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arXiv · 2504.15773

Clifford Group Equivariant Diffusion Models for 3D Molecular Generation

Cong Liu·Sharvaree Vadgama·David Ruhe·Erik Bekkers·Patrick Forré
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Abstract

This paper explores leveraging the Clifford algebra's expressive power for $\E(n)$-equivariant diffusion models. We utilize the geometric products between Clifford multivectors and the rich geometric information encoded in Clifford subspaces in \emph{Clifford Diffusion Models} (CDMs). We extend the diffusion process beyond just Clifford one-vectors to incorporate all higher-grade multivector subspaces. The data is embedded in grade-$k$ subspaces, allowing us to apply latent diffusion across complete multivectors. This enables CDMs to capture the joint distribution across different subspaces of the algebra, incorporating richer geometric information through higher-order features. We provide empirical results for unconditional molecular generation on the QM9 dataset, showing that CDMs provide a promising avenue for generative modeling.

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Cong Liu, Sharvaree Vadgama, David Ruhe, Erik Bekkers, Patrick Forré. 2025-04-22. Clifford Group Equivariant Diffusion Models for 3D Molecular Generation. https://arxiv.org/abs/2504.15773

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