Clifford Group Equivariant Diffusion Models for 3D Molecular Generation

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.

@article{liu2025_2504.15773,
  title={ Clifford Group Equivariant Diffusion Models for 3D Molecular Generation },
  author={ Cong Liu and Sharvaree Vadgama and David Ruhe and Erik Bekkers and Patrick Forré },
  journal={arXiv preprint arXiv:2504.15773},
  year={ 2025 }
}