Molecular Generation

Accurate generation of crystal structures is the foundation to the discovery of high-performance materials for extreme-environment applications, such as aerospace, additive manufacturing, and fusion energy systems. Although generative modeling has emerged as a promising approach for crystal design, its performance remains limited by the complex crystal structures and diverse chemical compositions. In this work, we develop UFO-MGen, a universal flow-based generative model that learns topological features of Wyckoff representations and leverages this information to accurately generate crystals across vast structural and chemical spaces. Compared with state-of-the-art generative models, UFO-MGen achieves the highest crystal generation success rate under a rigorous multi-stability evaluation framework, the highest SUN (stable, unique, novel) rate, and a remarkable extrapolation capability that has not been reported by previous models. Furthermore, a fine-tuning module is implemented to UFO-MGen for property-constrained crystal generation, enabling the inverse materials design toward target properties. The UFO-MGen opens a new avenue for accelerated materials discovery and providing a foundation for universal materials intelligence.

Deep generative models are widely reported to enable de novo crystal structure prediction (CSP), but their capability has not been measured consistently against template-based methods. We evaluate 12 representative generative CSP models, spanning latent-variable, diffusion, flow-matching, autoregressive, and manifold random-walk architectures, against TCSP 2.0 on 180 test structures and a leakage-controlled subset of 46. All methods use identical structure-matching, symmetry, and consensus criteria. Template retrieval is the strongest single method, reaching 68.3% top-1 success; symmetry-aware EquiCSP (66.4%) and Uni-3DAR (62.9%) form the next tier. However, comparison with TCSP 2.0 shows that most structures correctly predicted by generative models are also correctly predicted by template substitution. Thus, the set of structures uniquely reachable by generation is small, limiting its practical advantage for discovering structures outside existing prototype libraries. To test the source of this performance, we removed entire stoichiometric prototype families from the training set and retrained the strongest generative model. Accuracy declined by 50-78% across four families, establishing that performance is substantially prototype-dependent. A small minority of structures survived removal of their prototype family, demonstrating a real but limited retrieval-independent predictive capacity. Present generative CSP models therefore function largely as implicit, softer-edged prototype libraries rather than genuinely de novo predictors. Enlarging this residual capacity, rather than aggregate match rate alone, is the central open problem.

Molecular design is typically approached as a problem of finding molecules which can adopt a single bioactive conformation. In reality, molecules occupy a distribution over conformations, and many of the properties which determine whether a candidate is viable depend on that distribution rather than on any single conformer. We reframe molecular design as an optimisation of both the modes and properties of molecules' conformational ensembles, where modes can be represented as shapes, pharmacophore profiles or protein pockets, and properties are aggregate scalars computed over the whole distribution. To realise this we introduce ensemble-conditioned guidance, a framework which conditions 3D molecular generative models on both axes simultaneously. Mode conditions are composed adaptively at inference by combining the vector fields produced under each condition. Conditions may be targeted or avoided, mixed across modalities and combined in arbitrary numbers, allowing a wide range of design tasks to be expressed with a single trained model. We introduce adaptive symmetry learning to allow conditions from different reference frames to be composed, and extend our generative framework to enable flexible-size generation. We evaluate on new benchmarks for multi-mode conditioning and ensemble property optimisation, and apply the framework to two practical drug discovery tasks, dual-target binder design and active-state-selective agonist design, where in both cases conditioning on the additional state improves the desired outcome over single-state conditioning.

Molecule generation has emerged as a powerful computational tool for de novo drug design, enabling the exploration of chemical space beyond the limits of conventional virtual screening. The field has progressed rapidly, driven by advances in molecular representations, generative architectures, and target-aware modeling strategies. However, existing reviews typically address specific model families or application scenarios in isolation, rather than offering an integrated perspective on how these components collectively form a coherent generation workflow. In this review, we present a comprehensive evaluation of molecule generation models for de novo drug design, covering 82 methods across five deep generative frameworks, including recurrent neural network (RNN)- and Transformer-based models, variational autoencoders (VAEs), generative adversarial networks (GANs), flow-based models, and diffusion models. We first summarize widely used benchmarks and molecular representations, and then examine the methodological principles underlying both general and pocket-conditioned generation. A central contribution of this work is a systematic synthesis and comparative analysis of reported performance across commonly used benchmarks and evaluation metrics. We also summarize representative experimentally validated case studies. Looking ahead, we discuss future directions in standardized 3D data, interaction-aware generation, receptor flexibility, and multi-objective molecular design, with the aim of improving the reliability and experimental relevance of molecule generation. All collected benchmark resources, evaluation metrics, and model references are provided in a publicly accessible repository at https://github.com/JacklinGroup/molecule-generation-review.

Molecular size is coupled to composition, structure, and function, yet most 3D molecular generators require a predefined atom count. We introduce Equivariant-Free Transformer-Autoencoded Latent Flow Matching, a two-stage framework that samples a fixed-dimensional latent vector using flow matching and uses an autoregressive Transformer to determine molecular size, atom types, coordinates, and chemical attributes. Canonical atom ordering and rigid-pose alignment enable Transformers without equivariant layers, while decoded attributes guide bond reconstruction. On PCQM4Mv2, unconditional generation yields 87.9% unique, novel molecules passing sanitization and PoseBusters checks, exceeding baselines with lower end-to-end training and sampling time and higher end-to-end throughput. Across ten target HOMO-LUMO gaps, internal ranking retains 30% of screened candidates and increases the density functional theory-verified hit rate within 0.1 eV from 25.0% to 52.4%, while largely preserving novelty and diversity. These results demonstrate fixed-dimensional latent generation with autoregressive decoding as a practical approach to molecular design without prespecifying size.

Protein-conditioned 3D molecule generation is a central challenge in structure-based drug design, requiring a balance between pocket compatibility, molecular properties, and physical geometry. We propose \textbf{PocketVE}, a protein-pocket-conditioned variance-exploding (VE) diffusion framework that couples stable coordinate denoising with inference-time property guidance. Specifically, PocketVE combines an EDM-style training and sampling setup for 3D denoising, classifier-free guidance for multi-property steering without external property classifiers, and adaptive protein perturbation as a training-time pocket regularizer. Evaluated on CrossDocked2020 under the GenBench3D protocol, PocketVE improves Valid$_{3\text{D}}$ from 58.6 to 80.6 and reduces strain energy from 457.4 to 127.9 relative to its TAGMol architectural baseline, while retaining competitive docking and molecular-property scores under moderate guidance. A guidance-scale study shows that moderate guidance gives a favorable balance between target-related objectives and geometric quality, whereas stronger guidance can degrade geometry and distributional fidelity. Pocket-permutation and PoseCheck diagnostics further support pocket-specific spatial compatibility with reduced steric conflicts. Overall, the results suggest that geometric stability and inference-time property guidance should be considered as coupled design objectives.

Crystal generators can now propose periodic structures, but their control interfaces remain poorly matched to the mixed descriptors used in materials design. Text provides a compact way to combine composition, symmetry, prototype and property cues, yet it has not been clear whether such information can steer flow-based crystal generation. Here we introduce TFMat, a text-conditioned flow-matching framework that uses structured materials language as a semantic prior for a CrystalFlow generator. Across Perov-5, Carbon-24 and MP-20 crystal structure prediction benchmarks, TFMat improves one-candidate match rates over CrystalFlow and reaches a 92.04% MP-20 match rate with 20 candidates; in de novo generation, it improves element-count and density distribution alignment while retaining coarse property consistency in composition-selected outputs. These results position structured text as an inspectable control layer for translating human-readable materials intent into candidate crystals for downstream simulation and validation.

Test-set accuracy is silent on two issues that matter when deploying autoregressive neural sequence models: how much probability mass the system under test (SUT) places on constraint-violating alternatives that are reachable under sampling and what fraction of the input population satisfies a domain requirement. We answer both with probabilistic model checking. The pipeline extracts a discrete-time Markov chain (DTMC) from the SUT's token-by-token generation, verifies formal PCTL specifications with the PRISM model checker, and aggregates the per-input verdicts into a coverage curve over the input space. A soundness theorem establishes the DTMC as an under-approximation, so every verdict yields a certified interval on the SUT's true reachability probability. The coverage built from those verdicts is, therefore, conservative by construction. A counterexample-guided abstraction refinement (CEGAR) loop adaptively tightens the interval, and a maximum-likelihood algorithm extracts the most probable falsifying trace. Two case studies exercise the pipeline. On a GPT-2 computer-aided process-planning (CAPP) model with 100% test accuracy, the pipeline quantifies the probability mass greedy decoding hides, but that is reachable with sampling; and identifies the smallest training fraction at which an ordering requirement holds population-wide, neither of which test accuracy can report. We then verify the SMILES molecular generator with a 50x larger vocabulary. The only change is an external chemical-validity oracle, and the pipeline identifies the gap between structural completeness and chemical validity.

Structure-based drug design (SBDD) requires ligands that satisfy both 3D target affinity and 1D chemical validity. Existing controllable generation methods often rely on task-specific fine-tuning or externally imposed sampling-time guidance, adding cost and potentially conflicting with evolving 3D geometric constraints. We propose LiFT, a language-informed cross-modal framework built on Flow Matching for trend-guided 3D molecular generation across both de novo design and scaffold hopping. LiFT uses a "Sense-Evolve-Assemble" agent to generate target-aware SMILES as intermediate chemical conditions, from which a pre-trained chemical foundation model extracts continuous semantic priors. These priors are integrated into geometric generation through a lightweight semantic projector with zero-initialized adaptive normalization for stable cross-modal conditioning. We further introduce a Self-Conditioned Decoupled Router (SCDR), which modulates the velocity field according to intermediate structural states during ODE integration. Experiments on Cross-Docked2020 show that LiFT achieves competitive distribution matching while improving medicinal chemistry metrics and maintaining competitive structural validity under task-steering settings without additional generator fine-tuning. Our results suggest that language-derived chemical priors provide effective trend-level guidance for 3D molecular generation. Code and released artifacts are available at https://github.com/kasurl/LiFT.

Generating crystals has recently attracted significant interest due to their broad applications in materials science. However, existing generative models struggle to produce complete crystallographic specifications, limiting their ability to capture global symmetry and structural dependencies. In particular, current state-of-the-art approaches generate crystals only up to site symmetries and rely on sampling space groups from empirical distributions during generation. Inspired by \emph{spontaneous symmetry breaking} in physics, where crystals break symmetries under external conditions, we propose a novel diffusion-based framework that generates full structure specifications by reversing from the lowest-symmetry priors. Our method leverages a Markovian jump-diffusion process to model these symmetry-breaking dynamics, enabling it to traverse different space groups in a physically motivated manner. Our model, dubbed \emph{Symmetry-breaking Crystal Diffusion} (SbCD), introduces a principled approach to explicitly incorporate inter-space-group transitions into the generative process. In de novo generation experiments on MP20 and MPTS-52, SbCD outperforms its symmetry-preserving counterpart by a substantial margin, offering a promising perspective for generative modeling of crystalline materials.

We consider the setting of Normalizing flows with approximate inverses, an established paradigm spanning both full-dimensional ($d=D$) and bottleneck ($d<D$) settings, and group these models under the term flow autoencoders. We present a theoretical investigation into their training dynamics and prove that the proposed loss used by existing approaches is suboptimal; specifically, both encoder and decoder surrogates must be optimized in alignment with reconstruction loss. Guided by these insights, we propose Normalizing Autoencoder (NAE), which employs a novel conditional loss that aligns the surrogate loss gradient with that of reconstruction loss, directly improving upon the current standard. Extensive experiments across molecule generation, tabular data, and image benchmarks demonstrate that NAE achieves state of the art performance. Our work highlights the importance of loss alignment in flow autoencoders and establishes NAE as a powerful generative framework.

The search for new crystalline materials spans an enormous compositional and structural space. Generating candidates in this space requires jointly modeling discrete crystallographic symmetry, elemental composition, and continuous geometry. We introduce DynaCrys, a generative model for crystals in which the space group co-evolves with Wyckoff occupations and elements through a coupled symbolic diffusion process. The structured space-group transitions follow crystallographic group-subgroup relations. As the space group changes, a shared, pretrained symmetry codebook provides both the legality-constrained stochastic decoder and the symmetry-constrained crystal-geometry model with a common representation of the corresponding Wyckoff vocabulary. Across large-scale evaluations using two independent relaxation-and-evaluation engines, DynaCrys achieves best-in-class performance in symmetry-aware discovery of stable, unique, and novel crystals, both overall and under the additional requirement of nontrivial post-relaxation symmetry. It also enables fast sampling while generating structures with consistently low relaxation-induced structural displacements.

Generative models for matter are often evaluated as samplers over output representations, and their latent spaces are commonly used as proxies for navigating chemical space. Much less is known about how these models internally arrange discrete chemical identities within those representations. We study this arrangement by making molecular identity explicit and pulling it back through the generative process. Through these pullbacks we probe the regions that generate the same object, exposing the trained model's internal repertoire: a fixed partition that determines which objects (novel or not) the model can produce. Across three molecular generative architectures, we find that this repertoire is arranged into piecewise-constant regions separated by recurring coarse-to-fine boundaries. Its organization depends on the representation probed, the identity convention, decoder stochasticity, and the metric used to compare coordinates. During training, local chemical organization stabilizes while the number of distinct molecular identities represented within each neighborhood continues to change. Internal organization must therefore be characterized, rather than assumed, before a generative space can be treated as chemically navigable.

Text-to-molecule generation is typically formulated as a one-shot sequence generation problem, where a model directly maps target descriptions to molecular representations. However, molecular descriptions often contain informative structural constraints, and violating such constraints can change the molecular identity. This makes chemical verification and error correction important but underexplored. To fill this gap, we propose MolGVR, a chemistry-grounded Generator--Verifier--Refiner framework. The Generator infers structural evidence and generates candidate molecules. The Verifier addresses the lack of chemical validation by converting descriptions into chemical constraints and checking candidates against them. The Refiner addresses generation failures by revising candidates rejected by the Verifier. Experiments on ChEBI-20 and PCDes show that MolGVR improves exact-match performance. These results suggest that coupling generation with executable verification and feedback-guided refinement is an effective way to improve text-to-molecule generation.

Quantum state preparation is a key component of many quantum algorithms. Performing this step efficiently is essential for realizing practical quantum advantage in quantum chemistry applications. Iterative algorithms like ADAPT-VQE can produce shallow ground-state preparation circuits, but become computationally prohibitive for the larger molecules relevant to materials science and pharmaceutical development. Here, we introduce ADAPT-GQE, a generative AI framework that learns to synthesize ground-state preparation circuits for electronic structure calculations. We first use ADAPT-VQE to generate high-quality reference circuits, which are then used as targets for training models for circuit generation. Once trained, the model can efficiently propose and score circuits, enabling reinforcement learning (RL) to drive circuit generation accuracy beyond the accuracy of the ADAPT-VQE training data. This pipeline achieves order-of-magnitude reductions in circuit generation time relative to ADAPT-VQE while maintaining comparable or improved state-preparation accuracy. We demonstrate ADAPT-GQE on imipramine, a well-established tricyclic antidepressant that serves as a representative, challenging target for computational modelling in drug stability protocols. We execute generated circuits on Quantinuum Helios-1, representing a milestone for AI-generated quantum chemistry circuits on state-of-the-art quantum hardware. These results establish a pathway toward automated quantum circuit synthesis for utility-scale quantum computational chemistry.

Molecular glue degraders have emerged as a promising strategy for targeted protein degradation by inducing ternary complex formation between an E3 ubiquitin ligase and a target protein. Despite their therapeutic potential, computational design of molecular glues remains largely unexplored. Unlike conventional structure-based drug design, molecular glue design is governed by the unknown protein-protein interface and requires the simultaneous modeling of ligand generation, protein-protein docking, and ternary complex assembly. In this work, we formulate molecular glue design as a ternary complex generation problem and propose a biology-inspired generative framework, TriGlue. Motivated by the mechanism of molecular glue action, we decompose ternary complex generation into two coupled stages: interface estimation and interface-conditioned complex generation. First, we develop an SE(3)-equivariant interface estimation module that predicts a geometrically constrained protein-protein interface from unbound monomer structures. Second, we introduce an interface-conditioned ternary flow matching network that jointly generates the molecular glue and predicts the rigid-body transformation required to assemble the ternary complex. Extensive experiments demonstrate that TriGlue generates chemically valid molecules and produces plausible ternary complexes, which highlight the potential of biology-inspired generative modeling for accelerating molecular glue discovery. Our code is available at https://github.com/yuliangyan0807/molecular-glue-design.

Integrating heterogeneous biomedical data, including clinical metadata, histopathology images, and molecular profiles, is crucial for comprehensive disease understanding. However, gene expression data acquisition remains constrained by high costs and privacy concerns, limiting its use in multimodal research and AI-driven applications. We present MultiModal Molecular Generation (M$^3$-Gen), a novel framework for the generation of gene expression profiles by conditioning a Generative Adversarial Network on histopathology images and clinical metadata. M$^3$-Gen learns a unified latent representation from the clinical variables and the images, leveraging contrastive learning, and exploits the embeddings of the two modalities to guide a generative model in producing biologically coherent gene expression profiles. Evaluations on the TCGA dataset demonstrate that M$^3$-Gen generates realistic and functionally meaningful gene expression data. Importantly, by integrating multiple modalities in an attention-based mechanism, M$^3$-Gen provides intrinsic explainability: it allows the identification of which regions of the histopathology images most strongly influenced the generation of specific gene expression profiles, making the model's decisions interpretable by design.

The development of organic light-emitting diode (OLED) materials faces the compounded challenges of an astronomically large chemical space, stringent quantum-chemical constraints, and a scarcity of labeled data. Although the question of OLED generation is important, few models have been trained effectively for this specific domain. We propose an inverse molecular design framework based on causal language models: given target optoelectronic properties (e.g., excitation energy, oscillator strength), our model directly generates OLED SMILES sequences satisfying the specified constraints. We employ a multi-stage strategy: first, we establish a foundational chemical language model using a LLaMA-style transformer architecture. To the best of our knowledge, this represents the first successful adaptation of LLMs specifically for the OLED domain, bridging the gap between generic molecular generation and the stringent structural requirements of optoelectronic materials. Second, we fine-tune property predictors based on a BERT model pre-trained on our large-scale OLED dataset. Then, we perform Reinforcement Learning on our fine-tuned model, leveraging our property predictor, for better SMILES generation. Finally, through DFT verification, we demonstrate that our framework can efficiently navigate the OLED chemical space, generating novel candidates with high structural validity and optimized optoelectronic properties.

Determining molecular structures from spectroscopic data remains fundamentally challenging because the inverse problem is intrinsically underdetermined: individual spectra are sparse, low-dimensional, and encode only partial structural evidence relative to the vast space of possible molecules. We address this challenge by formulating automated structure elucidation as a scalable hypothesis-refinement paradigm that tightly integrates spectral evidence with large-scale molecular priors. To supply structure-resolving NMR signals for multimodal learning, we construct \textbf{QM9SPIN}, a DFT-derived dataset comprising diverse 1D and 2D spectra, including J-coupling, DEPT experiments, and explicit spin--spin interactions. On this foundation, we introduce \textbf{SpectroMol}, a spectrum-to-structure model that proposes chemically valid molecular hypotheses conditioned on multimodal spectral inputs. Complementarily, we develop \textbf{MS-Mol2Mol}, a high-resolution mass-constrained molecular generator that integrates molecular formula, exact mass, and degree of unsaturation within a conditional generative prior trained on 400 million molecules, ensuring global compositional consistency and chemically realistic refinement. The integrated system achieves 93.8% top-1 accuracy on the simulated benchmark, adapts effectively from simulated to experimental spectra with limited experimental fine-tuning, and further improves experimental predictions through mass-guided refinement, establishing a scalable route toward automated, data-driven organic structure elucidation.

Most 3D properties relevant to molecular design, including free energies and shape descriptors, are $\textit{expectations}$ over the Boltzmann distribution over 3D configurations of a molecular graph. However, existing property-guided generative models tie each property to a single structure, ignoring the underlying ensemble. We recast 3D molecular design as $\textbf{Boltzmann-expected design}$ and realise it with $\textbf{DECAF}$ (Decoupled Annealing Flows), which factorise the joint distribution over graphs and coordinates into two conditional flow models: a graph-conditioned flow $p(x\mid\mathcal{G})$, acting as a $\textit{Boltzmann emulator}$, and a coordinate-conditioned flow $p(\mathcal{G}\mid x)$, proposing new graphs from 3D information. By alternating the two flows, DECAF optimises molecular graphs with a simulated-annealing acceptance rule whose scoring function is evaluated on ensembles drawn from $p(x\mid\mathcal{G})$, making ensemble statistics, not single-conformer properties, the design target. The resulting loop requires no retraining to change objectives. On GEOM-Drugs, we show that ensemble-aware optimisation produces graphs whose mean radius of gyration and solvent-accessible surface area consistently shift toward targets, while single-conformer optimisation degrades on larger drug-like molecules where Boltzmann distributions are broadest. DECAF extends to multi-objective trade-offs and, uniquely among 3D generative models, to $\textbf{higher-moment design}$: jointly optimising an ensemble property's variance and skewness to produce flexible molecules biased to a prescribed conformational regime: we verify the conformational distributions of these higher-moment designs with all-atom MD simulations.

Leveraging large language models (LLMs) for molecular generation has shown remarkable potential in chemical and drug design. Current methods primarily rely on supervised training or fine-tuning with limited datasets, which are insufficient to capture complex molecular design objectives. While some approaches attempt to guide generation toward specific goals, they often lack direct optimization mechanisms, making it difficult to align generated molecules with desired properties. To tackle these challenges, we propose \textbf{LLMol}, a principled reinforcement learning framework that directly incorporates verifiable rewards for targeted molecule generation. The key insight is to formulate molecular design as a goal-conditioned sequence prediction task, where verifiable rewards serve as explicit supervision to drive generation toward desired objectives. LLMol follows a two-stage training paradigm combining supervised learning and reinforcement learning. In the first stage, large language models are supervised fine-tuned to capture chemical syntax and molecular distributions. In the second stage, we introduce Reinforcement Learning with Verifiable Rewards (RLVR), which directly integrates property-based reward signals to guide molecular generation toward task-specific objectives. To address the high variance and instability common in discrete sequence optimization, we adopt Group Relative Policy Optimization (GRPO), a stable on-policy algorithm that smooths reward signals and improves training robustness. This framework enables LLMol to effectively handle a range of molecular design tasks, including single-property targeting (e.g., penalized logP, QED) and structure-constrained optimization. Experimental results demonstrate that LLMol consistently outperforms existing methods, achieving higher success rates and improved efficiency across diverse molecular benchmarks.

Structure-based drug design (SBDD) leverages the 3D structure of protein targets, often complemented by other spatial constraints, to generate candidate binding molecules. While diffusion models have dominated as a leading paradigm for high-quality 3D molecule generation, LLM-based methods are rapidly emerging in molecular design and have shown competitive performance in pocket-conditioned molecular generation. However, their ability to reason about physics and 3D spatial environments is largely underexplored. In this work, we systematically analyze whether current general-purpose LLMs are capable of navigating complex 3D constraints compared to established baselines such as specialized diffusion models. We consider 3D ligand generation conditioned on protein pockets together with ligand- and interaction-derived spatial constraints, including anchor fragments, pharmacophore points, and mandatory pocket-ligand interactions. To enable this evaluation, we introduce 3D-Fit - a token-efficient benchmarking strategy for assessing LLM performance on multi-conditioned spatial molecule generation. Our findings reveal a clear pattern in LLM spatial capabilities: while they still lag behind state-of-the-art approaches, they are promising and can handle multiple spatial constraints simultaneously, enabling scaling to heterogeneous setups.

Generative artificial intelligence is rapidly transforming materials design by enabling de novo exploration of immense chemical spaces. Yet a large proportion of AI-generated compositions remain implausible, violating established chemical principles, which limits the reliability and interpretability of generative materials design. Here, we introduce a chemical validity operator that recasts heuristic chemical rules as a configurable algorithmic prior for evaluating and guiding generative materials discovery. Built on the open-source SMACT package, a data-informed oxidation-state model exposes tunable thresholds, allowing users to interpolate continuously between permissive and conservative chemical constraints, while supporting both exploratory and conservative materials-design workflows. Benchmarking six state-of-the-art generative models for inorganic crystals shows that most reproduce stoichiometry but under-represent realistic oxidation-state combinations, and that filtering removes compositions reliant on rarely observed oxidation states while preserving low-energy compounds near the convex hull. Beyond screening, the same operator can also serve as a reinforcement-learning reward, steering a latent diffusion model towards chemically grounded compositions. By encoding chemical heuristics and observations, this work establishes a foundation for oxidation-state-aware generative models.

Generative molecular models can support early drug discovery by proposing new candidate compounds de novo. In practice, useful candidates must balance target-relevant activity, synthetic accessibility, physicochemical properties, and other multiparameter design constraints. However, metrics commonly used to evaluate molecular generators only weakly reflect whether the generated compounds are medicinally plausible and suitable for downstream computation. This can produce false positives in model evaluation, incorrect assumptions, and inefficient use of computational resources. We introduce HEDGEHOG, a unified six-stage filtration benchmark that is inspired by industrial hit identification workflows: (i) preprocessing; (ii) physicochemical descriptor screening; (iii) structural alerts and graph-sanity checks; (iv) synthesis feasibility; (v) docking and binding affinity estimation; and (vi) three-dimensional pose and interaction checks. We evaluate 23 molecular generators across three model classes under a standardized protocol. Across 230,000 generated molecules, only 0.65% of initial molecules survive all stages. Our results expose a central limitation of current molecular generators: molecules that appear acceptable under isolated criteria rarely satisfy medicinal chemistry, synthesis, docking, and 3D pose filters simultaneously.

Small molecules, crystals, and proteins all reduce to atoms in 3D space, yet their generative pipelines remain fragmented across domains, each with its Small molecules, crystals, and proteins all reduce to atoms in 3D space, yet their generative pipelines remain fragmented across domains, each with its own graph, equivariant, or frame-based architecture. Cross-domain training would mitigate per-domain data scarcity, but direct generation in 3D coordinate space cannot easily handle the heterogeneous structural priors of all three domains, and no prior latent autoencoder is simultaneously lossless and architecturally general across all three. We introduce SinAE, a single-architecture flow-matching autoencoder for molecules, crystals, and proteins, with vanilla Transformer encoder and decoder and no equivariant, graph, or domain-specific operators. Rather than requiring the encoder to capture fine-grained geometry, SinAE shifts the reconstruction burden into an iterative flow-matching decoder, achieving near-lossless reconstruction across domains and reducing reconstruction errors by orders of magnitude relative to prior latent baselines. The same per-token latent supports a standard Diffusion Transformer prior that reaches strong performance on molecular, crystal, and protein generation benchmarks. Joint molecule--crystal training strictly improves both domains, providing direct evidence of cross-domain transfer through a shared atomic latent. Code is available at https://github.com/BlueWhaleLab/SinAE .

Precision molecular design aims to discover personalized drug candidates through joint control of multiple conditions, such as biological relevance and molecular design strategies. Biological relevance reflects cellular functional states under disease or perturbation conditions, while molecular design strategies provide complementary guidance in terms of structural intentions and property optimization. In this study, we propose JoPMol, a jointly controlled precision molecular generative model that integrates biological states encoded by gene expression profiles with molecular structure information expressed in text, and chemical properties quantified by numerical values within a unified modeling framework. This formulation enables coordinated generation and optimization of candidate molecules under joint condition control. Experimental results show that JoPMol outperforms state-of-the-art methods across multiple evaluation metrics. Moreover, JoPMol demonstrates strong generalization ability in both transfer tasks and biologically grounded simulation scenarios, validating its effectiveness for precision molecular design. The source code is publicly available at https://github.com/hala-yh/JoPMol.

Three-dimensional (3D) molecule generation has been dominated by diffusion models, which achieve strong generation quality but typically require the molecular size to be specified a priori. Recent autoregressive approaches have substantially narrowed the performance gap while naturally supporting variable-length generation and conditioning on partial molecular context. However, balancing unconditional and context-conditioned generation remains challenging. We introduce KRONOS, a latent autoregressive diffusion framework that generates molecules in the latent space of a pre-trained autoencoder, jointly modeling molecular graph topology and geometry, while retaining the flexibility of autoregressive generation. We further introduce a mixed training strategy inspired by Fill-in-the Middle (FIM) paradigm, enabling both unconditional and fragment-conditioned molecular generation within a single left-to-right autoregressive model. Experiments on QM9 and GEOM-Drugs demonstrate that KRONOS achieves leading unconditional generation performance among autoregressive methods, while remaining competitive with diffusion models. Moreover, fragment-conditioned generation is achieved with negligible impact on unconditional generation performance, demonstrating that both generation paradigms can be supported within a single architecture.

Current computational approaches for drug design typically focus on generating molecules conditioned on specific targets or general molecular properties, often neglecting the influence of disease context on target behavior and therapeutic outcomes. To address this gap, we introduce DrugGen-2, a novel generative model that designs small molecules conditioned on both disease ontology and target protein sequences. DrugGen-2 was developed by fine-tuning a pre-trained GPT-2 model on a curated dataset of approved drugs linked to their diseases and targets, using a two-step strategy of supervised fine-tuning followed by reinforcement learning via group relative policy optimization (GRPO). This process was guided by reward functions optimizing for chemical validity, novelty, diversity, and high predicted binding affinity. When evaluated on five protein targets relevant to diabetic nephropathy, DrugGen-2 significantly outperformed baseline models (DrugGPT and DrugGen). It demonstrated a superior capacity to generate unique molecules, exhibited greater structural similarity to approved drugs, and achieved improved predicted binding affinities across all targets. Molecular docking analyses further supported these findings, identifying candidate ligands with strong binding potential, including compounds with predicted affinities (-9.917, -9.485, and -9.367) exceeding those of reference drugs such as enalapril for angiotensin-converting enzyme (-8.283). By integrating disease-specific context into molecular generation, DrugGen-2 advances AI-assisted drug discovery, offering a powerful tool for de novo design and drug repurposing that accounts for the complex interplay between diseases and molecular targets.

We propose PRECEDE, a precedent-guided co-scientist for side-effect-aware drug redesign that revises a parent compound to mitigate a specified side effect while preserving therapeutic function. Rather than isolated molecular generation, PRECEDE frames redesign as evidence-grounded reasoning over drug--side-effect associations, biomedical knowledge graphs, and precedents of safety-driven optimization, coordinated by an LLM orchestrator with explicit policies and human-review checkpoints. We position PRECEDE as a human-supervised AI-for-science workflow in which hypotheses remain auditable, falsifiable, and bounded by prior pharmacology.

Diffusion models are increasingly utilized for modeling molecular structures and conformational ensembles, yet the thermodynamic meaning of their learned representations and scores remains elusive. To resolve this ambiguity, we introduce a mathematically consistent action-operator framework natively compatible with diffusion models. By defining a fixed molecular environment as a base action $S_0(x)$ and an alchemical perturbation as an operator $O(x)$, standard diffusion noising induces effective noised actions and operators whose gradients and alchemical derivatives are directly represented by the model's learned fields. This rigorous self-consistency enables a ``noisy operator bridge'' capable of reading out free-energy differences ($ΔF$) from endpoint ensembles and per-frame evaluations. In controlled experiments on alanine dipeptide systems, we show that incorporating physical inductive biases enables partial recovery of the base action and perturbation operator. When applied to a challenging C6-H to C6-F ligand-pocket nonbonded perturbation (185L/IND) with negligible phase-space overlap, our supervised bridge estimates the alchemical $ΔF$ within approximately $1\ k_\mathrm{B}T$ of a stable 19-state MBAR reference. Finally, we demonstrate that endpoint coordinates and binary labels alone are sufficient to partially recover the operator shape and a centered free-energy scale without any force or action supervision. This work provides a rigorous path toward transforming generative molecular diffusion models from black-box coordinate samplers into auditable thermodynamic estimators.

Closed-loop materials discovery iterates between proposing candidate structures and evaluating their properties, and property evaluation dominates the cost. In the generative variant, a learned prior proposes candidate crystals and a property oracle scores them; we ask whether a cheap probabilistic surrogate can triage the generator's output, and what such a surrogate must do well. Across three architecturally distinct pretrained diffusion priors (MatterGen, CrystalFlow, ADiT) and two targets (room-temperature heat capacity and bulk modulus), we insert a Gaussian process acquisition gate between structure generation and the oracle in an RL-steered generative workflow. The gate matches or exceeds ungated fine-tuning of the generative model while capping oracle calls at a fixed per-cycle budget. Budget-matched ablations isolate the mechanism. At an identical four-call budget, ranking-based selection outperforms arbitrary selection, confirming that the gain comes from the surrogate's choice; the gate comes within $\sim$9% of exhaustive oracle spending at roughly one-fifth of the calls. A density-functional-theory check of the bulk-modulus discoveries confirms the learned oracle to within 2.5% on average and the surrogate's ranking of the generated structures at Spearman $ρ= 0.94$. A cross-factorial benchmark of surrogate performance spanning mechanical, electronic, and vibrational properties identifies pretrained ORB embeddings with a Gaussian process as the most reliable combination, which we adopt as the building blocks of the proposed workflow. The complete pipeline is released as open-source software.

Molecule generation methods that leverage generative models have been successfully applied to drug discovery. However, they often require extensive pre-training, suffer statistical biases in the training data, and might suffer from limited interpretability of generated chemical structures. In this work, we introduce SpectralMol, an algorithm based on evolutionary computation that processes chemical structures as a compact matrix of Fourier coefficients, projected onto a fixed basis to generate position-wise latent vectors for SELFIES decoding. The NSGA-II algorithm enforces diversity and enable separate objective functions rather than collapsed objectives into a scalar reward. The quality of the algorithm was tested against standardized benchmarks. The results show comparable aggregate benchmark performance with a task-dependent profile: SpectralMol is strongest on several multi-parameter optimization tasks. The same benchmark was used to perform an ablation study to demonstrate the advantages of a structured latent matrix. Finally, method was tested on a realistic ClpP-targeted drug-discovery benchmark, comparing it with the reinforcement-learning-based model under a fixed oracle-call budget. SpectralMol generates more docking hits and more diverse scaffolds while maintaining competitive physicochemical properties. The representation adopted in this work can cleanly separates scaffold-level modifications from localized substructure variations, as the former occur with perturbations of low-frequency Fourier modes and the latter with perturbations of high-frequency Fourier modes. The results support the evidence that frequency-controlled evolutionary dynamics provide an interpretable, efficient, and training-free route to multi-objective molecular design.

Generative molecular models for drug design are a promising direction with much active research. In the next phase of computational drug design, such models will need to understand small molecule structure and protein-ligand interactions, and they will need to possess the machinery to generate molecules de novo. Incorporating each feature poses a critical challenge. Equally important, yet often treated as secondary, is the ability to grow a molecule from a partial starting point -- a scaffold or fragment supplied by a chemist -- which is the central operation of lead optimization. We present Sesame (Spatial Evoformer for a Structure-Aware Molecular Engine), a diffusion-based molecular generation model that leverages a novel spatial pairformer module to condition on partial molecular structure and the surrounding protein pocket, both expressed as continuous spatial density maps. This single conditioning mechanism supports both de novo generation and fragment-conditioned lead optimization, letting a medicinal chemist prune a hit to a scaffold and have Sesame grow it in productive ways. In addition to this module, we also introduce a diffusion framework for joint denoising of atom types, bond types, and positions, along with a trajectory finetuning scheme that trains on the model's own sampling rollouts to improve generation quality. Sesame is trained on a large corpus of ligand-only and protein-ligand datasets.

We present JEDEL, a framework for generating synthesis-ready DNA-encoded libraries (DELs) directly from three-dimensional pharmacophore representations of active ligands. JEDEL is the first model to map pharmacophore interaction patterns to actionable, scalable synthesis instructions, enabling the design of targeted libraries comprising potentially millions of molecules. Unlike existing generative approaches that produce virtual compounds requiring downstream synthesis planning, JEDEL operates within the space of purchasable building blocks and validated reactions, ensuring that every output is experimentally realizable by construction. JEDEL learns a predictive alignment between pharmacophore geometry and molecular structure and decodes this into combinatorial synthesis routes at scale. Across 18 protein targets, it generates focused libraries that outperform random and diversity-based baselines in predicted binding affinity, pharmacophore recovery, and sample efficiency, without target-specific retraining. JEDEL enables a shift from virtual molecule generation to experimentally deployable library design.

Deep learning has demonstrated significant success for modeling biochemical molecular systems, where inputs are commonly represented as graphs or 3D grids. A major challenge is that computational cost scales with resolution, making full graph/grid computation of molecular densities expensive and often unstable. We introduce a multigrid training strategy that leverages low-resolution optimization to accelerate learning at higher resolution through parameter transfer across discretizations. For graph molecular representations, we progressively transfer parameters learned from a coarse graph to a sequence of increasingly finer graphs via biased random walk upsampling. For 3D molecular generation, we voxelize the molecular structures at multiple resolutions, pretrain a coarse-resolution conditional Variational Autoencoder (CVAE), and initialize a fine-resolution CVAE by transferring shape compatible convolutional parameters from the coarse model. Numerical experiments on receptor-conditioned 3D Ligand generation show that multigrid training accelerates convergence and improves generalization compared to training from scratch.

Generative models can produce individually plausible samples while deviating substantially from a target set in the distribution of key features. For example, a model pretrained on broad drug-like chemical space may generate molecules whose molecular features differ from those of a therapeutic class of interest, such as known antibiotics. Correcting such distributional miscalibration is challenging: direct finetuning on the target set can overfit and does not control which features are matched. To fill this gap, we introduce kernel Calibrating Generative Models (kCGM). kCGM minimizes a maximum mean discrepancy (MMD) between generated and target feature distributions using an unbiased score-function estimator, with KL regularization to remain close to the pretrained model. On a target set of 174 antibiotics, direct finetuning sacrifices chemical validity for feature-distribution matching, whereas kCGM improves target feature matching while increasing validity. We further demonstrate kCGM in protein and DNA generation tasks, showing it can adapt autoregressive, continuous-space diffusion, and discrete diffusion models using only feature-level supervision. Code is available at https://github.com/smithhenryd/cgm.

Inverse design of heterogeneous catalysts remains challenging because catalyst surfaces exhibit substantial structural complexity with coupled surface-adsorbate interactions across a vast chemical space that is difficult to explore efficiently through conventional screening alone. Although machine learning-based high-throughput screening has accelerated catalyst discovery, its efficiency inevitably declines as the search space grows, motivating the development of generative models that can directly construct catalysts with target properties. Here, we present a conditional catalyst generative model based on the Generative Pretrained Transformer architecture with a numerical embedding layer that enables the generation of catalyst structures conditioned on both categorical and continuous properties within a single autoregressive framework. The model was pretrained on 133 million catalyst structures and subsequently fine-tuned on approximately 460,000 optimized structures with associated categorical properties and binding energies for conditional generation. The resulting model achieved 98% structural validity, 95% optimization validity, and high categorical condition fidelity, with a 93 % joint match rate for adsorbate type and composition. For binding energy conditioning, the match rate of approximately 20% represents a four-fold improvement over the baseline training distribution, and the generated distributions shift systematically toward the target values, enabling a 1.5 to 4-fold improvement in screening efficiency for reaction-targeted catalyst discovery without additional fine-tuning. These results show that large-scale autoregressive pre-training, combined with explicit property conditioning, provides a practical route toward controllable catalyst generation and accelerated catalysts discovery.

Macrocyclic peptides are promising therapeutic candidates for intracellular targets, but their design requires simultaneous control over non-natural monomer chemistry, ring topology, membrane permeability, and target binding. Existing SMILES- or HELM-string generative models either operate in long atom-level sequence spaces or treat monomers as symbolic tokens with limited chemical grounding. We introduce PepALD, an Autoregressive Latent Diffusion (ALD) foundation model for \textit{de novo} macrocyclic peptide generation. The model represents HELM monomers with structured chemical embeddings, generates each residue through context-conditioned diffusion in chemically informed latent space, predicts R-group-aware ring closures during autoregressive generation, and aligns the denoiser to affinity rewards using winner-protected diffusion-adapted preference optimization. In silico experiments demonstrate PepALD's generation quality and reward-optimization performance against representative peptide generation baselines.

Latent diffusion is a promising framework for scalable 3D molecular generation, but it requires a latent space that remains smooth, valid, and navigable beyond posterior samples. Existing molecular VAEs, however, are typically learned through reconstruction-based objectives, which do not guarantee such a latent space. We show that this leads to dark areas: regions of latent space that are reachable during diffusion sampling but decode to disconnected or chemically invalid molecules. Unlike in image generation, molecular decoding requires strict structural and chemical precision, so even small latent perturbations can produce catastrophic failures. We therefore propose TopVAE, a topology-optimized VAE that reduces dark areas by making the decoder internalize structural and chemical constraints during training, eliminating the need for test-time chemical correction. TopVAE greatly improves off-posterior robustness, and when paired with a standard DiT, achieves $77\%$ lower FCD-3D on QM9, the highest V&C, $52\%$ lower FCD-3D on GEOM-Drugs, and $1.29{\times}$ more stable and connected molecules on zero-shot scaffold inpainting.

Diffusion models have seen wide adoption for 3D molecular generation, yet they offer no principled signal of when a generated molecule is likely to be of low quality. We propose a post-hoc method for estimating per-sample uncertainty in pretrained molecular diffusion models. Building on a Laplace approximation of the denoising network, we measure the variability of the noise prediction across the generation trajectory. Empirically, we show that the resulting uncertainty score is informative of sample quality, exhibiting a negative correlation with established sample-level quality metrics. We further study how the proposed uncertainty score can be used to filter generated samples, improving model performance via test-time scaling.

Proton dissociation constants (pKa) are critical for functional molecule discovery and molecular modeling. Building on iBonD, the largest experimental pKa database established, we and other researchers have developed several methods including machine-learning-based empirical prediction and high-accuracy energy calculations. Despite this foundation, the rapid augmentation of high-quality pKa data remains fundamentally constrained. As part of this work, we performed large-scale regression-based pKa prediction on unlabeled molecular datasets using a collection of extensively optimized machine-learning models. The results indicate that, since the feature distributions of unlabeled molecular datasets, the pKa data distribution approximates normality, with extreme scarcity of tail-region samples. Although such augmentation is highly valuable for improving overall data availability and predictive modeling, it remains insufficient for efficiently discovering molecules with broad-spectrum pKa properties. To address this, we explore the targeted generation of molecules with sparse pKa properties from the vast chemical space. Given that traditional continuous latent space VAE-RNN methods for molecular generation suffer from insufficient stability and fail to demonstrate clear advantages in complementing sparse data, we design and implement a quantum-assisted sparse-pKa molecular generation. Feasibility is validated on a simulated quantum annealer, and superior extreme-value sampling is further achieved on physical coherent Ising machines (CIMs). (to be continued)

Standard flow and diffusion pre-training matches the distribution of available data (e.g., molecules), which often covers only a small fraction of the valid design space. In generative discovery, however, one aims to sample valid new-to-nature designs, assigned negligible probability under, and thus inaccessible to, standard models fitted to the observed data. To overcome this limitation, we depart from data distribution matching and view a generative model through its generable set: the region it covers with non-negligible probability. This allows to introduce a new learning principle for out-of-distribution flow modeling: enlarging a model's generable set to increase coverage of the valid design space. We propose Active Flow Expansion (ActFlow), a continued pre-training method that employs verifier feedback to expand a pre-trained model over new valid regions by iteratively adapting to synthetic data generated through active exploration in the learned flow representation. Theoretically, we establish to our knowledge first-of-their-kind statistical learning guarantees for out-of-distribution flow modeling, analyzing generable set expansion as a local-to-global reachability process over a learned representation. Empirically, we assess ActFlow with suitable out-of-distribution generative modeling metrics across small organic molecules, mid-sized drug-like molecules, therapeutic peptides, and protein sequence design tasks. Results show that ActFlow expands valid coverage far beyond the region modeled by the initial pre-trained model, significantly outperforming widely adopted synthetic flow pre-training methods.

Designing OLED molecules with targeted optical properties remains challenging due to the scarcity of high-quality data and the limited reliability of conditional control in generative models across chemical motifs. Here, we benchmark a token-conditioned autoregressive language model for OLED molecular generation in a realistic low-data regime. A GPT2 model is pretrained on large chemical corpora, augmented with discrete property tokens, and fine-tuned using multi-task optimisation. Conditioning targets vertical absorption energy and oscillator strength, with the HOMO-LUMO gap included as an auxiliary electronic descriptor. Generated molecules are evaluated at the TDDFT level to assess distributional fidelity and controllability. The generated library reproduces the dominant optical-property support of the training distribution while shifting towards lower molecular weight and fewer heavy atoms. Token-level control is consistently directional across conditioning bins, but is not fully orthogonal and exhibits local calibration irregularities. A chemotype-resolved analysis further shows that controllability depends strongly on local electronic environments: moderately conjugated aromatic-carbon motifs are associated with improved joint target satisfaction, whereas electron-withdrawing motifs, particularly aryl nitriles, show systematic red-shifting and reduced controllability. These results establish a quantitative benchmark for conditional OLED molecular generation and show that model reliability must be assessed in chemically meaningful subspaces rather than from aggregate property distributions alone.

Progress in AI-driven crystal materials science has so far been carried by narrow architectures purpose-built for individual tasks -- graph neural networks for property prediction, diffusion and flow-matching models for crystal generation -- each excelling within its niche yet unable to act as a shared backbone across the full spectrum of materials problems. Generative large language models offer a fundamentally different paradigm, in which structural representation, quantitative prediction, and structure-activity reasoning can be unified within one model, but the materials community has yet to see this paradigm realized at a level competitive with established narrow specialists. Here we present MatMind, a generative foundation model purpose-built for crystal materials science under this paradigm, developed through the coordinated activation of structure-activity knowledge and physics-informed feedback within a progressive training framework -- combining structure-activity knowledge injection, a dual-head architecture that jointly trains language reasoning and numerical regression in a shared representation space, and multi-objective physics-informed reinforcement learning over stability, novelty, and structural diversity. Across three task families, MatMind attains the lowest mean absolute error on energy above hull, bulk modulus, and band gap -- surpassing graph neural network predictors purpose-built for these tasks -- reaches an S.U.N. rate of 65.3% on unconditional crystal generation, and achieves a comparable multiplicative improvement on magnetization-density-conditioned generation, where only 21 positive samples exist within over 600000 training entries. By matching or surpassing narrow specialists on their own ground while operating within a single unified model, MatMind shows that the LLM-based paradigm can serve as a viable backbone for crystal materials science going forward.

The success of generative molecular design hinges on a model's steerability toward high-reward samples. Because many molecular properties are intrinsically linked to molecular size, accurately capturing the joint distribution of properties and the number of atoms is essential. However, current diffusion and flow-based models fix the number of atoms, which ultimately limits their ability to navigate this complex relationship. To address this, we introduce Morph, a flexible-size generative model for conditional and unconditional 3D molecular design based on geometric graphs. By dynamically adapting size, Morph can seamlessly integrate existing structural priors, like scaffolds, and significantly enhances property steering. We show that Morph matches current fixed-size state-of-the-art models while offering the benefit of unparalleled sampling flexibility. We demonstrate out-of-distribution generation in regimes where previous models fail, paving the way for enhanced generative modeling for molecular design.

Inverse materials design is shifting materials discovery from forward prediction to targeted proposal of candidates that satisfy objectives under physical constraints. Here, we review recent advances in generative crystal structure modeling, multimodal learning, and closed-loop design pipelines for crystalline solids. We survey how modern generators learn chemical-structural priors from large databases to enable controllable sampling of periodic structures, and compare leading model classes including variational autoencoders, normalizing flows, autoregressive formulations, and diffusion models. Particular attention is given to how feasibility constraints and physical priors are enforced across the workflow, through representation choices, training objectives, sampling-time guidance, and post-generation screening and relaxation. We also discuss how multimodal learning fuses diverse materials modalities, including crystal structures, thermodynamic, electronic information, microscopy, spectroscopy, processing context, and scientific text, to construct a more universal, transferable representation of chemical space. In addition, diverse inverse-design strategies are examined, particularly those that integrate conditional generation with latent optimization, Bayesian optimization, reinforcement learning, and active learning. Finally, we highlight recurring failure modes, such as surrogate exploitation, diversity collapse, distribution shift, and the stability-synthesizability gap, and outline discovery-grade evaluation practices based on staged reporting of validity, novelty, uniqueness, stability, and cost.

Mosquito-borne infectious diseases cause more than 700000 deaths worldwide each year. The long-term use of conventional chemical insecticides has induced serious resistance problems, creating an urgent need to develop novel, highly effective, and ecologically sustainable alternatives. While existing artificial intelligence approaches in this domain have focused primarily on activity prediction and classification, they leave a critical gap in the de~novo generation of novel molecular scaffolds. In this study, we propose Mos-Gen, a motif-aware generative collaborative framework that couples the pretrained molecular representation model Uni-Mol with a variational autoencoder (VAE), specifically tailored for the design of disulfide-containing allicin derivatives as mosquito insecticides. Among the generated candidates, fourteen compounds -- comprising nine predicted positives and five predicted negatives -- were selected for chemical synthesis and experimental validation. The hit rate among the predicted positives reached 78%, whereas none of the predicted negatives exhibited mosquitocidal activity. These experimental results fully validated the high-precision screening capability of the Mos-Gen framework.

Bayesian inference provides a principled framework for modeling epistemic uncertainty in neural networks by treating predictions as distributions rather than deterministic values. Meanwhile, diffusion-based models for 3D molecular graph generation operate on fragile geometric structures governed by strict chemical constraints, making inference highly sensitive to uncertainty miscalibration. A largely overlooked issue is that epistemic uncertainty arising from the learned denoiser interacts with the aleatoric uncertainty intentionally injected during reverse diffusion, leading to systematic variance inflation and a mismatch between the true distribution and the simulated distribution. This effect is particularly detrimental for high-precision molecular generation, where even small deviations can violate chemical validity. In this work, we provide a theoretical and empirical analysis of how epistemic uncertainty propagates through diffusion inference and degrades sampling quality. Building on this investigation, we propose UCD (Uncertainty-Calibrated Diffusion), a simple yet effective method that calibrates the reverse diffusion process to account for epistemic uncertainty. Extensive experiments on standard 3D molecular benchmarks demonstrate that UCD consistently improves sampling quality across diverse baseline methods, establishing new state-of-the-art performance for 3D molecular diffusion. The code is available at https://github.com/jiuguaiwf/UCD.

Developing effective anticancer therapeutics remains challenging due to tumor heterogeneity and the absence of well-defined molecular targets across cancer subtypes. Generative models conditioned on cancer genotypes offer a promising avenue for personalized drug discovery, yet existing approaches lack explicit optimization for simultaneous sensitivity, synthesizability, and mechanistic binding plausibility. We present a latent-space optimization approach for a pretrained genotype-to-drug diffusion model, introducing a learnable perturbation over the molecular latent space optimized via gradient ascent to maximize a composite reward combining predicted drug sensitivity (AUC), drug-likeness (QED), and synthetic accessibility (SAS). Critically, biological realism is enforced by grounding both reward design and evaluation in experimentally-derived cancer cell line data and validated pharmacologic signals, anchoring candidate generation in real-world clinical evidence. Mechanistic consistency plausibility is further assessed by a multi-agent LLM pipeline grounded in the diffusion model's attention mechanism. Experiments across 15 cancer cell lines from three held-out evaluation sets demonstrate consistent and noticeable improvements over competing baselines in sensitivity, drug-likeness, synthesizability, and chemical validity.

Generating molecules that simultaneously satisfy drug-like properties and conform to the 3D structure of a target protein is a core challenge in structure-based drug design (SBDD). Existing generative approaches, however, often rely on costly post-hoc processing during Sampling or require carefully curated datasets during training, yet still achieve modest gains. These limitations are especially pronounced in multi-objective settings, where balancing conflicting criteria remains a core challenge. To address these challenges, We propose FTDiff, a reinforcement learning fine-tuning framework tailored for diffusion-based molecular generation under structural constraints. To ensure stable and sample-efficient optimization, FTDiff adopts a group relative policy optimization (GRPO) style strategy. Furthermore, FTDiff builds upon a time-free pretrained diffusion model and incorporates a fast sampling mechanism that reduces the number of denoising steps, significantly accelerating both training and inference while maintaining generation quality. By optimizing a fixed threshold-aware reward, FTDiff effectively guides the model to produce valid, diverse, and high- quality molecules that balance multiple drug design objectives. Extensive experiments on benchmark datasets demonstrate that FTDiff consistently outperforms prior methods, without requiring expensive post-hoc optimization or intricate data engineering.

Transition metal complexes are central to catalysis, drug design, and materials science, with relevant properties strongly sensitive to their three-dimensional geometry. However, the electronic diversity and unconventional bonding environments of transition metal complexes pose a major challenge for accurate structure generation. In this work, we introduce TMCgen, a manifold diffusion machine learning model that efficiently and accurately generates geometries of transition metal complexes. By formulating the diffusion process over the metal-ligand coordination angles, combined with torsional and rotational diffusion of the ligands, TMCgen focuses on the key geometric degrees of freedom of transition metal complexes. TMCgen shows strong performance in generating accurate coordination environments on a diverse set of experimentally derived bioinorganic and organometallic complexes while requiring only few inference steps, enabling efficient generation. Our results demonstrate the potential of manifold-based generative modeling for data-efficient geometry generation, paving the way for property-conditioned design of transition metal complexes.

Designing novel inorganic materials through generative models remains an important challenge for material science, driven by the complexity and diversity of inorganic structures across expansive chemical compositions and structural landscape. The vast combinatorial space of inorganic compounds demands innovative, AI-driven approaches to overcome limitations in generative accuracy and efficiency. To address this, we introduce a novel method that redefines the encoding and generation of inorganic materials by utilizing domain-specific symmetry-aware representation. Our approach not only refines the representation of intricate inorganic structures but also contributes to the field of material discovery by enhancing the precision and stability of generated candidates. Central to our methodology is a novel padding technique that exploits crystal symmetry information to enhance the encoding process. By integrating Wyckoff position length-aware padding into an encoder architecture, we achieve a more robust informed representation of inorganic materials. This symmetry-driven enhancement improves deep learning models to generate stable, previously unexplored inorganic structures with superior accuracy and computational efficiency. Furthermore, we introduce an end-to-end system that leverages the machine learning potential models to seamlessly generate novel, even those unseen in the training data, and stable inorganic materials from initial data to validated output. This pipeline integrates advanced generative models with stability analysis, marking a significant leap forward in the automated exploration and design of next-generation inorganic materials. Our method improved reconstruction accuracy 5.3% in proton conductor data, and generated 63.5% more novel stable inorganic material to baseline model on the perov-5 dataset.

Property-conditional molecular generation should produce valid, diverse molecules while responding to continuous target values at low sampling cost. We introduce DriftingMol, a two-stage framework that adapts drifting models to a SELFIES latent molecular space. A frozen SELFIES beta-VAE provides the latent space, and the hidden representation of its decoder serves as the drift feature map. In decoder-coupled drift, decoder weights remain fixed, but drift gradients are backpropagated through the decoder feature map to a DiT generator, inducing a pullback metric aligned with molecular decoding. On ZINC250K, the default setting achieves QED Spearman correlation 0.493 with 94.7% uniqueness, while the strongest decoder-coupled condition reaches 0.510. Under protocol-matched four-property conditioning, decoder-coupled drift reaches mean Spearman correlation up to 0.598. Across 15 controlled variants, models that preserve the gradient path through decoder features achieve higher correlations than the tested latent-space, random-feature, and external-feature drift variants, while detached or stop-gradient decoder controls yield near-zero QED correlation and very low uniqueness. These results indicate that decoder-coupled drift is a useful low-cost mechanism for property-biased molecular generation, requiring one generator evaluation and one frozen decoder pass.

Large Language Models (LLMs) are central to the one-for-all intelligent paradigm, but they face a fundamental challenge when dealing with heterogeneous scientific data such as molecules: the inherent gap between discrete linguistic symbols and topological molecular or continuous reaction data leads to significant information loss and semantic noise in text-based reasoning. We propose SciCore-Mol, a modular framework that bridges this gap through three deeply integrated pluggable cognitive modules: a topology-aware perception module, a latent diffusion-based molecular generation module, and a reaction-aware reasoning module. Each module is coupled to the LLM backbone through learned representation interfaces, enabling richer information exchange than is possible with text-only tool feedback. Our experiments on diverse chemical tasks demonstrate that SciCore-Mol achieves strong comprehensive performance across molecular understanding, generation, reaction prediction, and general chemistry knowledge, with an 8B-parameter open-source system that is competitive with and in several dimensions surpasses proprietary large models. This work provides a systematic blueprint for equipping LLMs with scientific expertise through decoupled, pluggable, and flexibly orchestrated modules, with direct implications for drug design, chemical synthesis, and broader scientific discovery.

Generating stable molecular conformations typically forces a tradeoff between the physical realism of energy-based relaxation and the sampling efficiency of data-driven generative models. While machine learning force fields (MLFFs) can sample stable conformations by relaxing molecular geometries according to physical forces, they require costly ab-initio training data. Conversely, diffusion models (DMs) learn from equilibrium data alone but are dependent on noise schedules and time-step conditioning. In this work, we propose generative pseudo-force fields (GPFFs) to bridge these paradigms by training an MLFF on a quadratic pseudo-potential energy surface relative to reference equilibrium structures. Because no ab-initio calculations are required for the perturbed geometries, non-equilibrium training data can be generated on the fly by perturbing the equilibria with Gaussian noise. We show that GPFFs constitute a time-step-agnostic variant of variance exploding DMs: the score comes from the predicted pseudo-forces but because force magnitudes implicitly encode the noise level, no time-step conditioning is needed. Our GPFF can hence be used as a drop-in replacement in standard diffusion sampling (ancestral, Heun) but also facilitates more efficient, adaptive variants and an MLFF inspired direct denoising scheme. Our proposed sampling algorithms support arbitrary structural priors and geometric constraints. On QM9, GPFF has 100 % validity at 256 neural function evaluations (NFE) and over 50 % at just 6 NFE, outperforming diffusion baselines across all samplers. Combined with custom priors, we showcase the fast and accurate generation process of our method in a molecular editor for a drug design setting, where a molecule is generated in real time.

Molecules in equilibrium follow a Boltzmann distribution, making the underlying energy landscape a physically grounded modeling objective. However, such landscapes are difficult to learn from data and, once learned, hard to sample from. Diffusion and flow-matching models sidestep these difficulties by learning a time-conditional score or transport field between noise and data, losing the energy inductive bias in exchange for a more tractable training objective. We introduce EBMol, an energy-based model (EBM) that restores this inductive bias by learning an atom-additive scalar potential without explicit simulation during training. Our method employs a flow-inspired Restoring Field Matching objective to approximate the energy landscape. We adopt the Mirror-Langevin algorithm for sampling, enabling unified updates of atomic positions and types, and incorporate parallel tempering for inference-time compute scaling. EBMol is the first EBM for 3D molecular generation to achieve state-of-the-art performance on QM9 and GEOM-Drugs. Moreover, we show that the learned energy landscape serves as a principled quality metric for ranking and filtering configurations, and demonstrate controllable generation without retraining through shape-steered sampling via potential composition and zero-shot linker design.

Diffusion models generate high-dimensional data with remarkable quality, yet how their training efficiently learns the score function, bypassing the curse of dimensionality when data is supported on low-dimensional manifolds, remains theoretically unexplained. We identify a collapse-and-refine mechanism driven by the geometry of the score function itself: at small noise scales, the diverging singularity of the score drives a rapid dimensional collapse of the induced denoising map onto the data manifold projection; at moderate noise scales, training refines the intrinsic density on the learned manifold. We instantiate this principle as Score-induced Latent Diffusion (SiLD), a two-stage framework in which both manifold learning and density estimation emerge from a single denoising score matching objective, replacing the heuristic KL regularization of VAE-based latent diffusion models. We prove that the resulting sample complexity depends on the intrinsic dimension rather than the ambient dimension. Experiments on Stacked MNIST, CelebA variants, and molecular generation benchmarks show that SiLD matches or outperforms VAE-based LDMs in generation quality and consistently improves reconstruction, validating our theoretical predictions.

Despite the success of foundation models in language and vision, molecular graph generation still lacks a unified framework for heterogeneous design tasks with reliable controllability. While reinforcement learning (RL) offers a natural post-training mechanism for task-specific optimization, applying it to graph generative models is hindered by the vast atom-wise action spaces and chemically invalid intermediate states. We propose \textbf{Co}ntrollable \textbf{Mole}cular Generative Foundation Models (CoMole), built with a unified motif-aware graph diffusion pipeline. By learning a motif-aware graph space, CoMole transfers pretrained structural priors into controllable generation, where RL optimizes conditional reverse policies over chemically meaningful decisions. We theoretically characterize the bottleneck of atom-level RL and justify motif-aware policy optimization. Across three heterogeneous benchmarks spanning materials and drug discovery, CoMole ranks first in controllability on all nine targets, reduces MAE by up to 48.2% relative to the strongest baselines, and maintains validity above 0.94 without rule-based correction or post-hoc filtering. We further show that CoMole transfers controllability to unseen properties by optimizing only task embeddings with the generator frozen, achieving performance competitive with strong task-specific baselines.

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.