# Graph Denoising Diffusion for Inverse Protein Folding

arXiv: https://arxiv.org/abs/2306.16819 · HTML: https://mlsanity.com/paper/2306.16819/

## Key facts

- Cited by 44 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 30 of its 56 references that are in the map.
- First posted on arXiv 29 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 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [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)
- [Diffsound: Discrete Diffusion Model for Text-to-sound Generation](https://mlsanity.com/paper/2207.09983/) (2022)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [ProtTrans: Towards Cracking the Language of Life's Code Through Self-Supervised Deep Learning and High Performance Computing](https://mlsanity.com/paper/2007.06225/) (2020)
- [ProGen2: Exploring the Boundaries of Protein Language Models](https://mlsanity.com/paper/2206.13517/) (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)
- [BERTology Meets Biology: Interpreting Attention in Protein Language Models](https://mlsanity.com/paper/2006.15222/) (2020)
- [PiFold: Toward effective and efficient protein inverse folding](https://mlsanity.com/paper/2209.12643/) (2022)
- [Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Docking](https://mlsanity.com/paper/2111.07786/) (2021)
- [Tranception: protein fitness prediction with autoregressive transformers and inference-time retrieval](https://mlsanity.com/paper/2205.13760/) (2022)
- [Structure-informed Language Models Are Protein Designers](https://mlsanity.com/paper/2302.01649/) (2023)
- [AlphaDesign: A graph protein design method and benchmark on AlphaFoldDB](https://mlsanity.com/paper/2202.01079/) (2022)
- [Accurate and Definite Mutational Effect Prediction with Lightweight Equivariant Graph Neural Networks](https://mlsanity.com/paper/2304.08299/) (2023)
- [Multi-level Protein Representation Learning for Blind Mutational Effect Prediction](https://mlsanity.com/paper/2306.04899/) (2023)

## Built on by (most cited first, 30 of 44)

- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [DPLM-2: A Multimodal Diffusion Protein Language Model](https://mlsanity.com/paper/2410.13782/) (2024)
- [Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory](https://mlsanity.com/paper/2403.11968/) (2024)
- [How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework](https://mlsanity.com/paper/2410.03601/) (2024)
- [Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms](https://mlsanity.com/paper/2502.00234/) (2025)
- [Full-Atom Peptide Design based on Multi-modal Flow Matching](https://mlsanity.com/paper/2406.00735/) (2024)
- [Harmonic Self-Conditioned Flow Matching for Multi-Ligand Docking and Binding Site Design](https://mlsanity.com/paper/2310.05764/) (2023)
- [Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks](https://mlsanity.com/paper/2504.02843/) (2025)
- [Generative Modelling of Structurally Constrained Graphs](https://mlsanity.com/paper/2406.17341/) (2024)
- [3D Vessel Graph Generation Using Denoising Diffusion](https://mlsanity.com/paper/2407.05842/) (2024)
- [TourSynbio: A Multi-Modal Large Model and Agent Framework to Bridge Text and Protein Sequences for Protein Engineering](https://mlsanity.com/paper/2408.15299/) (2024)
- [Bridge-IF: Learning Inverse Protein Folding with Markov Bridges](https://mlsanity.com/paper/2411.02120/) (2024)
- [Generative AI for Controllable Protein Sequence Design: A Survey](https://mlsanity.com/paper/2402.10516/) (2024)
- [All-atom inverse protein folding through discrete flow matching](https://mlsanity.com/paper/2507.14156/) (2025)
- [PDB-Struct: A Comprehensive Benchmark for Structure-based Protein Design](https://mlsanity.com/paper/2312.00080/) (2023)
- [Reinforcement learning on structure-conditioned categorical diffusion for protein inverse folding](https://mlsanity.com/paper/2410.17173/) (2024)
- [ProtInvTree: Deliberate Protein Inverse Folding with Reward-guided Tree Search](https://mlsanity.com/paper/2506.00925/) (2025)
- [ProteinZero: Self-Improving Protein Generation via Online Reinforcement Learning](https://mlsanity.com/paper/2506.07459/) (2025)
- [Fast non-autoregressive inverse folding with discrete diffusion](https://mlsanity.com/paper/2312.02447/) (2023)
- [Secondary Structure-Guided Novel Protein Sequence Generation with Latent Graph Diffusion](https://mlsanity.com/paper/2407.07443/) (2024)
- [Improving Inverse Folding for Peptide Design with Diversity-regularized Direct Preference Optimization](https://mlsanity.com/paper/2410.19471/) (2024)
- [Mask prior-guided denoising diffusion improves inverse protein folding](https://mlsanity.com/paper/2412.07815/) (2024)
- [RADAR: Redundancy-Aware Diffusion for Multi-Agent Communication Structure Generation](https://mlsanity.com/paper/2605.09907/) (2026)
- [Mamba-Based Graph Convolutional Networks: Tackling Over-smoothing with Selective State Space](https://mlsanity.com/paper/2501.15461/) (2025)
- [ProteinEngine: Empower LLM with Domain Knowledge for Protein Engineering](https://mlsanity.com/paper/2405.06658/) (2024)
- [Backdoor Attacks on Discrete Graph Diffusion Models](https://mlsanity.com/paper/2503.06340/) (2025)
- [Flowette: Flow Matching with Graphette Priors for Graph Generation](https://mlsanity.com/paper/2602.23566/) (2026)
- [Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems](https://mlsanity.com/paper/2603.12635/) (2026)
- [Diffusion-based Graph Generative Methods](https://mlsanity.com/paper/2401.15617/) (2024)
- [Designing Cyclic Peptides via Harmonic SDE with Atom-Bond Modeling](https://mlsanity.com/paper/2505.21452/) (2025)

## Abstract (arXiv)

Inverse protein folding is challenging due to its inherent one-to-many mapping characteristic, where numerous possible amino acid sequences can fold into a single, identical protein backbone. This task involves not only identifying viable sequences but also representing the sheer diversity of potential solutions. However, existing discriminative models, such as transformer-based auto-regressive models, struggle to encapsulate the diverse range of plausible solutions. In contrast, diffusion probabilistic models, as an emerging genre of generative approaches, offer the potential to generate a diverse set of sequence candidates for determined protein backbones. We propose a novel graph denoising diffusion model for inverse protein folding, where a given protein backbone guides the diffusion process on the corresponding amino acid residue types. The model infers the joint distribution of amino acids conditioned on the nodes' physiochemical properties and local environment. Moreover, we utilize amino acid replacement matrices for the diffusion forward process, encoding the biologically-meaningful prior knowledge of amino acids from their spatial and sequential neighbors as well as themselves, which reduces the sampling space of the generative process. Our model achieves state-of-the-art performance over a set of popular baseline methods in sequence recovery and exhibits great potential in generating diverse protein sequences for a determined protein backbone structure.