Permutation-Symmetrized Diffusion for Unconditional Molecular Generation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910069057126400 |
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| author | Ko, Gyeonghoon Lee, Juho |
| author_facet | Ko, Gyeonghoon Lee, Juho |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23255 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Permutation-Symmetrized Diffusion for Unconditional Molecular Generation Ko, Gyeonghoon Lee, Juho Machine Learning 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. |
| title | Permutation-Symmetrized Diffusion for Unconditional Molecular Generation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.23255 |