[2603.23255] Permutation-Symmetrized Diffusion for Unconditional Molecular Generation

Computer Science > Machine Learning arXiv:2603.23255 (cs) [Submitted on 24 Mar 2026] Title:Permutation-Symmetrized Diffusion for Unconditional Molecular Generation Authors:Gyeonghoon Ko, Juho Lee View a PDF of the paper titled Permutation-Symmetrized Diffusion for Unconditional Molecular Generation, by Gyeonghoon Ko and 1 other authors View PDF HTML (experimental) Abstract: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. Subjects: Machine Learning (cs.LG) Cite as: arXiv:2603.2...