Quotient-Space Diffusion Models
For generative modeling of symmetric data like molecular structures, this provides a principled framework that simplifies learning and guarantees correct sampling, outperforming heuristic alignment methods.
The paper establishes a formal framework for diffusion modeling on quotient spaces to handle symmetries, applying it to molecular structure generation with SE(3) symmetry. The quotient-space diffusion model reduces learning difficulty and outperforms previous group-equivariant models on small molecule and protein generation tasks.
Diffusion-based generative models have reformed generative AI, and have enabled new capabilities in the science domain, for example, generating 3D structures of molecules. Due to the intrinsic problem structure of certain tasks, there is often a symmetry in the system, which identifies objects that can be converted by a group action as equivalent, hence the target distribution is essentially defined on the quotient space with respect to the group. In this work, we establish a formal framework for diffusion modeling on a general quotient space, and apply it to molecular structure generation which follows the special Euclidean group $\text{SE}(3)$ symmetry. The framework reduces the necessity of learning the component corresponding to the group action, hence simplifies learning difficulty over conventional group-equivariant diffusion models, and the sampler guarantees recovering the target distribution, while heuristic alignment strategies lack proper samplers. The arguments are empirically validated on structure generation for small molecules and proteins, indicating that the principled quotient-space diffusion model provides a new framework that outperforms previous symmetry treatments.