SSD: Shell-Guided Spherical Diffusion for Molecular Geometry Generation

Diffusion models for 3D molecular geometry almost universally adopt an isotropic Gaussian prior, whose Frobenius-norm scale $\sigma_T\sqrt{3n}$ is governed by the noise level and atom count rather than by chemistry, producing a scale mismatch whose effects grow with $n$ and yield high spatial entropy and unstable early trajectories. We introduce \textbf{Shell-guided Spherical Diffusion (SSD)}, a model-agnostic framework that replaces the Gaussian prior with a chemically scaled spherical-shell initialization and augments both the forward and reverse processes with coordinated radial attraction, short-range repulsion, and an SE(3)-equivariant correction field. This joint design of initialization and dynamics is essential: neither a shell alone nor radial fields alone reproduces the stability or accuracy of SSD. We evaluate SSD across five representative coordinate-space backbones---GeoDiff, SubGDiff, EDM, SemlaFlow-style flow matching, and MCF---each under its canonical evaluation protocol. SSD consistently improves both quality and diversity under identical training and sampling budgets, upgrading weaker backbones such as GeoDiff and EDM to match or surpass stronger diffusion-, VAE-, and flow-based baselines. SSD therefore serves as a plug-in geometric enhancement that strengthens coordinate-space molecular generation models without modifying their architectures, loss functions, or training pipelines.