Recently, diffusion models have achieved remarkable performance in data
generation, e.g., generating high-quality images. Nevertheless, chemistry
molecules often have complex non-Euclidean spatial structures, with the
behavior changing dynamically and unpredictably. Most existing diffusion models
highly rely on computing the probability distribution, i.e., Gaussian
distribution, in Euclidean space, which cannot capture internal non-Euclidean
structures of molecules, especially the hierarchical structures of the implicit
manifold surface represented by molecules. It has been observed that the
complex hierarchical structures in hyperbolic embedding space become more
prominent and easier to be captured. In order to leverage both the data
generation power of diffusion models and the strong capability to extract
complex geometric features of hyperbolic embedding, we propose to extend the
diffusion model to hyperbolic manifolds for molecule generation, namely,
Hyperbolic Graph Diffusion Model (HGDM). The proposed HGDM employs a hyperbolic
variational autoencoder to generate the hyperbolic hidden representation of
nodes and then a score-based hyperbolic graph neural network is used to learn
the distribution in hyperbolic space. Numerical experimental results show that
the proposed HGDM achieves higher performance on several molecular datasets,
compared with state-of-the-art methods.

提出了一种叫做 HGDM 的模型，将扩散模型拓展到超螺旋流形上，以便更好地生成化学分子，使用超螺旋嵌入的复杂几何信息实现更好的效果。