# Designing Cyclic Peptides via Harmonic SDE with Atom-Bond Modeling

arXiv: https://arxiv.org/abs/2505.21452 · HTML: https://mlsanity.com/paper/2505.21452/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 119 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 30 of 36)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (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)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction](https://mlsanity.com/paper/2202.05146/) (2022)
- [Diffusion Language Models Are Versatile Protein Learners](https://mlsanity.com/paper/2402.18567/) (2024)
- [Iterative Refinement Graph Neural Network for Antibody Sequence-Structure Co-design](https://mlsanity.com/paper/2110.04624/) (2021)
- [PiFold: Toward effective and efficient protein inverse folding](https://mlsanity.com/paper/2209.12643/) (2022)
- [Structure-informed Language Models Are Protein Designers](https://mlsanity.com/paper/2302.01649/) (2023)
- [DPLM-2: A Multimodal Diffusion Protein Language Model](https://mlsanity.com/paper/2410.13782/) (2024)
- [EigenFold: Generative Protein Structure Prediction with Diffusion Models](https://mlsanity.com/paper/2304.02198/) (2023)
- [End-to-End Full-Atom Antibody Design](https://mlsanity.com/paper/2302.00203/) (2023)
- [Graph Denoising Diffusion for Inverse Protein Folding](https://mlsanity.com/paper/2306.16819/) (2023)
- [Improved motif-scaffolding with SE(3) flow matching](https://mlsanity.com/paper/2401.04082/) (2024)
- [PepTune: De Novo Generation of Therapeutic Peptides with Multi-Objective-Guided Discrete Diffusion](https://mlsanity.com/paper/2412.17780/) (2024)
- [State-specific protein-ligand complex structure prediction with a multi-scale deep generative model](https://mlsanity.com/paper/2209.15171/) (2022)
- [AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodies](https://mlsanity.com/paper/2308.05027/) (2023)
- [Full-Atom Peptide Design based on Multi-modal Flow Matching](https://mlsanity.com/paper/2406.00735/) (2024)
- [Antigen-Specific Antibody Design via Direct Energy-based Preference Optimization](https://mlsanity.com/paper/2403.16576/) (2024)
- [DecompOpt: Controllable and Decomposed Diffusion Models for Structure-based Molecular Optimization](https://mlsanity.com/paper/2403.13829/) (2024)
- [PPFlow: Target-aware Peptide Design with Torsional Flow Matching](https://mlsanity.com/paper/2405.06642/) (2024)
- [ProteinBench: A Holistic Evaluation of Protein Foundation Models](https://mlsanity.com/paper/2409.06744/) (2024)
- [Re-Dock: Towards Flexible and Realistic Molecular Docking with Diffusion Bridge](https://mlsanity.com/paper/2402.11459/) (2024)
- [De novo protein design using geometric vector field networks](https://mlsanity.com/paper/2310.11802/) (2023)

## Built on by (most cited first, 2 of 2)

- [MacroGuide: Topological Guidance for Macrocycle Generation](https://mlsanity.com/paper/2602.14977/) (2026)
- [FAR-DPO: Feasibility-Aware and Robust Direct Preference Optimization for Cyclic Peptide Design](https://mlsanity.com/paper/2608.19808/) (2026)

## Abstract (arXiv)

Cyclic peptides offer inherent advantages in pharmaceuticals. For example, cyclic peptides are more resistant to enzymatic hydrolysis compared to linear peptides and usually exhibit excellent stability and affinity. Although deep generative models have achieved great success in linear peptide design, several challenges prevent the development of computational methods for designing diverse types of cyclic peptides. These challenges include the scarcity of 3D structural data on target proteins and associated cyclic peptide ligands, the geometric constraints that cyclization imposes, and the involvement of non-canonical amino acids in cyclization. To address the above challenges, we introduce CpSDE, which consists of two key components: AtomSDE, a generative structure prediction model based on harmonic SDE, and ResRouter, a residue type predictor. Utilizing a routed sampling algorithm that alternates between these two models to iteratively update sequences and structures, CpSDE facilitates the generation of cyclic peptides. By employing explicit all-atom and bond modeling, CpSDE overcomes existing data limitations and is proficient in designing a wide variety of cyclic peptides. Our experimental results demonstrate that the cyclic peptides designed by our method exhibit reliable stability and affinity.