Clifford Group Equivariant Diffusion Models for 3D Molecular Generation

• URL: http://arxiv.org/abs/2504.15773v2
• Date: Thu, 24 Apr 2025 04:27:13 GMT
• Title: Clifford Group Equivariant Diffusion Models for 3D Molecular Generation
• Authors: Cong Liu, Sharvaree Vadgama, David Ruhe, Erik Bekkers, Patrick Forré,
• Abstract summary: We utilize the geometric products between Clifford multivectors and the rich geometric information encoded in Clifford subspaces in emphClifford Diffusion Models (CDMs)<n>The data is embedded in grade-$k$ subspaces, allowing us to apply latent diffusion across complete multivectors.<n>We provide empirical results for unconditional molecular generation on the QM9 dataset, showing that CDMs provide a promising avenue for generative modeling.
• Score: 15.650651682148842
• License: http://creativecommons.org/licenses/by/4.0/
• 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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