Title: From Shell to Structure: Spherical Shell Diffusion for Molecular Geometry Generation
Primary area: generative models
Keywords: 3D molecular generation, diffusion models, flow matching

Abstract: Diffusion-based generative models have recently advanced the state of the art in 3D molecular conformation generation, yet most existing methods rely on an isotropic Gaussian prior and unstructured Gaussian noise in Euclidean space. By concentration of measure, such Gaussians place most of their mass on a thin high-dimensional shell, but this shell is a statistical artifact of dimensionality rather than a chemically meaningful scale. As a result, initialization and early dynamics are often mismatched, leading to dispersed trajectories, high entropy, and unstable convergence. We propose Spherical Shell Diffusion (SSD), a framework that explicitly replaces the Gaussian prior with a chemically scaled spherical-shell initialization and substitutes Gaussian noise with a structured dynamics field combining radial contraction, short-range repulsion, and an SE(3)-equivariant correction. This design avoids wasted radial drift, stabilizes early trajectories, and yields denoising processes that better align with molecular geometry. Empirical results on GEOM-Drugs and GEOM-QM9 show that SSD consistently improves both quality and diversity across multiple diffusion backbones, underscoring the value of combining structured geometric priors with geometry-aware dynamics for 3D molecular generation.

TL;DR: We propose Spherical Shell Diffusion (SSD), a geometry-aware framework for 3D molecular generation that replaces Gaussian priors with spherical shells and structured dynamics, achieving state-of-the-art results.