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.

💡 Research Summary

VecMol introduces a fundamentally new way to represent and generate three‑dimensional molecules by treating each molecule as a continuous vector field defined over Euclidean space. Instead of the conventional graph‑or point‑cloud representations that require simultaneous generation of discrete atom types and continuous coordinates, VecMol maps any spatial location q∈ℝ³ to K three‑dimensional vectors v_k(q), one for each atom element type. Each vector points toward the nearest atom of that type, with its magnitude modulated by a soft‑max over distances and a clipped Gaussian term. This formulation encodes both atomic occupancy and geometric structure in a resolution‑free, atom‑count‑agnostic manner.

To learn such fields, the authors build a neural‑field autoencoder. The encoder converts a variable‑size molecular graph (coordinates X and types T) into a fixed‑size latent grid z∈ℝ^{L³×d}. This is achieved through a cross‑graph message‑passing scheme that connects each grid anchor to its k_g nearest atoms while also allowing intra‑atomic k_a nearest‑neighbor communication. The decoder is an E(n)‑equivariant Graph Neural Network (EGNN) that, given query points Q and the latent grid, predicts a virtual source location s_k(i) for each atom type k at each query point i. The vector field is then defined as v_k(q_i)=s_k(i)−q_i, guaranteeing translation equivariance and stabilizing training by forcing vectors to point toward implicit attractors. Training minimizes the mean‑squared error between predicted and ground‑truth vector fields over a sampled set of query points.

Generation proceeds in two stages. First, a Latent Diffusion Probabilistic Model (LDPM) is trained on the latent codes produced by the encoder. During sampling, Gaussian noise z_T is iteratively denoised by the diffusion model to obtain a novel latent grid z_0. The shared decoder then reconstructs a continuous vector field V from z_0. Atomic positions are recovered by solving an ordinary differential equation (gradient ascent) from random initial points toward the field’s attractors, followed by a merging step that consolidates points belonging to the same atom. This pipeline eliminates the need for a predefined atom count and allows generation at arbitrary spatial resolution.

Empirical evaluation on QM9 and GEOM‑Drugs demonstrates that VecMol matches or exceeds state‑of‑the‑art E(3)‑equivariant diffusion models (e.g., EDM) in terms of structural fidelity (RMSD), chemical validity (valence checks), and diversity. The directional information inherent in the vector field accelerates convergence during the ODE‑based reconstruction and reduces memory overhead compared to voxel‑grid approaches, which scale cubically with resolution.

The paper also discusses limitations: the need to model K separate vector fields, sensitivity to hyper‑parameters governing the soft‑max temperature and Gaussian clipping, and the computational cost of the ODE reconstruction step. Future directions include combining vector fields with scalar density fields for improved atom‑type discrimination, designing more efficient atom extraction mechanisms (e.g., flow‑based samplers), and extending the framework to conditional generation tasks such as property‑guided or protein‑ligand design. Overall, VecMol opens a promising new avenue for 3D molecular generation by leveraging continuous, physics‑inspired representations and latent diffusion.