reliable generation as set size and density increase, under both independent and optimal-transport couplings. To resolve this challenge, we introduce GLASS---Global Latent Aggregation with Slot-based Set Decoding, which encodes structures in a permutation-invariant global latent space and learns their distribution via flow matching. A learned-slot decoder constructs all atoms in parallel, removing atom-wise correspondence from generative transport. On MP20, GLASS is competitive with particle-space models, and flow training can reach the validity of the training data at every structure size. On a QMOF subset, GLASS generates MOFs with up to 150 atoms per unit cell without conditioning on building blocks, topology, or composition, and approaches the structural validity of the training data. On both datasets, flow training exposes a validity--novelty tradeoff, and MOF novelty remains limited by autoencoder generalization on the available data. These results show that separating correspondence assignment from generative transport provides a simple route toward high-validity generation of larger atomistic systems.