Clifford Group Equivariant Diffusion Models for 3D Molecular Generation
This work addresses molecular generation for computational chemistry, presenting an incremental improvement through novel geometric encoding.
The paper tackled 3D molecular generation by developing Clifford Group Equivariant Diffusion Models (CDMs) that leverage Clifford algebra to incorporate higher-grade multivectors for richer geometric information, showing promising results on the QM9 dataset.
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.