Molecular Generation

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.

Advances in large language models (LLMs) have recently opened new and promising avenues for small-molecule drug discovery. Yet existing LLM-based approaches for molecular generation often suffer from high rates of invalid and low-quality ligand candidates, a result of the syntactic limitations of current models with regard to molecular strings. In this paper, we introduce $\texttt{ToolMol}$, an evolutionary agentic framework for de novo drug design. $\texttt{ToolMol}$ combines a multi-objective genetic algorithm with an agentic LLM operator that iteratively updates the ligand population. We build a comprehensive toolbox of RDKit-backed functions that allows our agentic operator to consisently make precise ligand modifications. $\texttt{ToolMol}$ achieves state-of-the-art performance on multi-objective property optimization tasks, discovering drug-like and synthesizable ligands that have $>10\%$ stronger predicted binding affinity compared to existing methods, evaluated on three protein targets. $\texttt{ToolMol}$ ligands additionally achieve state-of-the-art results in gold-standard Absolute Binding Free Energy scores, gaining over existing methods by over $35\%$. By studying chain-of-thought reasoning traces, we observe that tool-calling enables the model to more faithfully execute its planned modifications, efficiently exploiting the strong chemical prior knowledge in LLMs.

We propose kernel-gradient drifting, a one-step generative modeling framework that replaces the fixed Euclidean displacement direction in drifting models with directions induced by the kernel itself. Standard drifting is attractive because it enables fast, high-quality generation without distilling a large pretrained diffusion model, but its theory is currently understood mainly for Gaussian kernels, where the drift coincides with smoothed score matching and is identifiable. Our gradient-based reformulation exposes this score-based structure for general kernels: the resulting drift is the score difference between kernel-smoothed data and model distributions, yielding identifiability for characteristic kernels and a smoothed-KL descent interpretation of the drifting dynamics. Since kernel gradients are intrinsic tangent vectors, the same construction extends naturally to Riemannian manifolds and to discrete data via the Fisher-Rao geometry of the probability simplex. Across spherical geospatial data, promoter DNA and molecule generation, kernel-gradient drifting enables state-of-the-art one-step generation beyond the Euclidean setting without distillation.

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.

Recent advances in generative modeling have enabled significant progress in structure-based drug design (SBDD). Existing methods typically condition molecule generation on empty binding pockets from holo complexes, overlooking informative components such as the filler (ligands and solvent). Here, we leverage low-resolution electron density (ED) derived from the filler as a physically grounded condition for \textit{de novo} drug design. We consider two types of ED, calculated and cryo-EM/X-ray, obtainable from computational or experimental sources, supporting unified pre-training and experimental integration. Compared with rigid pocket representations, experimental ED naturally captures conformational flexibility and provides a more faithful description of the binding environment. Based on this, we introduce EDMolGPT, a decoder-only autoregressive framework that generates molecules from low-resolution ED point clouds. By grounding generation in physically meaningful density signals, EDMolGPT mitigates structural bias and produces molecules with 3D conformations. Evaluations on 101 biological targets verify the effectiveness. Our project page: https://jiahaochen1.github.io/EDMolGPT_Page/.

Geometric representation-conditioned molecule generation provides an effective paradigm that decouples molecule representation modeling from structure generation. By decoupling molecule generation into two stages-first generating a meaningful molecule representation, and then generating a 3D molecule conditioned on this representation-the efficiency and quality of the generation process can be significantly enhanced. However, its effectiveness is fundamentally limited by the quality of the representation space: pretrained molecular encoders, such as UniMol, produce representations that are non-smooth and not fully exploited during the generative training process. In this work, we propose LENSEs, a framework that better exploits the potential of molecule representations in representation-conditioned generation methods. In particular, LENSEs introduces three complementary mechanisms: (1) a representation head, simultaneously trained during generative tasks, that extracts multi-level representations from the pretrained encoder; (2) a molecule perceptual loss that optimizes the generator in a semantic-informative representation space; and (3) a node-level representation alignment (REPA) loss that explicitly aligns the generator's hidden states with encoder representations, reducing the semantic gap between pretraining and generation. We demonstrate the effectiveness of these improvements through extensive molecule generation tasks. Specifically, on the challenging molecule generation dataset GEOM-DRUG, LENSEs achieves 97.28% validity and 98.51% molecule stability, surpassing existing advanced methods. Further analyses through Lipschitz constant reduction (4.6x) and QM9 probing tasks also demonstrate the smoother, more informative refined representations, establishing generative training with alignment objectives as a potential pretraining paradigm for molecular encoders.

De novo molecular generation from tandem mass spectra is a challenging inverse problem whose core difficulty lies in the circular dependency between atom-level and bond-level reasoning: determining a bond's type requires knowing its endpoint atoms' chemical environment, yet an atom's environment is in turn defined by its incident bonds. Existing graph diffusion methods process atoms and bonds within a single computation stream, where atom-bond information synchronization can only occur implicitly across layers. We argue that this single-stream paradigm, rather than the choice of any particular aggregation kernel, is a key architectural bottleneck. We propose DualLGD (Dual-stream Line Graph Diffusion), which reformulates molecular graph denoising as the alternating solution of two coupled subproblems: atom-level reasoning and bond-level reasoning, each operating in its own dedicated representation space. The line graph provides a natural mathematical construction for the bond space, in which bond angles, dihedrals, conjugation chains, and rings correspond to local topological motifs between bonds. Incidence-constrained bidirectional cross-attention synchronizes the two streams at every layer, ensuring that each atom attends only to its incident bonds and vice versa, respecting the fundamental chemical principle that an atom's environment is determined by its bonding context. On the NPLIB1 and MassSpecGym benchmarks, DualLGD achieves top-1 accuracy of 34.37% and 23.89%, approximately $3\times$ the previous state of the art. Ablation studies confirm the architecture as the primary source of improvement: DualLGD without any pre-training already surpasses the previous best fully pretrained model.

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.

Generating chemically valid 3D molecular conformations is critical for computational drug discovery. Classical diffusion-based models like GeoLDM perform well but require hundreds of steps, making large-scale in silico screening impractical. Recent efforts on few-step molecular generation have accelerated this process to 12-50 steps, but they often largely sacrifice sample stability. In this work, we present FlashMol, an ultra-fast molecule generative model producing high-quality molecular conformations in as few as 4 steps. To achieve this, we adapt distribution matching distillation (DMD) - a reverse KL-divergence minimization objective - to the molecular domain for effective distillation. Considering the local minimization behavior of DMD, we respace the molecule generation timesteps, providing the generator with much better initialization and enables effective distillation. Additionally, to mitigate the mode-seeking behavior of DMD and improve diversity, we further regularize it with a Jensen-Shannon divergence term, which incorporates the mean-seeking behavior of the forward KL divergence. Extensive experiments on QM9 and GEOM-DRUG datasets demonstrate that FlashMol matches and even surpasses the original 1000-step teacher, achieving up to 250$\times$ acceleration in sampling speed while maintaining high molecular quality.

Language models for molecular design have scaled to hundreds of millions of parameters, yet how they learn chemical grammar is poorly understood. We train SMolLM, a 53K-parameter weight-shared transformer, to generate novel SMILES with 95% validity on the ZINC-250K drug-like-molecule benchmark, outperforming a standard GPT with 10 times more parameters. Mechanistically, the same block resolves SMILES constraints across passes in a fixed hierarchy: brackets first, rings second, and valence last, as shown by error classification and linear probing, with ablation isolating the bracket-matching head. Together, these results yield a compact, mechanistically interpretable molecular generator and a testbed for studying iterative computation in formal-language domains.

Molecular generative models often assume meaningful latent geometry, but apparent property predictability can reflect sequence-level shortcuts rather than chemical organization. We study this issue in an unsupervised autoregressive Transformer-VAE trained on SELFIES. After training, we freeze the model, fit linear probes to RDKit descriptors, and use the probe weights as candidate global steering directions. To separate chemical signal from SELFIES artifacts, we introduce a confound-aware evaluation based on residualization, confound-direction alignment analysis, and decoded-molecule traversal. This is necessary because SELFIES length, branch tokens, ring tokens, and token entropy are strongly encoded in the latent space. Under this confound-aware evaluation, we find robust monotonic steering for cLogP, FractionCSP3, HeavyAtomCount, TPSA, BertzCT, and HBA. Nonlinear probes further show that some properties admit stable global directions, while others are better described by local latent gradients. Overall, our results show that chemically meaningful steering can emerge in entangled molecular latent spaces, but only when validated through decoded molecules and controlled for representation-level confounds.

Generative modeling of physical systems, such as molecules, requires learning distributions that are invariant under global symmetries, such as rotations in three-dimensional space. Equivariant diffusion and flow matching models can incorporate such invariances effectively, even when trained on a non-invariant empirical distribution, but they typically rely on costly multi-step sampling. Recently, drifting models have emerged as an efficient alternative, enabling single-step generation and achieving state-of-the-art performance in generative modeling tasks. However, we show that drifting models face a symmetry-specific challenge, since an equivariant generator does not generally produce the same drifting field as the one obtained from the symmetrized target distribution. Addressing this issue would require expensive symmetrization of the empirical distribution. To avoid this cost, we propose SymDrift, a framework that makes the drifting field itself symmetry-aware. We introduce two complementary strategies: (i) a symmetrized drift in coordinate space based on optimal alignment, and (ii) a $G$-invariant embedding that removes symmetry ambiguity by construction. Empirically, SymDrift outperforms existing one-shot methods on standard benchmarks for conformer and transition state generation, while remaining competitive with significantly more expensive multi-step approaches. By enabling one-shot inference, SymDrift reduces computational overhead by up to 40$\times$ compared to existing baselines, making it promising for high-throughput applications such as virtual drug screening and large-scale reaction network exploration.

We present A-CODE, a fully atomic unified one-stage protein co-design model that simultaneously refines discrete atom types and continuous atom coordinates. Unlike predominant two-stage methods that cascade structure design with amino acid-level sequence design, our approach is fully atomic within a unified multimodal diffusion framework, in which residue identities are inferred solely from atom-level predictions. Built upon the powerful all-atom architecture, A-CODE achieves superior designability for unconditional protein generation, outperforming all existing one-stage and two-stage design models. For binder design, A-CODE rivals and even outperforms existing state-of-the-art two-stage design models and, compared with the existing one-stage co-design model, achieves a drastic tenfold improvement in success rate on hard tasks. The inherent flexibility of our atomic formulation enables, for the first time, seamless adaptation to non-canonical amino acid (ncAA) modeling. Our fully atomic framework establishes a new, versatile foundation for all-atom generative modeling that can be naturally extended to complex biomolecular systems.

Large Language Models (LLMs) are increasingly being used to support scientific discovery. In chemistry, tasks such as reaction prediction and structure elucidation require reasoning about the structures of molecules. As such, LLM-based systems for chemistry must interact reliably with molecular structures. Most previous studies of LLMs in chemistry have used SMILES strings or IUPAC names as molecular representations; however, the suitability of these formats has not been systematically assessed. In this work, we introduce MolJSON, a novel molecular representation for LLMs, and systematically compare it with five common chemical formats. We evaluated each representation with GPT-5-nano, GPT-5-mini, GPT-5, and Claude Haiku 4.5 using a set of 78,045 questions spanning translation, shortest path, and constrained generation reasoning tasks. We observed substantial variation across representations in the ability of LLMs to interpret and generate molecular graphs, with MolJSON consistently outperforming existing formats. On translation tasks, GPT-5 achieved 71.0% accuracy when converting IUPAC names to MolJSON, compared with 43.7% when converting the same inputs to SMILES. For constrained generation, GPT-5 reached 95.3% accuracy generating MolJSON, compared with 76.3% for IUPAC and 64.0% for SMILES. As an input format for shortest-path reasoning, GPT-5 successfully answered 98.5% of questions with MolJSON, compared with 92.2% for SMILES and 82.7% for IUPAC, whilst also using fewer reasoning tokens. We observed systematic errors associated with atom count and ring complexity for SMILES strings and IUPAC names, whereas MolJSON was more robust to these failure modes. Our results show that the choice of molecular representation has a material impact on LLM performance, and that explicit molecular graph schemas, such as MolJSON, are a promising direction for LLM-based systems in chemistry.

Many diffusion based molecule generation methods ignore the symbolic information of molecules and represent the atom and bond type as one hot representation. Methods based on Morgan fingerprints produce hash collisions and are hard to embed into a continuous space without information loss and random fingerprints correspond to no valid molecule. To circumvent this issue we use another paradigm and consider atom and bond codes as latent variables of VQ-VAE. We introduce VQ-SAD which first trains a VQ-VAE and uses the frozen pretrained VQ-VAE model and considers the codebooks for both atom and bond types as tokenizers for the downstream diffusion process. VQ-SAD is a neuro-symbolic model that utilizes both symbolic and neural structural information for a diffusion based model with learnable forward process. The large discrete code space provides a more balanced atom and bond types which enhances the denoising process. VQ-VAE slightly outperforms SOTA models for diffusion based molecule generation on QM9 and ZINC250k datasets.

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.

Amorphous (disordered) materials are solids that have shown great potential in various domains, including energy storage, thermal management, and advanced materials. Unlike crystalline materials that can be described by unit cells containing a few to hundreds of atoms, amorphous materials require larger simulation cells with at least hundreds to thousands of atoms. To advance the design of amorphous materials with desired properties and facilitate the exploration of their vast design space, generative inverse design has emerged as a promising approach. It aims to directly output materials with properties closely aligned with the desired ones using probabilistic generative models conditioned on desired properties, which can be more resource efficient than the traditional trial-and-error approach. However, due to the inherent stochasticity of probabilistic generative models, when element assignments are unconstrained, a large portion of generated materials may be charge unbalanced, and no existing methods can effectively mitigate this limitation. In this work, we propose AMGenC, a new generative inverse design method for amorphous materials that can guarantee the generation of charge balanced samples, with minimal additional computational overhead and without sacrificing inverse design accuracy. AMGenC achieves this through an element noise that gives the generation process a starting point centered around charge balance, and the combination of a per-step soft projection and a final discrete projection for steering the elements toward exact charge balance throughout the generation. We perform extensive experiments on two amorphous materials datasets. Experimental results provide evidence that AMGenC achieves its design goal.

Molecular similarity plays a central role in ligand-based drug discovery, such as virtual screening, analog searching, and goal-directed molecular generation. However, traditional similarity measures, ranging from fingerprint-based Tanimoto coefficients to 3D shape overlays, are often computationally expensive at scale or rely on hand-crafted molecular descriptors. Meanwhile, many deep learning approaches to similarity-aware design still depend on similarity-specific supervision or costly data curation, limiting their generality across targets. In this work, we propose pretrained embedding distance (PED) as an effective alternative, computed directly from pretrained molecular models without task-specific training. Experimental results show that PED exhibits distinct correlations with traditional similarity metrics, and performs effectively in both ranking molecules for virtual screening and guiding molecular generation via reward design. These findings suggest that pretrained molecular embeddings capture rich structural information and can serve as a promising and scalable similarity measurement for modern AI-aided drug discovery.

Bridging molecular structures and natural language is essential for controllable design. Autoregressive models struggle with long-range dependencies, while standard diffusion processes apply uniform corruption across positions, which can distort structurally informative tokens. We present BiMol-Diff, a unified diffusion framework for the paired tasks of text-conditioned molecule generation and molecule captioning. Our key component is a token-aware noise schedule that assigns position-dependent corruption based on token recovery difficulty, preserving harder-to-recover substructures during the forward process. On ChEBI-20 and M3-20M, BiMol-Diff improves molecule reconstruction with a 15.4% relative gain in Exact Match and achieves strong captioning results, attaining best BLEU and BERTScore among compared baselines. These results indicate token-aware noising improves fidelity in molecular structure-language modelling.

Dual-target molecule generation, which focuses on discovering compounds capable of interacting with two target proteins, has garnered significant attention due to its potential for improving therapeutic efficiency, safety and resistance mitigation. Existing approaches face two critical challenges. First, by simplifying the complex dual-target optimization problem to scalarized combinations of individual objectives, they fail to capture important trade-offs between target engagement and molecular properties. Second, they typically do not integrate synthetic planning into the generative process. This highlights a need for more appropriate objective function design and synthesis-aware methodologies tailored to the dual-target molecule generation task. In this work, we propose CombiMOTS, a Pareto Monte Carlo Tree Search (PMCTS) framework that generates dual-target molecules. CombiMOTS is designed to explore a synthesizable fragment space while employing vectorized optimization constraints to encapsulate target affinity and physicochemical properties. Extensive experiments on real-world databases demonstrate that CombiMOTS produces novel dual-target molecules with high docking scores, enhanced diversity, and balanced pharmacological characteristics, showcasing its potential as a powerful tool for dual-target drug discovery. The code and data is accessible through https://github.com/Tibogoss/CombiMOTS.

Diffusion-based generative models have reformed generative AI, and also enabled new capabilities in the science domain, e.g., fast generation of 3D structures of molecules. In such tasks, there is often a symmetry in the system, identifying elements that can be converted by certain transformations as equivalent. Equivariant diffusion models guarantee a symmetric distribution, but miss the opportunity to make learning easier, while alignment-based simplification attempts fail to preserve the target distribution. In this work, we develop quotient-space diffusion models, a principled generative framework to fully handle and leverage symmetry. By viewing the intrinsic generation process on the quotient space, the exact construction that removes symmetry redundancy, the framework simplifies learning by allowing model output to have an arbitrary intra-equivalence-class movement, while generating the correct symmetric target distribution with guarantee. We instantiate the framework for molecular structure generation which follows $\mathrm{SE}(3)$ (rigid-body movement) symmetry. It improves the performance over equivariant diffusion models and outperforms alignment-based methods universally for small molecules and proteins, representing a new framework that surpasses previous symmetry treatments in generative models.

Molecule generation requires satisfying multiple chemical and biological constraints while searching a large and structured chemical space. This makes it a non-binary problem, where effective models must identify non-obvious solutions under constraints while maintaining exploration to improve success by escaping local optima. From this perspective, creativity is a functional requirement in molecular generation rather than an aesthetic notion. Large language models (LLMs) can generate molecular representations directly from natural language prompts, but it remains unclear what type of creativity they exhibit in this setting and how it should be evaluated. In this work, we study the creative behavior of LLMs in molecular generation through a systematic empirical evaluation across physicochemical, ADMET, and biological activity tasks. We characterize creativity along two complementary dimensions, convergent creativity and divergent creativity, and analyze how different factors shape these behaviors. Our results indicate that LLMs exhibit distinct patterns of creative behavior in molecule generation, such as an increase in constraint satisfaction when additional constraints are imposed. Overall, our work is the first to reframe the abilities required for molecule generation as creativity, providing a systematic understanding of creativity in LLM-based molecular generation and clarifying the appropriate use of LLMs in molecular discovery pipelines.

In this work, we present FRIGID, a framework with a novel diffusion language model that generates molecular structures conditioned on mass spectra via intermediate fingerprint representations and determined chemical formulae, training at the scale of hundreds of millions of unlabeled structures. We then demonstrate how forward fragmentation models enable inference-time scaling by identifying spectrum-inconsistent fragments and refining them through targeted remasking and denoising. While FRIGID already achieves strong performance with its diffusion base, inference-time scaling significantly improves its accuracy, surpassing 18% Top-1 accuracy on the challenging MassSpecGym benchmark and tripling the Top-1 accuracy of the leading methods on NPLIB1. Further empirical analyses show that FRIGID exhibits log-linear performance scaling with increasing inference-time compute, opening a promising new direction for continued improvements in de novo structural elucidation. FRIGID code is publicly available at https://github.com/coleygroup/FRIGID

Consider an auto-regressive model that produces outputs x (e.g., answers to questions, molecules) each of which can be summarized by an attribute vector y (e.g., helpfulness vs. harmlessness, or bio-availability vs. lipophilicity). An arbitrary reward function r(y) encodes tradeoffs between these properties. Typically, tilting the model's sampling distribution to increase this reward is done at training time via reinforcement learning. However, if the reward function changes, re-alignment requires re-training. In this paper, we show that a reward weighted classifier-free guidance (RCFG) can act as a policy improvement operator in this setting, approximating tilting the sampling distribution by the Q function. We apply RCFG to molecular generation, demonstrating that it can optimize novel reward functions at test time. Finally, we show that using RCFG as a teacher and distilling into the base policy to serve as a warm start significantly speeds up convergence for standard RL.

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.

Flow matching models generate high-fidelity molecular geometries but incur significant computational costs during inference, requiring hundreds of network evaluations. This inference overhead becomes the primary bottleneck when such models are employed in practice to sample large numbers of molecular candidates. This work discusses a training-free caching strategy that accelerates molecular geometry generation by predicting intermediate hidden states across solver steps. The proposed method operates directly on the SE(3)-equivariant backbone, is compatible with pretrained models, and is orthogonal to existing training-based accelerations and system-level optimizations. Experiments on the GEOM-Drugs dataset demonstrate that caching achieves a twofold reduction in wall-clock inference time at matched sample quality and a speedup of up to 3x compared to the base model with minimal sample quality degradation. Because these gains compound with other optimizations, applying caching alongside other general, lossless optimizations yield as much as a 7x speedup.

A major bottleneck in scientific discovery consists of narrowing an exponentially large set of objects, such as proteins or molecules, to a small set of promising candidates with desirable properties. While this process can rely on expert knowledge, recent methods leverage reinforcement learning (RL) guided by a proxy reward function to enable this filtering. By employing various forms of entropy regularization, these methods aim to learn samplers that generate diverse candidates that are highly rated by the proxy function. In this work, we make two main contributions. First, we show that these methods are liable to generate overly diverse, suboptimal candidates in large search spaces. To address this issue, we introduce a novel unified operator that combines several regularized RL operators into a general framework that better targets peakier sampling distributions. Secondly, we offer a novel, robust RL perspective of this filtering process. The regularization can be interpreted as robustness to a compositional form of uncertainty in the proxy function (i.e., the true evaluation of a candidate differs from the proxy's evaluation). Our analysis leads us to a novel, easy-to-use algorithm we name trajectory general mellowmax (TGM): we show it identifies higher quality, diverse candidates than baselines in both synthetic and real-world tasks. Code: https://github.com/marcojira/tgm.

Although generative models hold promise for discovering molecules with optimized desired properties, they often fail to suggest synthesizable molecules that improve upon the properties of the structures represented in the training distribution. We find that this limitation arises not only from the molecule generation process itself, but also from the poor generalization capabilities of molecular property predictors. We address this challenge by creating a closed-loop molecule generation pipeline with iterative retraining on new quantum chemical simulation data. Compared against static, single-pass generative modeling approaches, only our closed-loop iterative workflow generates molecules with properties extending beyond the training distribution (up to 0.44 standard deviations beyond the original range) and achieves a 79% improvement in out-of-distribution molecule classification accuracy. Furthermore, by conditioning molecular generation on thermodynamic stability data obtained during the iterative loop, the proportion of stable and hence potentially synthesizable molecules generated is 3.5x higher than the next-best model.

We introduce MolMiner, a fragment-based, geometry-aware, and order-agnostic autoregressive model for molecular design. MolMiner supports high-dimensional conditional control over twelve physicochemical and structural properties from partial specifications, constructs molecules via symmetry-aware fragment attachments, and conditions each generation step on force-field-relaxed three-dimensional geometry of the partial structure. Conditional control emerges without auxiliary property losses. On targeted property windows, conditioning lifts hit rates by up to 5.25x over unconditional generation and 3.5x over the training distribution itself -- overriding the model's intrinsic biases -- at the cost of a small reduction in unconditional distributional fidelity. MolMiner unifies dynamic geometry, symmetry handling, order-agnostic generation, and scalable multi-property conditioning within a single framework.