Permutation-Symmetrized Diffusion for Unconditional Molecular Generation

Permutation invariance is fundamental in molecular point-cloud generation, yet most diffusion models enforce it indirectly via permutation-equivariant networks on an ordered space. We propose to model diffusion directly on the quotient manifold $\tilde{\calX}=\sR^{d\times N}/S_N$, where all atom permutations are identified. We show that the heat kernel on $\tilde{\calX}$ admits an explicit expression as a sum of Euclidean heat kernels over permutations, which clarifies how diffusion on the quotient differs from ordered-particle diffusion. Training requires a permutation-symmetrized score involving an intractable sum over $S_N$; we derive an expectation form over a posterior on permutations and approximate it using MCMC in permutation space. We evaluate on unconditional 3D molecule generation on QM9 under the EQGAT-Diff protocol, using SemlaFlow-style backbone and treating all variables continuously. The results demonstrate that quotient-based permutation symmetrization is practical and yields competitive generation quality with improved efficiency.

VecMol: Vector-Field Representations for 3D Molecule Generation

Generative modeling of three-dimensional (3D) molecules is a fundamental yet challenging problem in drug discovery and materials science. Existing approaches typically represent molecules as 3D graphs and co-generate discrete atom types with continuous atomic coordinates, leading to intrinsic learning difficulties such as heterogeneous modality entanglement and geometry-chemistry coherence constraints. We propose VecMol, a paradigm-shifting framework that reimagines molecular representation by modeling 3D molecules as continuous vector fields over Euclidean space, where vectors point toward nearby atoms and implicitly encode molecular structure. The vector field is parameterized by a neural field and generated using a latent diffusion model, avoiding explicit graph generation and decoupling structure learning from discrete atom instantiation. Experiments on the QM9 and GEOM-Drugs benchmarks validate the feasibility of this novel approach, suggesting vector-field-based representations as a promising new direction for 3D molecular generation.

Equivariant Asynchronous Diffusion: An Adaptive Denoising Schedule for Accelerated Molecular Conformation Generation

Recent 3D molecular generation methods primarily use asynchronous auto-regressive or synchronous diffusion models. While auto-regressive models build molecules sequentially, they're limited by a short horizon and a discrepancy between training and inference. Conversely, synchronous diffusion models denoise all atoms at once, offering a molecule-level horizon but failing to capture the causal relationships inherent in hierarchical molecular structures. We introduce Equivariant Asynchronous Diffusion (EAD) to overcome these limitations. EAD is a novel diffusion model that combines the strengths of both approaches: it uses an asynchronous denoising schedule to better capture molecular hierarchy while maintaining a molecule-level horizon. Since these relationships are often complex, we propose a dynamic scheduling mechanism to adaptively determine the denoising timestep. Experimental results show that EAD achieves state-of-the-art performance in 3D molecular generation.

Zatom-1: A Multimodal Flow Foundation Model for 3D Molecules and Materials

General-purpose 3D chemical modeling encompasses molecules and materials, requiring both generative and predictive capabilities. However, most existing AI approaches are optimized for a single domain (molecules or materials) and a single task (generation or prediction), which limits representation sharing and transfer. We introduce Zatom-1, the first foundation model that unifies generative and predictive learning of 3D molecules and materials. Zatom-1 is a Transformer trained with a multimodal flow matching objective that jointly models discrete atom types and continuous 3D geometries. This approach supports scalable pretraining with predictable gains as model capacity increases, while enabling fast and stable sampling. We use joint generative pretraining as a universal initialization for downstream multi-task prediction of properties, energies, and forces. Empirically, Zatom-1 matches or outperforms specialized baselines on both generative and predictive benchmarks, while reducing the generative inference time by more than an order of magnitude. Our experiments demonstrate positive predictive transfer between chemical domains from joint generative pretraining: modeling materials during pretraining improves molecular property prediction accuracy.

Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation

Many generative tasks in chemistry and science involve distributions invariant to group symmetries (e.g., permutation and rotation). A common strategy enforces invariance and equivariance through architectural constraints such as equivariant denoisers and invariant priors. In this paper, we challenge this tradition through the alternative canonicalization perspective: first map each sample to an orbit representative with a canonical pose or order, train an unconstrained (non-equivariant) diffusion or flow model on the canonical slice, and finally recover the invariant distribution by sampling a random symmetry transform at generation time. Building on a formal quotient-space perspective, our work provides a comprehensive theory of canonical diffusion by proving: (i) the correctness, universality and superior expressivity of canonical generative models over invariant targets; (ii) canonicalization accelerates training by removing diffusion score complexity induced by group mixtures and reducing conditional variance in flow matching. We then show that aligned priors and optimal transport act complementarily with canonicalization and further improves training efficiency. We instantiate the framework for molecular graph generation under $S_n \times SE(3)$ symmetries. By leveraging geometric spectra-based canonicalization and mild positional encodings, canonical diffusion significantly outperforms equivariant baselines in 3D molecule generation tasks, with similar or even less computation. Moreover, with a novel architecture Canon, CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.

MolFM-Lite: Multi-Modal Molecular Property Prediction with Conformer Ensemble Attention and Cross-Modal Fusion

Most machine learning models for molecular property prediction rely on a single molecular representation (either a sequence, a graph, or a 3D structure) and treat molecular geometry as static. We present MolFM-Lite, a multi-modal model that jointly encodes SELFIES sequences (1D), molecular graphs (2D), and conformer ensembles (3D) through cross-attention fusion, while conditioning predictions on experimental context via Feature-wise Linear Modulation (FiLM). Our main methodological contributions are: (1) a conformer ensemble attention mechanism that combines learnable attention with Boltzmann-weighted priors over multiple RDKit-generated conformers, capturing the thermodynamic distribution of molecular shapes; and (2) a cross-modal fusion layer where each modality can attend to others, enabling complementary information sharing. We evaluate on four MoleculeNet scaffold-split benchmarks using our model's own splits, and report all baselines re-evaluated under the same protocol. Comprehensive ablation studies across all four datasets confirm that each architectural component contributes independently, with tri-modal fusion providing 7-11% AUC improvement over single-modality baselines and conformer ensembles adding approximately 2% over single-conformer variants. Pre-training on ZINC250K (~250K molecules) using cross-modal contrastive and masked-atom objectives enables effective weight initialization at modest compute cost. We release all code, trained models, and data splits to support reproducibility.

3D Molecule Generation from Rigid Motifs via SE(3) Flows

Three-dimensional molecular structure generation is typically performed at the level of individual atoms, yet molecular graph generation techniques often consider fragments as their structural units. Building on the advances in frame-based protein structure generation, we extend these fragmentation ideas to 3D, treating general molecules as sets of rigid-body motifs. Utilising this representation, we employ SE(3)-equivariant generative modelling for de novo 3D molecule generation from rigid motifs. In our evaluations, we observe comparable or superior results to state-of-the-art across benchmarks, surpassing it in atom stability on GEOM-Drugs, while yielding a 2x to 10x reduction in generation steps and offering 3.5x compression in molecular representations compared to the standard atom-based methods.

TerraBind: Fast and Accurate Binding Affinity Prediction through Coarse Structural Representations

We present TerraBind, a foundation model for protein-ligand structure and binding affinity prediction that achieves 26-fold faster inference than state-of-the-art methods while improving affinity prediction accuracy by $\sim$20\%. Current deep learning approaches to structure-based drug design rely on expensive all-atom diffusion to generate 3D coordinates, creating inference bottlenecks that render large-scale compound screening computationally intractable. We challenge this paradigm with a critical hypothesis: full all-atom resolution is unnecessary for accurate small molecule pose and binding affinity prediction. TerraBind tests this hypothesis through a coarse pocket-level representation (protein C$_β$ atoms and ligand heavy atoms only) within a multimodal architecture combining COATI-3 molecular encodings and ESM-2 protein embeddings that learns rich structural representations, which are used in a diffusion-free optimization module for pose generation and a binding affinity likelihood prediction module. On structure prediction benchmarks (FoldBench, PoseBusters, Runs N' Poses), TerraBind matches diffusion-based baselines in ligand pose accuracy. Crucially, TerraBind outperforms Boltz-2 by $\sim$20\% in Pearson correlation for binding affinity prediction on both a public benchmark (CASP16) and a diverse proprietary dataset (18 biochemical/cell assays). We show that the affinity prediction module also provides well-calibrated affinity uncertainty estimates, addressing a critical gap in reliable compound prioritization for drug discovery. Furthermore, this module enables a continual learning framework and a hedged batch selection strategy that, in simulated drug discovery cycles, achieves 6$\times$ greater affinity improvement of selected molecules over greedy-based approaches.

Breaking the Bottlenecks: Scalable Diffusion Models for 3D Molecular Generation

Diffusion models have emerged as a powerful class of generative models for molecular design, capable of capturing complex structural distributions and achieving high fidelity in 3D molecule generation. However, their widespread use remains constrained by long sampling trajectories, stochastic variance in the reverse process, and limited structural awareness in denoising dynamics. The Directly Denoising Diffusion Model (DDDM) mitigates these inefficiencies by replacing stochastic reverse MCMC updates with deterministic denoising step, substantially reducing inference time. Yet, the theoretical underpinnings of such deterministic updates have remained opaque. In this work, we provide a principled reinterpretation of DDDM through the lens of the Reverse Transition Kernel (RTK) framework by Huang et al. 2024, unifying deterministic and stochastic diffusion under a shared probabilistic formalism. By expressing the DDDM reverse process as an approximate kernel operator, we show that the direct denoising process implicitly optimizes a structured transport map between noisy and clean samples. This perspective elucidates why deterministic denoising achieves efficient inference. Beyond theoretical clarity, this reframing resolves several long-standing bottlenecks in molecular diffusion. The RTK view ensures numerical stability by enforcing well-conditioned reverse kernels, improves sample consistency by eliminating stochastic variance, and enables scalable and symmetry-preserving denoisers that respect SE(3) equivariance. Empirically, we demonstrate that RTK-guided deterministic denoising achieves faster convergence and higher structural fidelity than stochastic diffusion models, while preserving chemical validity across GEOM-DRUGS dataset. Code, models, and datasets are publicly available in our project repository.

DeepMoLM: Leveraging Visual and Geometric Structural Information for Molecule-Text Modeling

AI models for drug discovery and chemical literature mining must interpret molecular images and generate outputs consistent with 3D geometry and stereochemistry. Most molecular language models rely on strings or graphs, while vision-language models often miss stereochemical details and struggle to map continuous 3D structures into discrete tokens. We propose DeepMoLM: Deep Molecular Language M odeling, a dual-view framework that grounds high-resolution molecular images in geometric invariants derived from molecular conformations. DeepMoLM preserves high-frequency evidence from 1024 $\times$ 1024 inputs, encodes conformer neighborhoods as discrete Extended 3-Dimensional Fingerprints, and fuses visual and geometric streams with cross-attention, enabling physically grounded generation without atom coordinates. DeepMoLM improves PubChem captioning with a 12.3% relative METEOR gain over the strongest generalist baseline while staying competitive with specialist methods. It produces valid numeric outputs for all property queries and attains MAE 13.64 g/mol on Molecular Weight and 37.89 on Complexity in the specialist setting. On ChEBI-20 description generation from images, it exceeds generalist baselines and matches state-of- the-art vision-language models. Code is available at https://github.com/1anj/DeepMoLM.