mlsanityData to 7 Oct 2026

SymDiff: Equivariant Diffusion via Stochastic Symmetrisation

arXiv 2410.06262 ↗First posted 8 Oct 2024cs.LG stat.MLcited by 0

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

We propose SymDiff, a method for constructing equivariant diffusion models using the framework of stochastic symmetrisation. SymDiff resembles a learned data augmentation that is deployed at sampling time, and is lightweight, computationally efficient, and easy to implement on top of arbitrary off-the-shelf models. In contrast to previous work, SymDiff typically does not require any neural network components that are intrinsically equivariant, avoiding the need for complex parameterisations or the use of higher-order geometric features. Instead, our method can leverage highly scalable modern architectures as drop-in replacements for these more constrained alternatives. We show that this additional flexibility yields significant empirical benefit for E(3)-equivariant molecular generation. To the best of our knowledge, this is the first application of symmetrisation to generative modelling, suggesting its potential in this domain more generally.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 41 of its 56 references that are in the map. First posted on arXiv 8 Oct 2024.

Builds on

41 of 56 references.

Closest ancestors · 7

Same direction, newest first

  1. 2023Swallowing the Bitter Pill: Simplified Scalable Conformer Generation27 Nov
  2. 2023Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation29 Sep
  3. 2023Geometric Latent Diffusion Models for 3D Molecule Generation2 May
  4. 2023SE(3) diffusion model with application to protein backbone generation5 Feb
  5. 2022Flow Matching for Generative Modeling6 Oct
  6. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  7. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar

Other references · 34

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2022Scalable Diffusion Models with Transformerscited by 5,931
  6. 2018Neural Ordinary Differential Equationscited by 3,733
  7. 2020GLU Variants Improve Transformercited by 1,724
  8. 2021Variational Diffusion Modelscited by 1,145
  9. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  10. 2021E(n) Equivariant Graph Neural Networkscited by 951
  11. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  12. 2023Understanding Diffusion Objectives as the ELBO with Simple Data Augmentationcited by 293
22 more
  1. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  2. 2020GEOM: Energy-annotated molecular conformations for property prediction and molecular generationcited by 238
  3. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
  4. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  5. 2021E(n) Equivariant Normalizing Flowscited by 165
  6. 2018Universal approximations of invariant maps by neural networkscited by 127
  7. 2022Equivariance with Learned Canonicalization Functionscited by 106
  8. 2018Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputscited by 96
  9. 2021Provably Strict Generalisation Benefit for Equivariant Modelscited by 90
  10. 2022One Transformer Can Understand Both 2D & 3D Molecular Datacited by 77
  11. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 72
  12. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
  13. 2024Scaling Diffusion Transformers to 16 Billion Parameterscited by 65
  14. 2019A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statisticscited by 55
  15. 2023MUDiff: Unified Diffusion for Complete Molecule Generationcited by 41
  16. 2024Equivariant Frames and the Impossibility of Continuous Canonicalizationcited by 41
  17. 2023Equivariant Adaptation of Large Pretrained Modelscited by 40
  18. 2021Top-N: Equivariant set and graph generation without exchangeabilitycited by 36
  19. 2023Learning Probabilistic Symmetrization for Architecture Agnostic Equivariancecited by 25
  20. 2024Improving Equivariant Model Training via Constraint Relaxationcited by 22
  21. 2024Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networkscited by 6
  22. 2024Stochastic Neural Network Symmetrisation in Markov Categoriescited by 5

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  3. 2025Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignment
  4. 2026Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation
  5. 2025Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusion
  6. 2026Quotient-Space Diffusion Models
  7. 2025Symmetry-Aware Generative Modeling through Learned Canonicalization
  8. 2024Equivariant Diffusion Policy