# Constraint Decoupled Latent Diffusion for Protein Backmapping

arXiv: https://arxiv.org/abs/2410.13264 · HTML: https://mlsanity.com/paper/2410.13264/

## Key facts

- Cited by 2 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 23 of its 59 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## 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, 23 of 23)

- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [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)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [AlphaFold Meets Flow Matching for Generating Protein Ensembles](https://mlsanity.com/paper/2402.04845/) (2024)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [Unsupervised Learning of Group Invariant and Equivariant Representations](https://mlsanity.com/paper/2202.07559/) (2022)
- [Machine Learning Coarse-Grained Potentials of Protein Thermodynamics](https://mlsanity.com/paper/2212.07492/) (2022)
- [Coarse-Graining Auto-Encoders for Molecular Dynamics](https://mlsanity.com/paper/1812.02706/) (2018)
- [A Latent Diffusion Model for Protein Structure Generation](https://mlsanity.com/paper/2305.04120/) (2023)
- [Coarse-to-Fine: a Hierarchical Diffusion Model for Molecule Generation in 3D](https://mlsanity.com/paper/2305.13266/) (2023)
- [FoldToken: Learning Protein Language via Vector Quantization and Beyond](https://mlsanity.com/paper/2403.09673/) (2024)
- [Generative Coarse-Graining of Molecular Conformations](https://mlsanity.com/paper/2201.12176/) (2022)
- [Chemically Transferable Generative Backmapping of Coarse-Grained Proteins](https://mlsanity.com/paper/2303.01569/) (2023)
- [DiAMoNDBack: Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping of Cα Protein Traces](https://mlsanity.com/paper/2307.12451/) (2023)
- [SidechainNet: An All-Atom Protein Structure Dataset for Machine Learning](https://mlsanity.com/paper/2010.08162/) (2020)
- [Backdiff: a diffusion model for generalized transferable protein backmapping](https://mlsanity.com/paper/2310.01768/) (2023)

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

- [An Iterative Framework for Generative Backmapping of Coarse Grained Proteins](https://mlsanity.com/paper/2505.18082/) (2025)
- [GEqTrain: A Configuration-Driven Framework for Retargeting Equivariant Graph Neural Networks Across 3D Scientific Tasks](https://mlsanity.com/paper/2607.19083/) (2026)

## Abstract (arXiv)

Coarse-grained (CG) molecular dynamics simulations enable efficient exploration of protein conformational ensembles. However, reconstructing atomic details from CG structures (backmapping) remains a challenging problem. Current approaches face an inherent trade-off between maintaining atomistic accuracy and exploring diverse conformations, often necessitating complex constraint handling or extensive refinement steps. To address these challenges, we introduce a novel two-stage framework, named CODLAD (COnstraint Decoupled LAtent Diffusion). This framework first compresses atomic structures into discrete latent representations, explicitly embedding structural constraints, thereby decoupling constraint handling from generation. Subsequently, it performs efficient denoising diffusion in this latent space to produce structurally valid and diverse all-atom conformations. Comprehensive evaluations on diverse protein datasets demonstrate that CODLAD achieves state-of-the-art performance in atomistic accuracy, conformational diversity, and computational efficiency while exhibiting strong generalization across different protein systems. Code is available at https://github.com/xiaoxiaokuye/CODLAD.