# Antibody Design and Optimization with Multi-scale Equivariant Graph Diffusion Models for Accurate Complex Antigen Binding

arXiv: https://arxiv.org/abs/2506.20957 · HTML: https://mlsanity.com/paper/2506.20957/

## Key facts

- Cited by 9 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 35 references that are in the map.
- First posted on arXiv 26 Jun 2025.

## 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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Iterative Refinement Graph Neural Network for Antibody Sequence-Structure Co-design](https://mlsanity.com/paper/2110.04624/) (2021)
- [Conditional Antibody Design as 3D Equivariant Graph Translation](https://mlsanity.com/paper/2208.06073/) (2022)
- [Deciphering antibody affinity maturation with language models and weakly supervised learning](https://mlsanity.com/paper/2112.07782/) (2021)
- [AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodies](https://mlsanity.com/paper/2308.05027/) (2023)
- [Molecular geometric deep learning](https://mlsanity.com/paper/2306.15065/) (2023)
- [Improving Antibody Design with Force-Guided Sampling in Diffusion Models](https://mlsanity.com/paper/2406.05832/) (2024)

## Built on by (most cited first, 9 of 9)

- [CHIMERA-Bench: A Benchmark Dataset for Epitope-Specific Antibody Design](https://mlsanity.com/paper/2603.13431/) (2026)
- [Transport-Coupled Bayesian Flows for Molecular Graph Generation](https://mlsanity.com/paper/2510.10211/) (2025)
- [PCEvo: Path-Consistent Molecular Representation via Virtual Evolutionary](https://mlsanity.com/paper/2601.19257/) (2026)
- [Variational Bayesian Flow Network for Graph Generation](https://mlsanity.com/paper/2601.22524/) (2026)
- [FP-AbDiff: Improving Score-based Antibody Design by Capturing Nonequilibrium Dynamics through the Underlying Fokker-Planck Equation](https://mlsanity.com/paper/2511.03113/) (2025)
- [From Single-Step Edit Response to Multi-Step Molecular Optimization](https://mlsanity.com/paper/2605.10035/) (2026)
- [EvoStruct: Bridging Evolutionary and Structural Priors for Antibody CDR Design via Protein Language Model Adaptation](https://mlsanity.com/paper/2605.21485/) (2026)
- [ConTact: Contact-First Antibody CDR Design via Explicit Interface Reasoning](https://mlsanity.com/paper/2605.21600/) (2026)
- [AgForce Enables Antigen-conditioned Generative Antibody Design](https://mlsanity.com/paper/2605.21610/) (2026)

## Abstract (arXiv)

Antibody design remains a critical challenge in therapeutic and diagnostic development, particularly for complex antigens with diverse binding interfaces. Current computational methods face two main limitations: (1) capturing geometric features while preserving symmetries, and (2) generalizing novel antigen interfaces. Despite recent advancements, these methods often fail to accurately capture molecular interactions and maintain structural integrity. To address these challenges, we propose AbMEGD, an end-to-end framework integrating Multi-scale Equivariant Graph Diffusion for antibody sequence and structure co-design. Leveraging advanced geometric deep learning, AbMEGD combines atomic-level geometric features with residue-level embeddings, capturing local atomic details and global sequence-structure interactions. Its E(3)-equivariant diffusion method ensures geometric precision, computational efficiency, and robust generalizability for complex antigens. Furthermore, experiments using the SAbDab database demonstrate a 10.13% increase in amino acid recovery, 3.32% rise in improvement percentage, and a 0.062~AA reduction in root mean square deviation within the critical CDR-H3 region compared to DiffAb, a leading antibody design model. These results highlight AbMEGD's ability to balance structural integrity with improved functionality, establishing a new benchmark for sequence-structure co-design and affinity optimization. The code is available at: https://github.com/Patrick221215/AbMEGD.