Clifford Group Equivariant Diffusion Models For 3D Molecular Generation

This paper explores leveraging the Clifford algebra's expressive power for $\mathbb{E}(n)$-equivariant diffusion models. We utilize the geometric products between Clifford multivectors and the rich geometric information encoded in Clifford subspaces in 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.