# EigenFold: Generative Protein Structure Prediction with Diffusion Models

arXiv: https://arxiv.org/abs/2304.02198 · HTML: https://mlsanity.com/paper/2304.02198/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 5 Apr 2023.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 13 of 13)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Protein structure generation via folding diffusion](https://mlsanity.com/paper/2209.15611/) (2022)
- [Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2205.15019/) (2022)

## Built on by (most cited first, 30 of 63)

- [AlphaFold Meets Flow Matching for Generating Protein Ensembles](https://mlsanity.com/paper/2402.04845/) (2024)
- [Transferable Boltzmann Generators](https://mlsanity.com/paper/2406.14426/) (2024)
- [Protein Conformation Generation via Force-Guided SE(3) Diffusion Models](https://mlsanity.com/paper/2403.14088/) (2024)
- [ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generation](https://mlsanity.com/paper/2410.22388/) (2024)
- [Sequence-Augmented SE(3)-Flow Matching For Conditional Protein Backbone Generation](https://mlsanity.com/paper/2405.20313/) (2024)
- [AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodies](https://mlsanity.com/paper/2308.05027/) (2023)
- [Harmonic Self-Conditioned Flow Matching for Multi-Ligand Docking and Binding Site Design](https://mlsanity.com/paper/2310.05764/) (2023)
- [Str2Str: A Score-based Framework for Zero-shot Protein Conformation Sampling](https://mlsanity.com/paper/2306.03117/) (2023)
- [A Survey of Generative AI for de novo Drug Design: New Frontiers in Molecule and Protein Generation](https://mlsanity.com/paper/2402.08703/) (2024)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [ProteinBench: A Holistic Evaluation of Protein Foundation Models](https://mlsanity.com/paper/2409.06744/) (2024)
- [Adjoint Schr"odinger Bridge Sampler](https://mlsanity.com/paper/2506.22565/) (2025)
- [Extracting Reward Functions from Diffusion Models](https://mlsanity.com/paper/2306.01804/) (2023)
- [Structure Language Models for Protein Conformation Generation](https://mlsanity.com/paper/2410.18403/) (2024)
- [SimpleFold: Folding Proteins is Simpler than You Think](https://mlsanity.com/paper/2509.18480/) (2025)
- [Geometric Trajectory Diffusion Models](https://mlsanity.com/paper/2410.13027/) (2024)
- [Solving Inverse Problems in Protein Space Using Diffusion-Based Priors](https://mlsanity.com/paper/2406.04239/) (2024)
- [Equivariant Neural Diffusion for Molecule Generation](https://mlsanity.com/paper/2506.10532/) (2025)
- [Generative diffusion model with inverse renormalization group flows](https://mlsanity.com/paper/2501.09064/) (2025)
- [Flow Matching for Accelerated Simulation of Atomic Transport in Crystalline Materials](https://mlsanity.com/paper/2410.01464/) (2024)
- [ConfRover: Simultaneous Modeling of Protein Conformation and Dynamics via Autoregression](https://mlsanity.com/paper/2505.17478/) (2025)
- [Energy based diffusion generator for efficient sampling of Boltzmann distributions](https://mlsanity.com/paper/2401.02080/) (2024)
- [Compositional Flows for 3D Molecule and Synthesis Pathway Co-design](https://mlsanity.com/paper/2504.08051/) (2025)
- [MarS-FM: Generative Modeling of Molecular Dynamics via Markov State Models](https://mlsanity.com/paper/2509.24779/) (2025)
- [Generative artificial intelligence for de novo protein design](https://mlsanity.com/paper/2310.09685/) (2023)
- [Boltzmann-Aligned Inverse Folding Model as a Predictor of Mutational Effects on Protein-Protein Interactions](https://mlsanity.com/paper/2410.09543/) (2024)
- [Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusion](https://mlsanity.com/paper/2502.09890/) (2025)
- [Aligning Protein Conformation Ensemble Generation with Physical Feedback](https://mlsanity.com/paper/2505.24203/) (2025)
- [Generative AI in Depth: A Survey of Recent Advances, Model Variants, and Real-World Applications](https://mlsanity.com/paper/2510.21887/) (2025)
- [Flow Sampling: Learning to Sample from Unnormalized Densities via Denoising Conditional Processes](https://mlsanity.com/paper/2605.03984/) (2026)

## Abstract (arXiv)

Protein structure prediction has reached revolutionary levels of accuracy on single structures, yet distributional modeling paradigms are needed to capture the conformational ensembles and flexibility that underlie biological function. Towards this goal, we develop EigenFold, a diffusion generative modeling framework for sampling a distribution of structures from a given protein sequence. We define a diffusion process that models the structure as a system of harmonic oscillators and which naturally induces a cascading-resolution generative process along the eigenmodes of the system. On recent CAMEO targets, EigenFold achieves a median TMScore of 0.84, while providing a more comprehensive picture of model uncertainty via the ensemble of sampled structures relative to existing methods. We then assess EigenFold's ability to model and predict conformational heterogeneity for fold-switching proteins and ligand-induced conformational change. Code is available at https://github.com/bjing2016/EigenFold.