VecMol: Vector-Field Representations for 3D Molecule Generation

Three-dimensional molecular generation is a crucial problem in drug discovery and materials science. Traditional methods often represent molecules as point clouds or voxels, which, while capturing local chemical environments and symmetries, are limited by the locality of message passing and computational costs that scale quadratically with the number of atoms. Moreover, point-cloud-based generative models often require an explicit upper bound on molecular size, introducing artificial cardinality constraints during training and sampling. Recent advances in diffusion models and equivariant architectures have shown promising performance on molecular generation tasks, but existing approaches continue to face a trade-off between structural fidelity and computational tractability.

Existing methods for 3D molecular generation typically represent molecules as discrete atom types with continuous atomic coordinates, leading to intrinsic learning difficulties such as heterogeneous modality entanglement and geometry-chemistry coherence constraints. These methods naturally capture local chemical environments and symmetries, yet their expressivity is constrained by the locality of message passing, and their computational cost typically scales quadratically with the number of atoms. Moreover, point-cloud-based generative models often require an explicit upper bound on molecular size, introducing artificial cardinality constraints during training and sampling.

VecMol proposes a novel representation of molecules as continuous vector fields over Euclidean space. Instead of treating a molecule as a set of atoms, VecMol represents it as a neural field that maps any spatial location to a vector pointing toward nearby atomic centers. This formulation aligns with the physical nature of molecular systems, whose interactions and energy landscapes are inherently continuous functions of space. By parameterizing these vector fields with a conditional neural field architecture, VecMol decouples global structural encoding from local geometric realization: a compact latent code captures the overall molecular structure, while a shared E(n)-equivariant decoder maps spatial coordinates to field values.

• �� VecMol redefines the problem of molecular generation by representing 3D molecules as continuous vector fields over Euclidean space.
• �� This method uses a neural field to parameterize the vector field and generates it using a latent diffusion model, avoiding explicit graph generation and decoupling structure learning from discrete atom instantiation.
• �� Specifically, VecMol employs a neural field autoencoder to compress molecular structures into a fixed-dimensional latent space, followed by a latent diffusion probabilistic model to generate novel latent codes, which are decoded into vector fields of novel molecules.
• �� In experiments, VecMol demonstrated outstanding performance on the QM9 and GEOM-Drugs benchmarks, validating its capability to generate molecules.

In experiments, VecMol demonstrated outstanding performance on the QM9 and GEOM-Drugs benchmarks, validating its capability to generate molecules. Compared to existing methods, VecMol excels in molecular stability, validity, and uniqueness, especially on the GEOM-Drugs dataset, where generated molecules show superior chemical realism and conformational quality. This indicates the potential of vector-field representations in molecular generation, pointing to new directions for future research.

VecMol achieved high levels of stability and validity in molecule generation, reaching 97.6% and 99.8%, respectively, demonstrating its robust performance in generation tasks. In terms of molecular geometric accuracy, VecMol maintains competitive performance in ring size distribution and atom type distribution, although it slightly underperforms in bond length and bond angle.

VecMol offers a new perspective for 3D molecular generation, particularly in drug discovery and materials science. By avoiding explicit graph generation, VecMol addresses issues of heterogeneous modality entanglement and geometry-chemistry coherence constraints present in existing methods. This approach not only enhances the structural fidelity of generated molecules but also reduces computational complexity, making high-resolution molecular modeling feasible.

VecMol slightly underperforms in bond length and bond angle accuracy compared to some benchmark methods, which may be related to model capacity and resolution. While VecMol performs well in atom type distribution, there is room for improvement in local geometric accuracy, especially in handling small coordinate deviations.