Graph generation has emerged as a critical task in fields ranging from molecule design to drug discovery. Contemporary approaches, notably diffusion and flow-based models, have achieved solid graph generative performance through constructing a probability path that interpolates between a reference distribution and the data distribution. However, these methods typically model the evolution of individual nodes and edges independently and use linear interpolations to build the path assuming that the data lie in Euclidean space. We show that this is suboptimal given the intrinsic non-Euclidean structure and interconnected patterns of graphs, and it poses risks to the sampling convergence. To build a better probability path, we model the joint evolution of the nodes and edges by representing graphs as connected systems parameterized by Markov random fields (MRF). We then leverage the optimal transport displacement between MRF objects to design the probability path for graph generation. Based on this, we introduce BWFlow, a flow-matching framework for graph generation that respects the underlying geometry of graphs and provides smooth velocities in the probability path. The novel framework can be adapted to both continuous and discrete flow-matching algorithms. Experimental evaluations in plain graph generation and 2D/3D molecule generation validate the effectiveness of BWFlow in graph generation with competitive performance, stable training, and guaranteed sampling convergence.
Equivariant diffusion models have achieved impressive performance in 3D molecule generation. These models incorporate Euclidean symmetries of 3D molecules by utilizing an SE(3)-equivariant denoising network. However, specialized equivariant architectures limit the scalability and efficiency of diffusion models. In this paper, we propose an approach that relaxes such equivariance constraints. Specifically, our approach learns a sample-dependent SO(3) transformation for each molecule to construct an aligned latent space. A non-equivariant diffusion model is then trained over the aligned representations. Experimental results demonstrate that our approach performs significantly better than previously reported non-equivariant models. It yields sample quality comparable to state-of-the-art equivariant diffusion models and offers improved training and sampling efficiency. Our code is available at https://github.com/skeletondyh/RADM
De novo 3D molecule generation is a pivotal task in drug discovery. However, many recent geometric generative models struggle to produce high-quality 3D structures, even if they maintain 2D validity and topological stability. To tackle this issue and enhance the learning of effective molecular generation dynamics, we present Megalodon-a family of scalable transformer models. These models are enhanced with basic equivariant layers and trained using a joint continuous and discrete denoising co-design objective. We assess Megalodon's performance on established molecule generation benchmarks and introduce new 3D structure benchmarks that evaluate a model's capability to generate realistic molecular structures, particularly focusing on energetics. We show that Megalodon achieves state-of-the-art results in 3D molecule generation, conditional structure generation, and structure energy benchmarks using diffusion and flow matching. Furthermore, doubling the number of parameters in Megalodon to 40M significantly enhances its performance, generating up to 49x more valid large molecules and achieving energy levels that are 2-10x lower than those of the best prior generative models.
Generative models of 3D molecular structure play a rapidly growing role in the design and simulation of molecules. Diffusion models currently dominate the space of 3D molecule generation, while autoregressive models have trailed behind. In this work, we present Quetzal, a simple but scalable autoregressive model that builds molecules atom-by-atom in 3D. Treating each molecule as an ordered sequence of atoms, Quetzal combines a causal transformer that predicts the next atom's discrete type with a smaller Diffusion MLP that models the continuous next-position distribution. Compared to existing autoregressive baselines, Quetzal achieves substantial improvements in generation quality and is competitive with the performance of state-of-the-art diffusion models. In addition, by reducing the number of expensive forward passes through a dense transformer, Quetzal enables significantly faster generation speed, as well as exact divergence-based likelihood computation. Finally, without any architectural changes, Quetzal natively handles variable-size tasks like hydrogen decoration and scaffold completion. We hope that our work motivates a perspective on scalability and generality for generative modelling of 3D molecules.
Deep generative models have shown significant promise in generating valid 3D molecular structures, with the GEOM-Drugs dataset serving as a key benchmark. However, current evaluation protocols suffer from critical flaws, including incorrect valency definitions, bugs in bond order calculations, and reliance on force fields inconsistent with the reference data. In this work, we revisit GEOM-Drugs and propose a corrected evaluation framework: we identify and fix issues in data preprocessing, construct chemically accurate valency tables, and introduce a GFN2-xTB-based geometry and energy benchmark. We retrain and re-evaluate several leading models under this framework, providing updated performance metrics and practical recommendations for future benchmarking. Our results underscore the need for chemically rigorous evaluation practices in 3D molecular generation. Our recommended evaluation methods and GEOM-Drugs processing scripts are available at https://github.com/isayevlab/geom-drugs-3dgen-evaluation.
3D molecule generation is crucial for drug discovery and material science, requiring models to process complex multi-modalities, including atom types, chemical bonds, and 3D coordinates. A key challenge is integrating these modalities of different shapes while maintaining SE(3) equivariance for 3D coordinates. To achieve this, existing approaches typically maintain separate latent spaces for invariant and equivariant modalities, reducing efficiency in both training and sampling. In this work, we propose \textbf{U}nified Variational \textbf{A}uto-\textbf{E}ncoder for \textbf{3D} Molecular Latent Diffusion Modeling (\textbf{UAE-3D}), a multi-modal VAE that compresses 3D molecules into latent sequences from a unified latent space, while maintaining near-zero reconstruction error. This unified latent space eliminates the complexities of handling multi-modality and equivariance when performing latent diffusion modeling. We demonstrate this by employing the Diffusion Transformer--a general-purpose diffusion model without any molecular inductive bias--for latent generation. Extensive experiments on GEOM-Drugs and QM9 datasets demonstrate that our method significantly establishes new benchmarks in both \textit{de novo} and conditional 3D molecule generation, achieving leading efficiency and quality.
Diffusion-based models have shown great promise in molecular generation but often require a large number of sampling steps to generate valid samples. In this paper, we introduce a novel Straight-Line Diffusion Model (SLDM) to tackle this problem, by formulating the diffusion process to follow a linear trajectory. The proposed process aligns well with the noise sensitivity characteristic of molecular structures and uniformly distributes reconstruction effort across the generative process, thus enhancing learning efficiency and efficacy. Consequently, SLDM achieves state-of-the-art performance on 3D molecule generation benchmarks, delivering a 100-fold improvement in sampling efficiency. Furthermore, experiments on toy data and image generation tasks validate the generality and robustness of SLDM, showcasing its potential across diverse generative modeling domains.
Protein backbone generation plays a central role in de novo protein design and is significant for many biological and medical applications. Although diffusion and flow-based generative models provide potential solutions to this challenging task, they often generate proteins with undesired designability and suffer computational inefficiency. In this study, we propose a novel rectified quaternion flow (ReQFlow) matching method for fast and high-quality protein backbone generation. In particular, our method generates a local translation and a 3D rotation from random noise for each residue in a protein chain, which represents each 3D rotation as a unit quaternion and constructs its flow by spherical linear interpolation (SLERP) in an exponential format. We train the model by quaternion flow (QFlow) matching with guaranteed numerical stability and rectify the QFlow model to accelerate its inference and improve the designability of generated protein backbones, leading to the proposed ReQFlow model. Experiments show that ReQFlow achieves state-of-the-art performance in protein backbone generation while requiring much fewer sampling steps and significantly less inference time (e.g., being 37x faster than RFDiffusion and 62x faster than Genie2 when generating a backbone of length 300), demonstrating its effectiveness and efficiency. The code is available at https://github.com/AngxiaoYue/ReQFlow.
3D molecule generation is crucial for drug discovery and material design. While prior efforts focus on 3D diffusion models for their benefits in modeling continuous 3D conformers, they overlook the advantages of 1D SELFIES-based Language Models (LMs), which can generate 100% valid molecules and leverage the billion-scale 1D molecule datasets. To combine these advantages for 3D molecule generation, we propose a foundation model -- NExT-Mol: 3D Diffusion Meets 1D Language Modeling for 3D Molecule Generation. NExT-Mol uses an extensively pretrained molecule LM for 1D molecule generation, and subsequently predicts the generated molecule's 3D conformers with a 3D diffusion model. We enhance NExT-Mol's performance by scaling up the LM's model size, refining the diffusion neural architecture, and applying 1D to 3D transfer learning. Notably, our 1D molecule LM significantly outperforms baselines in distributional similarity while ensuring validity, and our 3D diffusion model achieves leading performances in conformer prediction. Given these improvements in 1D and 3D modeling, NExT-Mol achieves a 26% relative improvement in 3D FCD for de novo 3D generation on GEOM-DRUGS, and a 13% average relative gain for conditional 3D generation on QM9-2014. Our codes and pretrained checkpoints are available at https://github.com/acharkq/NExT-Mol.
Structure-based drug design (SBDD) leverages the 3D structure of biomolecular targets to guide the creation of new therapeutic agents. Recent advances in generative models, including diffusion models and geometric deep learning, have demonstrated promise in optimizing ligand generation. However, the scarcity of high-quality protein-ligand complex data and the inherent challenges in aligning generated ligands with target proteins limit the effectiveness of these methods. We propose BoKDiff, a novel framework that enhances ligand generation by combining multi-objective optimization and Best-of-K alignment methodologies. Built upon the DecompDiff model, BoKDiff generates diverse candidates and ranks them using a weighted evaluation of molecular properties such as QED, SA, and docking scores. To address alignment challenges, we introduce a method that relocates the center of mass of generated ligands to their docking poses, enabling accurate sub-component extraction. Additionally, we integrate a Best-of-N (BoN) sampling approach, which selects the optimal ligand from multiple generated candidates without requiring fine-tuning. BoN achieves exceptional results, with QED values exceeding 0.6, SA scores above 0.75, and a success rate surpassing 35%, demonstrating its efficiency and practicality. BoKDiff achieves state-of-the-art results on the CrossDocked2020 dataset, including a -8.58 average Vina docking score and a 26% success rate in molecule generation. This study is the first to apply Best-of-K alignment and Best-of-N sampling to SBDD, highlighting their potential to bridge generative modeling with practical drug discovery requirements. The code is provided at https://github.com/khodabandeh-ali/BoKDiff.git.
We introduce a new representation for 3D molecules based on their continuous atomic density fields. Using this representation, we propose a new model based on walk-jump sampling for unconditional 3D molecule generation in the continuous space using neural fields. Our model, FuncMol, encodes molecular fields into latent codes using a conditional neural field, samples noisy codes from a Gaussian-smoothed distribution with Langevin MCMC (walk), denoises these samples in a single step (jump), and finally decodes them into molecular fields. FuncMol performs all-atom generation of 3D molecules without assumptions on the molecular structure and scales well with the size of molecules, unlike most approaches. Our method achieves competitive results on drug-like molecules and easily scales to macro-cyclic peptides, with at least one order of magnitude faster sampling. The code is available at https://github.com/prescient-design/funcmol.
Understanding and predicting the diverse conformational states of molecules is crucial for advancing fields such as chemistry, material science, and drug development. Despite significant progress in generative models, accurately generating complex and biologically or material-relevant molecular structures remains a major challenge. In this work, we introduce a diffusion model for three-dimensional (3D) molecule generation that combines a classifiable diffusion model, Diffusion Transformer, with multihead equivariant self-attention. This method addresses two key challenges: correctly attaching hydrogen atoms in generated molecules through learning representations of molecules after hydrogen atoms are removed; and overcoming the limitations of existing models that cannot generate molecules across multiple classes simultaneously. The experimental results demonstrate that our model not only achieves state-of-the-art performance across several key metrics but also exhibits robustness and versatility, making it highly suitable for early-stage large-scale generation processes in molecular design, followed by validation and further screening to obtain molecules with specific properties.
We consider the conditional generation of 3D drug-like molecules with \textit{explicit control} over molecular properties such as drug-like properties (e.g., Quantitative Estimate of Druglikeness or Synthetic Accessibility score) and effectively binding to specific protein sites. To tackle this problem, we propose an E(3)-equivariant Wasserstein autoencoder and factorize the latent space of our generative model into two disentangled aspects: molecular properties and the remaining structural context of 3D molecules. Our model ensures explicit control over these molecular attributes while maintaining equivariance of coordinate representation and invariance of data likelihood. Furthermore, we introduce a novel alignment-based coordinate loss to adapt equivariant networks for auto-regressive de-novo 3D molecule generation from scratch. Extensive experiments validate our model's effectiveness on property-guided and context-guided molecule generation, both for de-novo 3D molecule design and structure-based drug discovery against protein targets.
n this work, we propose a latent molecular diffusion model that can make the generated 3D molecules rich in diversity and maintain rich geometric features. The model captures the information of the forces and local constraints between atoms so that the generated molecules can maintain Euclidean transformation and high level of effectiveness and diversity. We also use the lowerrank manifold advantage of the latent variables of the latent model to fuse the information of the forces between atoms to better maintain the geometric equivariant properties of the molecules. Because there is no need to perform information fusion encoding in stages like traditional encoders and decoders, this reduces the amount of calculation in the back-propagation process. The model keeps the forces and local constraints of particle bonds in the latent variable space, reducing the impact of underfitting on the surface of the network on the large position drift of the particle geometry, so that our model can converge earlier. We introduce a distribution control variable in each backward step to strengthen exploration and improve the diversity of generation. In the experiment, the quality of the samples we generated and the convergence speed of the model have been significantly improved.
The de novo generation of molecules with targeted properties is crucial in biology, chemistry, and drug discovery. Current generative models are limited to using single property values as conditions, struggling with complex customizations described in detailed human language. To address this, we propose the text guidance instead, and introduce TextSMOG, a new Text-guided Small Molecule Generation Approach via 3D Diffusion Model which integrates language and diffusion models for text-guided small molecule generation. This method uses textual conditions to guide molecule generation, enhancing both stability and diversity. Experimental results show TextSMOG's proficiency in capturing and utilizing information from textual descriptions, making it a powerful tool for generating 3D molecular structures in response to complex textual customizations.
Diffusion models have demonstrated great potential in generating high-quality content for images, natural language, protein domains, etc. However, how to perform user-preferred targeted generation via diffusion models with only black-box target scores of users remains challenging. To address this issue, we first formulate the fine-tuning of the targeted reserve-time stochastic differential equation (SDE) associated with a pre-trained diffusion model as a sequential black-box optimization problem. Furthermore, we propose a novel covariance-adaptive sequential optimization algorithm to optimize cumulative black-box scores under unknown transition dynamics. Theoretically, we prove a $O(\frac{d^2}{\sqrt{T}})$ convergence rate for cumulative convex functions without smooth and strongly convex assumptions. Empirically, experiments on both numerical test problems and target-guided 3D-molecule generation tasks show the superior performance of our method in achieving better target scores.
A remarkable advance in geometric deep generative models with accumulated structural data enables structure-based drug design (SBDD) with target protein information only. However, most existing models struggle to address multi-objectives simultaneously while performing well only in their specialized tasks. Here, we present BInD, a diffusion model with knowledge-based guidance for multi-objective SBDD. BInD is designed to co-generate molecules and their interactions with a target protein to consider all key objectives equally well, including target-specific interactions, molecular properties, and local geometry. Comprehensive evaluations show that BInD achieves robust performance for all objectives while outperforming or matching state-of-the-art methods for each. Finally, we propose a train-free optimization method empowered by retrieving target-specific interactions, highlighting the role of non-covalent interactions in achieving higher selectivity and binding affinities to a target protein.
This paper proposes a new 3D molecule generation framework, called GOAT, for fast and effective 3D molecule generation based on the flow-matching optimal transport objective. Specifically, we formulate a geometric transport formula for measuring the cost of mapping multi-modal features (e.g., continuous atom coordinates and categorical atom types) between a base distribution and a target data distribution. Our formula is solved within a unified, equivalent, and smooth representation space. This is achieved by transforming the multi-modal features into a continuous latent space with equivalent networks. In addition, we find that identifying optimal distributional coupling is necessary for fast and effective transport between any two distributions. We further propose a flow refinement and purification mechanism for optimal coupling identification. By doing so, GOAT can turn arbitrary distribution couplings into new deterministic couplings, leading to a unified optimal transport path for fast 3D molecule generation. The purification filters the subpar molecules to ensure the ultimate generation performance. We theoretically prove the proposed method indeed reduced the transport cost. Finally, extensive experiments show that GOAT enjoys the efficiency of solving geometric optimal transport, leading to a double speedup compared to the sub-optimal method while achieving the best generation quality regarding validity, uniqueness, and novelty.
Due to the vast design space of molecules, generating molecules conditioned on a specific sub-structure relevant to a particular function or therapeutic target is a crucial task in computer-aided drug design. Existing works mainly focus on specific tasks, such as linker design or scaffold hopping, each task requires training a model from scratch, and many well-pretrained De Novo molecule generation model parameters are not effectively utilized. To this end, we propose a two-stage training approach, consisting of condition learning and condition optimization. In the condition learning stage, we adopt the idea of ControlNet and design some meaningful adjustments to make the unconditional generative model learn sub-structure conditioned generation. In the condition optimization stage, by using human preference learning, we further enhance the stability and robustness of sub-structure control. In our experiments, only trained on randomly partitioned sub-structure data, the proposed method outperforms previous techniques by generating more valid and diverse molecules. Our method is easy to implement and can be quickly applied to various pre-trained molecule generation models.
Deep generative models that produce novel molecular structures have the potential to facilitate chemical discovery. Diffusion models currently achieve state of the art performance for 3D molecule generation. In this work, we explore the use of flow matching, a recently proposed generative modeling framework that generalizes diffusion models, for the task of de novo molecule generation. Flow matching provides flexibility in model design; however, the framework is predicated on the assumption of continuously-valued data. 3D de novo molecule generation requires jointly sampling continuous and categorical variables such as atom position and atom type. We extend the flow matching framework to categorical data by constructing flows that are constrained to exist on a continuous representation of categorical data known as the probability simplex. We call this extension SimplexFlow. We explore the use of SimplexFlow for de novo molecule generation. However, we find that, in practice, a simpler approach that makes no accommodations for the categorical nature of the data yields equivalent or superior performance. As a result of these experiments, we present FlowMol, a flow matching model for 3D de novo generative model that achieves improved performance over prior flow matching methods, and we raise important questions about the design of prior distributions for achieving strong performance in flow matching models. Code and trained models for reproducing this work are available at https://github.com/dunni3/FlowMol