mlsanityData to 7 Oct 2026

SE(3) diffusion model with application to protein backbone generation

arXiv 2302.02277 ↗First posted 5 Feb 2023cs.LG q-bio.QM stat.MLcited by 214

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

Abstract (arXiv)

The design of novel protein structures remains a challenge in protein engineering for applications across biomedicine and chemistry. In this line of work, a diffusion model over rigid bodies in 3D (referred to as frames) has shown success in generating novel, functional protein backbones that have not been observed in nature. However, there exists no principled methodological framework for diffusion on SE(3), the space of orientation preserving rigid motions in R3, that operates on frames and confers the group invariance. We address these shortcomings by developing theoretical foundations of SE(3) invariant diffusion models on multiple frames followed by a novel framework, FrameDiff, for learning the SE(3) equivariant score over multiple frames. We apply FrameDiff on monomer backbone generation and find it can generate designable monomers up to 500 amino acids without relying on a pretrained protein structure prediction network that has been integral to previous methods. We find our samples are capable of generalizing beyond any known protein structure.

Key facts. Cited by 214 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 21 of its 71 references that are in the map. First posted on arXiv 5 Feb 2023.

Builds on

21 of 71 references.

Closest ancestors · 4

Same direction, newest first

  1. 2022Protein structure generation via folding diffusion30 Sep
  2. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem8 Jun
  3. 2022Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models26 May
  4. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar

Other references · 17

  1. 2017Attention Is All You Needcited by 59,932
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2016Layer Normalizationcited by 5,579
  6. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  7. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  8. 2022Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioningcited by 362
  9. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  10. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  11. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  12. 2022Riemannian Score-Based Generative Modellingcited by 216
5 more
  1. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matchingcited by 182
  2. 2022Riemannian Diffusion Modelscited by 120
  3. 2018A micro Lie theory for state estimation in roboticscited by 117
  4. 2021Provably Strict Generalisation Benefit for Equivariant Modelscited by 90
  5. 2021Introduction to Normalizing Flows for Lattice Field Theorycited by 35

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 35; 2024: 71; 2025: 64; 2026: 44.

214 papers.

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  1. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Designcited by 294
  2. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  3. 2023SE(3)-Stochastic Flow Matching for Protein Backbone Generationcited by 147
  4. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  5. 2024AlphaFold Meets Flow Matching for Generating Protein Ensemblescited by 105
  6. 2024Diffusion Language Models Are Versatile Protein Learnerscited by 93
  7. 2025Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Reviewcited by 82
  8. 2025All-atom Diffusion Transformers: Unified generative modelling of molecules and materialscited by 75
  9. 2023Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Modelscited by 65
  10. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  11. 2025Proteina: Scaling Flow-based Protein Structure Generative Modelscited by 63
  12. 2023Diffusion Models for Constrained Domainscited by 60
38 more
  1. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 59
  2. 2024DPLM-2: A Multimodal Diffusion Protein Language Modelcited by 59
  3. 2023Scalable Diffusion for Materials Generationcited by 52
  4. 2023Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulationcited by 51
  5. 2024Generative Modeling of Molecular Dynamics Trajectoriescited by 48
  6. 2024Target Score Matchingcited by 46
  7. 2024Protein Conformation Generation via Force-Guided SE(3) Diffusion Modelscited by 44
  8. 2024Improved motif-scaffolding with SE(3) flow matchingcited by 43
  9. 2023GSURE-Based Diffusion Model Training with Corrupted Datacited by 40
  10. 2024Efficient Diffusion Models: A Comprehensive Survey from Principles to Practicescited by 39
  11. 2023SE(3) Equivariant Augmented Coupling Flowscited by 37
  12. 2023Geometry-Complete Diffusion for 3D Molecule Generation and Optimizationcited by 36
  13. 2024Sequence-Augmented SE(3)-Flow Matching For Conditional Protein Backbone Generationcited by 36
  14. 2024The Superposition of Diffusion Models Using the Ito Density Estimatorcited by 36
  15. 2023AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodiescited by 35
  16. 2025Diffusion Generative Modeling for Spatially Resolved Gene Expression Inference from Histology Imagescited by 35
  17. 2024Full-Atom Peptide Design based on Multi-modal Flow Matchingcited by 34
  18. 2024Out of Many, One: Designing and Scaffolding Proteins at the Scale of the Structural Universe with Genie 2cited by 33
  19. 2024DiffAssemble: A Unified Graph-Diffusion Model for 2D and 3D Reassemblycited by 31
  20. 2024Antigen-Specific Antibody Design via Direct Energy-based Preference Optimizationcited by 30
  21. 2023Str2Str: A Score-based Framework for Zero-shot Protein Conformation Samplingcited by 29
  22. 2023Harmonic Self-Conditioned Flow Matching for Multi-Ligand Docking and Binding Site Designcited by 29
  23. 2024A Survey of Generative AI for de novo Drug Design: New Frontiers in Molecule and Protein Generationcited by 29
  24. 2023A Latent Diffusion Model for Protein Structure Generationcited by 28
  25. 2023Metropolis Sampling for Constrained Diffusion Modelscited by 28
  26. 2024PPFlow: Target-aware Peptide Design with Torsional Flow Matchingcited by 26
  27. 2025La-Proteina: Atomistic Protein Generation via Partially Latent Flow Matchingcited by 26
  28. 2023NAP: Neural 3D Articulation Priorcited by 25
  29. 2024ActionFlow: Equivariant, Accurate, and Efficient Policies with Spatially Symmetric Flow Matchingcited by 25
  30. 2023DiffPack: A Torsional Diffusion Model for Autoregressive Protein Side-Chain Packingcited by 24
  31. 2023MOFDiff: Coarse-grained Diffusion for Metal-Organic Framework Designcited by 23
  32. 2023Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processescited by 21
  33. 2024Trivialized Momentum Facilitates Diffusion Generative Modeling on Lie Groupscited by 19
  34. 2025Diffuse Everything: Multimodal Diffusion Models on Arbitrary State Spacescited by 19
  35. 2023Confronting Ambiguity in 6D Object Pose Estimation via Score-Based Diffusion on SE(3)cited by 17
  36. 2025SimpleFold: Folding Proteins is Simpler than You Thinkcited by 16
  37. 2023Learning to design protein-protein interactions with enhanced generalizationcited by 15
  38. 2024EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolantscited by 15

50 most cited of 214 All 214 (JSON)

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  1. 2025Protein-SE(3): Benchmarking SE(3)-based Generative Models for Protein Structure Design
  2. 2023EigenFold: Generative Protein Structure Prediction with Diffusion Models
  3. 2026SE(3)-MeanFlow: Few-Step Protein Backbone Generation on Lie Groups
  4. 2025From thermodynamics to protein design: Diffusion models for biomolecule generation towards autonomous protein engineering
  5. 2023Generating Novel, Designable, and Diverse Protein Structures by Equivariantly Diffusing Oriented Residue Clouds
  6. 2025The Dance of Atoms-De Novo Protein Design with Diffusion Model
  7. 2025Torsion-Space Diffusion for Protein Backbone Generation with Geometric Refinement
  8. 2025Frame-based Equivariant Diffusion Models for 3D Molecular Generation