# Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem

arXiv: https://arxiv.org/abs/2206.04119 · HTML: https://mlsanity.com/paper/2206.04119/

## Key facts

- Cited by 236 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 14 of its 53 references that are in the map.
- First posted on arXiv 8 Jun 2022.

## 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, 14 of 14)

- [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)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2205.15019/) (2022)
- [EBM-Fold: Fully-Differentiable Protein Folding Powered by Energy-based Models](https://mlsanity.com/paper/2105.04771/) (2021)

## Built on by (most cited first, 30 of 236)

- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [DiffusionDet: Diffusion Model for Object Detection](https://mlsanity.com/paper/2211.09788/) (2022)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Diffusion Models for Medical Image Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2211.07804/) (2022)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [DiffRF: Rendering-Guided 3D Radiance Field Diffusion](https://mlsanity.com/paper/2212.01206/) (2022)
- [SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control](https://mlsanity.com/paper/2210.17432/) (2022)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [DDP: Diffusion Model for Dense Visual Prediction](https://mlsanity.com/paper/2303.17559/) (2023)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding](https://mlsanity.com/paper/2408.08252/) (2024)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [Protein structure generation via folding diffusion](https://mlsanity.com/paper/2209.15611/) (2022)
- [Stochastic interpolants with data-dependent couplings](https://mlsanity.com/paper/2310.03725/) (2023)
- [Diffusion Language Models Are Versatile Protein Learners](https://mlsanity.com/paper/2402.18567/) (2024)
- [Test-time Alignment of Diffusion Models without Reward Over-optimization](https://mlsanity.com/paper/2501.05803/) (2025)
- [Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review](https://mlsanity.com/paper/2501.09685/) (2025)
- [Variational Flow Matching for Graph Generation](https://mlsanity.com/paper/2406.04843/) (2024)
- [DiffusionDepth: Diffusion Denoising Approach for Monocular Depth Estimation](https://mlsanity.com/paper/2303.05021/) (2023)
- [Generative Diffusion Models on Graphs: Methods and Applications](https://mlsanity.com/paper/2302.02591/) (2023)
- [Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Design](https://mlsanity.com/paper/2410.13643/) (2024)

## Abstract (arXiv)

Construction of a scaffold structure that supports a desired motif, conferring protein function, shows promise for the design of vaccines and enzymes. But a general solution to this motif-scaffolding problem remains open. Current machine-learning techniques for scaffold design are either limited to unrealistically small scaffolds (up to length 20) or struggle to produce multiple diverse scaffolds. We propose to learn a distribution over diverse and longer protein backbone structures via an E(3)-equivariant graph neural network. We develop SMCDiff to efficiently sample scaffolds from this distribution conditioned on a given motif; our algorithm is the first to theoretically guarantee conditional samples from a diffusion model in the large-compute limit. We evaluate our designed backbones by how well they align with AlphaFold2-predicted structures. We show that our method can (1) sample scaffolds up to 80 residues and (2) achieve structurally diverse scaffolds for a fixed motif.