mlsanityData to 14 Oct 2026

Symphony: Symmetry-Equivariant Point-Centered Spherical Harmonics for 3D Molecule Generation

arXiv 2311.16199 ↗First posted 27 Nov 2023cs.LG q-bio.BMcited by 17

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Abstract (arXiv)

We present Symphony, an E(3)-equivariant autoregressive generative model for 3D molecular geometries that iteratively builds a molecule from molecular fragments. Existing autoregressive models such as G-SchNet and G-SphereNet for molecules utilize rotationally invariant features to respect the 3D symmetries of molecules. In contrast, Symphony uses message-passing with higher-degree E(3)-equivariant features. This allows a novel representation of probability distributions via spherical harmonic signals to efficiently model the 3D geometry of molecules. We show that Symphony is able to accurately generate small molecules from the QM9 dataset, outperforming existing autoregressive models and approaching the performance of diffusion models.

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). Builds on 9 of its 31 references that are in the map. First posted on arXiv 27 Nov 2023.

Builds on

9 of 31 references.

References · 9

  1. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
  2. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 571
  3. 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 172
  4. 2021Inverse design of 3d molecular structures with conditional generative neural networkscited by 93
  5. 2021Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifoldcited by 65
  6. 2020Symmetry-Aware Actor-Critic for 3D Molecular Designcited by 55
  7. 2020Reinforcement Learning for Molecular Design Guided by Quantum Mechanicscited by 51
  8. 2022Incompleteness of graph neural networks for points clouds in three dimensionscited by 19
  9. 2015Harmonic Exponential Families on Manifoldscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 7; 2026: 7.

17 papers.

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  1. 2025All-atom Diffusion Transformers: Unified generative modelling of molecules and materialscited by 75
  2. 2025Equivariant Neural Diffusion for Molecule Generationcited by 13
  3. 2024Equivariant Symmetry Breaking Setscited by 9
  4. 2024A Recipe for Charge Density Predictioncited by 9
  5. 2025Straight-Line Diffusion Model for Efficient 3D Molecular Generationcited by 8
  6. 2025Scalable Autoregressive 3D Molecule Generationcited by 8
  7. 2026Zatom-1: Towards a Multimodal Foundation Model for 3D Molecules and Materialscited by 5
  8. 2025Equivariant Masked Position Prediction for Efficient Molecular Representationcited by 4
  9. 2025Guiding Diffusion Models with Reinforcement Learning for Stable Molecule Generationcited by 4
  10. 2025NEAT: Neighborhood-Guided, Efficient, Autoregressive Set Transformer for 3D Molecular Generationcited by 3
  11. 2024Equivariant Machine Learning on Graphs with Nonlinear Spectral Filterscited by 2
  12. 2026Generative Molecular Morphing for Flexible-Size Design via Unbalanced Optimal Transportcited by 2
5 more
  1. 2026AtomComposer: Discovering Chemical Space from First Principles with Reinforcement Learningcited by 1
  2. 2026Autoregressive latent diffusion for 3D molecule generationcited by 1
  3. 2026Equivariant Asynchronous Diffusion: An Adaptive Denoising Schedule for Accelerated Molecular Conformation Generationcited by 0
  4. 2026Generating Physically Consistent Molecules with Energy-Based Modelscited by 0
  5. 2026GEqTrain: A Configuration-Driven Framework for Retargeting Equivariant Graph Neural Networks Across 3D Scientific Taskscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignment
  2. 2022Equivariant Diffusion for Molecule Generation in 3D
  3. 2023Geometric Latent Diffusion Models for 3D Molecule Generation
  4. 2025D3MES: Diffusion Transformer with multihead equivariant self-attention for 3D molecule generation
  5. 2026Quotient-Space Diffusion Models
  6. 2023Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation
  7. 2025Frame-based Equivariant Diffusion Models for 3D Molecular Generation
  8. 2022MDM: Molecular Diffusion Model for 3D Molecule Generation