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This paper explores leveraging the Clifford algebra's expressive power for$\E(n)$-equivariant diffusion models. We utilize the geometric products betweenClifford multivectors and the rich geometric information encoded in Cliffordsubspaces in \emph{Clifford Diffusion Models} (CDMs). We extend the diffusionprocess beyond just Clifford one-vectors to incorporate all higher-grademultivector subspaces. The data is embedded in grade-$k$ subspaces, allowing usto apply latent diffusion across complete multivectors. This enables CDMs tocapture the joint distribution across different subspaces of the algebra,incorporating richer geometric information through higher-order features. Weprovide empirical results for unconditional molecular generation on the QM9dataset, showing that CDMs provide a promising avenue for generative modeling.

Clifford Group Equivariant Diffusion Models for 3D Molecular Generation