Diffusion models with group symmetries for biomolecule generation

Generative artificial intelligence is a promising approach and has achieved great success in various protein generation tasks. Notably, diffusion models stand out for their robust mathematical foundations and impressive generative capabilities, offering unique advantages in certain applications such as protein design. This review summarizes Special Euclidean group $SE(3)$-invariant and Euclidean group $E(3)$-invariant diffusion models tailored to the structural properties of proteins and small molecules, respectively. We examine why $SE(3)$-equivariant models are predominantly used in protein design, while $E(3)$-equivariant models are favored for molecule generation. Finally, we discuss future directions, including multiscale modeling, dynamic integration, and cross-domain applications, to advance biomolecular design and drug discovery.