Crystal Structure Generation

De novo crystal generation, a central task in materials discovery, aims to generate crystals that are simultaneously valid, stable, unique, and novel. Existing methods mainly rely on black-box stochastic sampling, providing limited control over how generated structures move beyond the observed distribution. In this paper, we introduce a concept-based compositional framework for crystal generation. We train a vector-quantized variational autoencoder to automatically discover a shared set of reusable crystal concepts, which serve as building blocks for guided generation. These learned concepts naturally exhibit interpretability from both local atomic environments and global symmetry patterns, and generalize to crystals from different distributions. By recombining such concepts, our framework enables controllable exploration of novel crystals beyond the training distribution, rather than relying solely on unconstrained random sampling. To further improve composition efficiency, we introduce a composition generator and iteratively refine it using high-quality samples generated by the model itself. The resulting concept compositions are then used to condition downstream crystal generation. Numerical experiments on MP-20 and Alex-MP-20 show that compositing concepts separately increase base model up to 53.2% and 51.7% on V.S.U.N metric, with particular gains in novelty.

De novo crystal generation seeks to discover materials that are not merely realistic, but also stable and novel. However, most existing generative models are trained to maximize the likelihood of observed crystals, which encourages samples to stay close to known materials yet not necessarily align with the criteria that matter in discovery. Our empirical analysis shows that current crystal generative models exhibit a clear conflict between stability and novelty: samples near the observed distribution tend to retain stability but offer limited novelty, whereas samples farther from it often lose stability rapidly. This suggests that the useful region for discovering crystals that are both stable and novel is extremely narrow. To move beyond this limitation, we introduce Crys-JEPA, a joint embedding predictive architecture for crystals that learns an energy-aware latent space preserving formation-energy differences. In this space, stability assessment can be reformulated as an embedding-based comparison against accessible training crystals, reducing the reliance on expensive energy evaluation and task-specific external references. Building on Crys-JEPA, we further develop a screening-and-refinement pipeline that identifies promising generated crystals and reintroduces them to refine the generative model. On MP-20 and Alex-MP-20 datasets, we achieve improvements over baselines up to 53.8% and 72.7% on V.S.U.N. metric, respectively.

Generative modeling has emerged as a promising approach for crystal structure discovery. However, existing LLM-based generative models struggle with low-level atomic precision, while diffusion-based methods fall short in integrating high-level scientific knowledge. As a result, generated structures are often invalid, unstable, or do not possess desirable properties. To address this gap, we propose CrystalReasoner (CrysReas), an end-to-end LLM framework that generates crystal structures from natural language instructions through reasoning and alignment. CrysReas introduces physical priors as thinking tokens, which include crystallographic symmetry, local coordination environments and predicted physical properties before generating atomic coordinates. This bridges the gap between natural language and 3D structures. CrysReas then employs reinforcement learning (RL) with a multi-objective, dense reward function to align generation with physical validity, chemical consistency, and thermodynamic stability. For property-conditioned tasks, we design task-specific reward functions and train specialized models for discrete constraints (e.g., space group) and continuous properties (e.g., elasticity, thermal expansion). Empirical results demonstrate that compared to prior works and baselines without thinking traces or RL, CrysReas obtains better performance on diverse metrics, triples S.U.N. ratio, and achieves better performance for property conditioned generation. CrysReas also exhibits adaptive reasoning, increasing reasoning lengths as the number of atoms increases. Our work demonstrates the potential of leveraging thinking traces and RL for generating valid, stable, and property-conditioned crystal structures.

Tackling the task of materials generation, we aim to enhance the previously proposed All-atom Diffusion Transformer (ADiT) by introducing SymADiT, a symmetry-aware variant. To do so, we use a representation of materials based on Wyckoff positions. We follow ADiT and perform generative modelling in latent space, adapted to our symmetry-aware representation. By forcing the output of the generative model to adhere to the symmetry restrictions imposed by the generated crystal's space group and each atom's Wyckoff-position, the generated materials exhibit more realistic symmetry properties. We benchmark our method against both symmetry-aware and symmetry-agnostic models for materials generation and show competitive performance, generating stable, symmetric materials with a simple Transformer architecture.

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 generative models have shown rapid progress for accelerating the discovery of bulk, periodic materials. However, many material systems such as 2D superconductors, thin film semiconductors, and catalytic surfaces are diperiodic, i.e., aperiodic along one of the lattice directions. These systems are invariant under the layer groups, which are known to influence materials properties yet not considered by existing models. In this paper, we propose SLayerGen, a generative model that produces crystals constrained to be invariant to any space or layer group. SLayerGen consists of coarse-to-fine discrete autoregressive lattice generation; transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space or layer group equivariant diffusion of atomic coordinates. For the diffusion component, we corrected an inconsistency in the loss from prior work arising from hexagonal groups being non-orthogonal in fractional coordinates. To facilitate progress in generative modeling of diperiodic materials, we assembled and filtered datasets of monolayers and bilayers, propose relevant evaluation metrics, and developed novel representations for layer group symmetries. For de novo generation of diperiodic materials, SLayerGen achieves consistent performance gains over bulk crystal generative models and is competitive when training jointly on bulk and diperiodic materials.

While machine-learned interatomic potentials (MLIPs) accelerate phonon dispersion calculations, merely identifying dynamical instabilities in computationally predicted materials is insufficient; automated pathways to resolve them are required. We introduce VibroML, an open-source Python toolkit driven by foundational MLIPs that shifts the paradigm from stability verification to automated structural remediation. VibroML employs an energy-guided genetic algorithm that vastly outperforms traditional soft-mode following, efficiently navigating the potential energy surface to uncover diverse, dynamically stable polymorphs. As 0 K harmonic stability does not guarantee macroscopic viability, an automated molecular dynamics workflow evaluates finite-temperature structural retention. VibroML also couples with ProtoCSP, our combinatorial structure prediction engine, to stabilize frustrated crystal topologies via targeted alloying, successfully rescuing functional perovskite networks like Cs$_2$KInI$_6$ and KTaSe$_3$. Demonstrating broader applicability, we mined the Alexandria database -- where ~50% of quaternary and 99.5% of quinary elemental combinations lack any structural entries -- to identify thousands of abandoned, high-symmetry stoichiometries. Deploying ProtoCSP's "cold start" retrieval and VibroML's evolutionary search on a sample, we successfully identified dynamically stable low-symmetry candidates. Through integrated structural remediation, thermal validation, and systematic compositional exploration, VibroML enables a comprehensive deep-screening approach, yielding physically sound structural propositions that far surpass standard high-throughput workflows.

Predicting stable and metastable structures is central to molecular and materials discovery, but remains limited by the cost of searching high-dimensional energy landscapes. Deep generative models offer efficient structure sampling, yet their outputs remain shaped by training data and can underexplore minima that are rare but physically relevant. We introduce generative structure search (GSS), a unified framework that formulates diffusion-based generation and random structure search (RSS) as limiting regimes of a common sampling process driven by learned score fields and physical forces. Coupling these drivers lets GSS use data priors to accelerate sampling while retaining energy-guided exploration of local minima. Across molecular and crystalline systems, GSS recovers diverse metastable structures with more than tenfold lower sampling cost than RSS for broad coverage and remains effective for compositions outside the training distribution. The results establish a physically grounded generative search strategy for discovering structures beyond the reach of data-driven sampling alone.

Crystalline materials are widely used in technological applications, yet their discovery remains a significant challenge. As their properties are driven by structure, crystal structure prediction (CSP) methods play a central role in computational approaches aiming to accelerate this process. Previously, CSP has been approached from a combinatorial optimization perspective, with the core challenge of allocating atoms on a fine grid of predefined discrete positions within a unit cell while minimizing their interaction energy. Exact mathematical optimization methods provide guaranteed solutions, but they become computationally expensive for large-scale instances, where the atomic configuration space grows rapidly, particularly in the absence of additional symmetry constraints. In this work, we introduce a neural combinatorial optimization approach to the atom allocation challenge and, subsequently, CSP, based on graph neural networks (GNNs), which can effectively sample from the distribution of feasible structures in an unsupervised manner. We leverage expander graphs to construct computational graphs over discrete positions that capture both short- and long-range interactions between atoms, and employ the Gumbel-Sinkhorn approach to enforce the desired stoichiometry of the generated structures. We demonstrate that our method outperforms classical heuristic approaches and is competitive with a commercial optimization solver across a range of chemical compositions. This enables the use of ever-expanding GPU infrastructure to tackle the inherent combinatorial challenges of CSP, paving the way for scaling beyond current capabilities.

Discovering materials that must simultaneously satisfy multiple competing constraints remains a central challenge in computational materials design, particularly in data-scarce regimes where conventional data-driven approaches are least effective. Magnetic insulators represent a stringent example: the electronic conditions that favor magnetic order often also promote metallicity, while insulating behavior suppresses the interactions that stabilize magnetism. As a result, experimentally viable magnetic insulators are rare and difficult to identify through conventional screening. Here, we introduce MagMatLLM, a constraint-guided generative discovery framework that integrates language-model-based crystal generation with evolutionary selection, surrogate screening, and first-principles validation to target simultaneous stability, magnetism, and insulating behavior. Unlike stability-first approaches, the framework enforces functional constraints during generation and selection, steering the search toward sparsely populated regions of materials space defined by competing physical requirements. Using this workflow, we identify twelve previously unreported candidate magnetic insulators, including Tm$_4$Co$_2$Cr$_2$O$_{12}$ and Cr$_4$Nb$_2$O$_{12}$. Of these, ten are dynamically stable by phonon analysis and exhibit finite band gaps and nonzero magnetic moments in spin-polarized density functional theory calculations. Beyond the specific compounds identified here, this work establishes a general constraint-guided paradigm for multi-objective materials discovery in sparse chemical spaces and provides a transferable strategy for the design of quantum materials under competing physical constraints.

Generative diffusion models have emerged as powerful tools for the discovery of inorganic crystal structures, yet steering their sampling process toward user-defined physical and chemical objectives remains challenging. We present a computational framework that integrates adaptive constraint guidance into a pre-trained crystal diffusion model, enabling the generation of candidate structures that satisfy targeted structural and chemical requirements without model retraining. The approach incorporates differentiable constraint functions directly during sampling, providing an interpretable mechanism for expert-driven exploration of the crystal structure space. To assess the reliability of generated candidates, we introduce a multi-stage validation workflow combining descriptor-based analysis, duplicate removal, comparison with reference crystal databases, graph neural network energy prediction, and thermodynamic stability evaluation through convex-hull analysis. The framework is applied to several classes of inorganic compounds and to constraints involving atomic volume, local coordination environments, and near-neighbor structural motifs. Results demonstrate that adaptive guidance effectively redirects the sampling distribution toward structures exhibiting the desired characteristics while preserving chemical plausibility. Subsequent validation reveals which generated candidates remain viable after energetic and thermodynamic screening. The proposed methodology provides a practical and transparent strategy for incorporating expert knowledge into crystal generative models and establishes a general computational framework for constrained materials discovery.

Generative models for crystalline materials often rely on equivariant graph neural networks, which capture geometric structure well but are costly to train and slow to sample. We present Crystalite, a lightweight diffusion Transformer for crystal modeling built around two simple inductive biases. The first is Subatomic Tokenization, a compact chemically structured atom representation that replaces high-dimensional one-hot encodings and is better suited to continuous diffusion. The second is the Geometry Enhancement Module (GEM), which injects periodic minimum-image pair geometry directly into attention through additive geometric biases. Together, these components preserve the simplicity and efficiency of a standard Transformer while making it better matched to the structure of crystalline materials. Crystalite achieves state-of-the-art results on crystal structure prediction benchmarks, and de novo generation performance, attaining the best S.U.N. discovery score among the evaluated baselines while sampling substantially faster than geometry-heavy alternatives.

Crystal structure prediction (CSP), which aims to predict the 3D atomic arrangement of a crystal from its composition, is central to materials discovery and mechanistic understanding. Crystal symmetry plays a crucial role in CSP, but given the composition in a unit cell, existing methods either struggle with the NP-hard combinatorial challenge of enforcing symmetry rigorously or rely on retrieving known templates, inherently limiting both physical fidelity and the discovery of genuinely new materials. To address this challenge, we introduce NextCrystal, a symmetry-driven generative framework that employs large language models to encode chemical semantics and directly generate fine-grained Wyckoff site patterns from atomic stoichiometry, eliminating reliance on database lookups. To overcome the combinatorial complexity of site assignments, we incorporate domain knowledge via an efficient, linear-complexity heuristic beam search, rigorously enforcing algebraic consistency between site multiplicities and atomic stoichiometry. By integrating this symmetry-consistent template into a diffusion backbone, the framework constrains the stochastic generative trajectory to a physically plausible geometric manifold. NextCrystal achieves state-of-the-art performance on stability, uniqueness, and novelty (SUN) benchmarks, as well as superior structural matching, establishing a rigorous paradigm for exploring previously unexplored crystallographic space without relying on prior structural templates. As a representative application, first-principles screening of HfO2 candidates generated by NextCrystal identifies a previously unreported dynamically stable Pnma phase, 0.056~eV/atom lower in energy than the conventional high-pressure Pnma phase.