# DiffPack: A Torsional Diffusion Model for Autoregressive Protein Side-Chain Packing

arXiv: https://arxiv.org/abs/2306.01794 · HTML: https://mlsanity.com/paper/2306.01794/

## Key facts

- Cited by 24 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 34 of its 77 references that are in the map.
- First posted on arXiv 1 Jun 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, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [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)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [Protein Representation Learning by Geometric Structure Pretraining](https://mlsanity.com/paper/2203.06125/) (2022)
- [Protein structure generation via folding diffusion](https://mlsanity.com/paper/2209.15611/) (2022)
- [Diffusion-based Molecule Generation with Informative Prior Bridges](https://mlsanity.com/paper/2209.00865/) (2022)
- [Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2205.15019/) (2022)
- [Molecular Geometry Pretraining with SE(3)-Invariant Denoising Distance Matching](https://mlsanity.com/paper/2206.13602/) (2022)
- [Generating Novel, Designable, and Diverse Protein Structures by Equivariantly Diffusing Oriented Residue Clouds](https://mlsanity.com/paper/2301.12485/) (2023)
- [Multi-Scale Representation Learning on Proteins](https://mlsanity.com/paper/2204.02337/) (2022)

## Built on by (most cited first, 24 of 24)

- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [Full-Atom Peptide Design based on Multi-modal Flow Matching](https://mlsanity.com/paper/2406.00735/) (2024)
- [PPFlow: Target-aware Peptide Design with Torsional Flow Matching](https://mlsanity.com/paper/2405.06642/) (2024)
- [Re-Dock: Towards Flexible and Realistic Molecular Docking with Diffusion Bridge](https://mlsanity.com/paper/2402.11459/) (2024)
- [An All-Atom Generative Model for Designing Protein Complexes](https://mlsanity.com/paper/2504.13075/) (2025)
- [Flexible MOF Generation with Torsion-Aware Flow Matching](https://mlsanity.com/paper/2505.17914/) (2025)
- [DiffGAD: A Diffusion-based Unsupervised Graph Anomaly Detector](https://mlsanity.com/paper/2410.06549/) (2024)
- [Hotspot-Driven Peptide Design via Multi-Fragment Autoregressive Extension](https://mlsanity.com/paper/2411.18463/) (2024)
- [Diffusion Generative Modeling on Lie Group Representations](https://mlsanity.com/paper/2502.02513/) (2025)
- [H-Packer: Holographic Rotationally Equivariant Convolutional Neural Network for Protein Side-Chain Packing](https://mlsanity.com/paper/2311.09312/) (2023)
- [De novo antibody design with SE(3) diffusion](https://mlsanity.com/paper/2405.07622/) (2024)
- [Multi-level Interaction Modeling for Protein Mutational Effect Prediction](https://mlsanity.com/paper/2405.17802/) (2024)
- [EnzymeFlow: Generating Reaction-specific Enzyme Catalytic Pockets through Flow Matching and Co-Evolutionary Dynamics](https://mlsanity.com/paper/2410.00327/) (2024)
- [SubGDiff: A Subgraph Diffusion Model to Improve Molecular Representation Learning](https://mlsanity.com/paper/2405.05665/) (2024)
- [AbFlowNet: Optimizing Antibody-Antigen Binding Energy via Diffusion-GFlowNet Fusion](https://mlsanity.com/paper/2505.12358/) (2025)
- [PolyConf: Unlocking Polymer Conformation Generation through Hierarchical Generative Models](https://mlsanity.com/paper/2504.08859/) (2025)
- [Surface-based Molecular Design with Multi-modal Flow Matching](https://mlsanity.com/paper/2601.04506/) (2026)
- [Integrating Protein Dynamics into Structure-Based Drug Design via Full-Atom Stochastic Flows](https://mlsanity.com/paper/2503.03989/) (2025)
- [Sifting through the Noise: A Survey of Diffusion Probabilistic Models and Their Applications to Biomolecules](https://mlsanity.com/paper/2406.01622/) (2024)
- [The Docking Game: Loop Self-Play for Fast, Dynamic, and Accurate Prediction of Flexible Protein-Ligand Binding](https://mlsanity.com/paper/2508.05006/) (2025)
- [Full-Atom Peptide Design via Riemannian-Euclidean Bayesian Flow Networks](https://mlsanity.com/paper/2511.14516/) (2025)
- [THFlow: A Temporally Hierarchical Flow Matching Framework for 3D Peptide Design](https://mlsanity.com/paper/2502.15855/) (2025)
- [Joint Design of Protein Surface and Structure Using a Diffusion Bridge Model](https://mlsanity.com/paper/2511.16675/) (2025)
- [MuCO: Generative Peptide Cyclization Empowered by Multi-stage Conformation Optimization](https://mlsanity.com/paper/2602.11189/) (2026)

## Abstract (arXiv)

Proteins play a critical role in carrying out biological functions, and their 3D structures are essential in determining their functions. Accurately predicting the conformation of protein side-chains given their backbones is important for applications in protein structure prediction, design and protein-protein interactions. Traditional methods are computationally intensive and have limited accuracy, while existing machine learning methods treat the problem as a regression task and overlook the restrictions imposed by the constant covalent bond lengths and angles. In this work, we present DiffPack, a torsional diffusion model that learns the joint distribution of side-chain torsional angles, the only degrees of freedom in side-chain packing, by diffusing and denoising on the torsional space. To avoid issues arising from simultaneous perturbation of all four torsional angles, we propose autoregressively generating the four torsional angles from chi1 to chi4 and training diffusion models for each torsional angle. We evaluate the method on several benchmarks for protein side-chain packing and show that our method achieves improvements of 11.9% and 13.5% in angle accuracy on CASP13 and CASP14, respectively, with a significantly smaller model size (60× fewer parameters). Additionally, we show the effectiveness of our method in enhancing side-chain predictions in the AlphaFold2 model. Code is available at https://github.com/DeepGraphLearning/DiffPack.