在分子生成中直接对称化排列，提升效率与质量
Permutation-Symmetrized Diffusion for Unconditional Molecular Generation
- 在商流形上直接建模扩散过程，天然满足原子排列不变性
- 相比传统方法，生成效率更高，且在QM9数据集上表现优异
- 适合需要高效高质量分子生成的药物设计研究者
排列不变性是分子点云生成的核心要求，但多数扩散模型通过有序空间中的排列等变网络间接实现。本文提出在商流形 $ ilde{ rakX} = bR^{d imes N}/S_N$ 上直接建模扩散，将所有原子排列视为等价。我们证明该流形上的热核可表示为所有排列下欧氏热核之和，揭示了商空间扩散与有序粒子扩散的本质差异。训练需对称化得分函数，包含 $S_N$ 上不可行的求和；我们推导其期望形式，并在排列空间中用MCMC近似。在QM9数据集上，采用SemlaFlow风格主干网络，连续变量处理，评估无条件3D分子生成。结果表明，基于商流形的对称化方法兼具实用性与竞争力，生成质量优越且效率提升。
原文摘要 · Abstract (English)
Permutation invariance is fundamental in molecular point-cloud generation, yet most diffusion models enforce it indirectly via permutation-equivariant networks on an ordered space. We propose to model diffusion directly on the quotient manifold $\tilde{\calX}=\sR^{d\times N}/S_N$, where all atom permutations are identified. We show that the heat kernel on $\tilde{\calX}$ admits an explicit expression as a sum of Euclidean heat kernels over permutations, which clarifies how diffusion on the quotient differs from ordered-particle diffusion. Training requires a permutation-symmetrized score involving an intractable sum over $S_N$; we derive an expectation form over a posterior on permutations and approximate it using MCMC in permutation space. We evaluate on unconditional 3D molecule generation on QM9 under the EQGAT-Diff protocol, using SemlaFlow-style backbone and treating all variables continuously. The results demonstrate that quotient-based permutation symmetrization is practical and yields competitive generation quality with improved efficiency.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。