Clifford Group Equivariant Diffusion Models for 3D Molecular Generation

Fuente: arXiv
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Autori principali: Liu, Cong, Vadgama, Sharvaree, Ruhe, David, Bekkers, Erik, Forré, Patrick
Natura: Preprint
Pubblicazione: 2025
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author Liu, Cong
Vadgama, Sharvaree
Ruhe, David
Bekkers, Erik
Forré, Patrick
author_facet Liu, Cong
Vadgama, Sharvaree
Ruhe, David
Bekkers, Erik
Forré, Patrick
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_15773
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Clifford Group Equivariant Diffusion Models for 3D Molecular Generation
Liu, Cong
Vadgama, Sharvaree
Ruhe, David
Bekkers, Erik
Forré, Patrick
Machine Learning
Artificial Intelligence
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.
title Clifford Group Equivariant Diffusion Models for 3D Molecular Generation
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2504.15773