Where Should Physics Enter a Molecular Crystal Generator?

Crystal generative models mainly learn what stable crystals look like, with little explicit supervision for what makes them stable. We reveal a substantial representation gap between state-of-the-art crystal generative models and pretrained universal machine learning interatomic potentials (MLIPs) via energy probing, and show this gap can be closed by a simple training-time alignment. We propose Crystal REPresentation Alignment (CrystalREPA), a plug-and-play framework that aligns the atom-wise hidden states of generative encoders with frozen MLIP representations through an element-aware contrastive objective, transferring stability-aware atomistic priors with marginal training overhead and no additional inference cost. Across three generative frameworks, ten MLIP teachers, and two benchmark datasets, CrystalREPA consistently improves the thermodynamic stability, structural validity, and structural fidelity of generated crystals. Equally important, we find that an MLIP's transfer effectiveness is poorly predicted by its accuracy on standard leaderboards (e.g., Matbench Discovery) but strongly predicted by the distinguishability of its atom-wise representation space, yielding a practical, accuracy-independent criterion for selecting MLIP teachers for generative transfer.

Crystal structure prediction (CSP) is fundamental to computational materials discovery. Generative models including CDVAE, DiffCSP, FlowMM, and CrystalFlow learn stable-crystal distributions directly, but diffusion and flow-matching inference requires tens to thousands of sequential network evaluations per candidate. We introduce uFlowCSP, a MeanFlow-based CSP model that learns the average, rather than instantaneous, probability-flow velocity. It generates a complete structure in one to five evaluations, delivering 5x-58x faster inference with equal or better performance. A chemistry- and symmetry-aware Transformer uses canonical atom ordering, global composition, and per-token chemistry embeddings. A coarse crystal-system token is used only during training; it provides additive gains, particularly improving space-group agreement despite being absent at inference, which remains formula-only. On MP-20 with 20 candidates per target, one step matches CrystalFlow (78.38% vs. 78.34%) with 100x fewer evaluations and about 10x lower wall-clock time. Five steps reach 83.64%, exceeding CrystalFlow (78.34% at 2,000 evaluations) and DiffCSP (77.93% at about 20,000), while using 20x fewer evaluations. uFlowCSP generates 10,000 structures in 0.39-1.31 minutes, versus 6.5 for CrystalFlow and 76.1 for DiffCSP. Under CSPBench's energy-ranked top-five structure-and-space-group criterion, five-step uFlowCSP reaches 72%/72%/65% structure, space-group, and consensus match rates. CrystalFlow reaches 78%/73%/68% at 100 steps but falls to 49%/32%/31% at five. Thus, uFlowCSP improves accuracy per network evaluation, not merely peak accuracy.

Crystal structure governs material properties, making crystal structure prediction (CSP) a fundamental problem in materials science. Generative models are a promising approach for solving this problem, but the prevalence of polymorphism, coupled with large unit cells and complex packing geometry, makes the molecular CSP task challenging for existing models. To address this, we introduce Coarse-Grained Open Materials Generation (CG-OMatG), an equivariant Riemannian flow-based generative model. CG-OMatG predicts molecular crystal structures \textit{via} a coarse-grained, hierarchical representation. CG-OMatG treats molecules as rigid bodies---performing both inter- and intra-molecular message passing to construct a geometric representation for molecular packings---and learns to reconstruct molecule centroid positions, orientations, and lattice parameters, conditioned on chemical species and conformer geometry. We train the model on subsets of the Open Molecular Crystals (OMC25) and Cambridge Structural Database (CSD) datasets. Further, we fine-tune the model \textit{via} policy gradient reinforcement learning to steer the model towards generating low-energy candidate structures. We validate the generated structures on the CSP blind test benchmark, assessing agreement with experimentally determined crystals using COMPACK packing-similarity analysis. CG-OMatG exhibits strong performance for generative molecular crystal structure prediction, paving the way for accelerated polymorph screening and organic solid-state materials discovery.