# DiAMoNDBack: Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping of Cα Protein Traces

arXiv: https://arxiv.org/abs/2307.12451 · HTML: https://mlsanity.com/paper/2307.12451/

## Key facts

- Cited by 10 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 27 of its 99 references that are in the map.
- First posted on arXiv 23 Jul 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, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [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)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [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)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [Machine Learning of coarse-grained Molecular Dynamics Force Fields](https://mlsanity.com/paper/1812.01736/) (2018)
- [Coarse Graining Molecular Dynamics with Graph Neural Networks](https://mlsanity.com/paper/2007.11412/) (2020)
- [ProteinNet: a standardized data set for machine learning of protein structure](https://mlsanity.com/paper/1902.00249/) (2019)
- [Machine Learning Coarse-Grained Potentials of Protein Thermodynamics](https://mlsanity.com/paper/2212.07492/) (2022)
- [Flow-matching -- efficient coarse-graining of molecular dynamics without forces](https://mlsanity.com/paper/2203.11167/) (2022)
- [Coarse-Graining Auto-Encoders for Molecular Dynamics](https://mlsanity.com/paper/1812.02706/) (2018)
- [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)
- [High-resolution Markov state models for the dynamics of Trp-cage miniprotein constructed over slow folding modes identified by state-free reversible VAMPnets](https://mlsanity.com/paper/1906.04890/) (2019)
- [Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics](https://mlsanity.com/paper/2302.07071/) (2023)
- [Contrastive Learning of Coarse-Grained Force Fields](https://mlsanity.com/paper/2205.10861/) (2022)
- [Discovery of Self-Assembling π-Conjugated Peptides by Active Learning-Directed Coarse-Grained Molecular Simulation](https://mlsanity.com/paper/2002.01563/) (2020)
- [SidechainNet: An All-Atom Protein Structure Dataset for Machine Learning](https://mlsanity.com/paper/2010.08162/) (2020)

## Built on by (most cited first, 10 of 10)

- [Backdiff: a diffusion model for generalized transferable protein backmapping](https://mlsanity.com/paper/2310.01768/) (2023)
- [Split-Flows: Measure Transport and Information Loss Across Molecular Resolutions](https://mlsanity.com/paper/2511.01464/) (2025)
- [Constraint Decoupled Latent Diffusion for Protein Backmapping](https://mlsanity.com/paper/2410.13264/) (2024)
- [Energy-Based Coarse-Graining in Molecular Dynamics: A Flow-Based Framework without Data](https://mlsanity.com/paper/2504.20940/) (2025)
- [Sifting through the Noise: A Survey of Diffusion Probabilistic Models and Their Applications to Biomolecules](https://mlsanity.com/paper/2406.01622/) (2024)
- [An Iterative Framework for Generative Backmapping of Coarse Grained Proteins](https://mlsanity.com/paper/2505.18082/) (2025)
- [HEroBM: a deep equivariant graph neural network for universal backmapping from coarse-grained to all-atom representations](https://mlsanity.com/paper/2404.16911/) (2024)
- [Operator Forces For Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2506.19628/) (2025)
- [GEqTrain: A Configuration-Driven Framework for Retargeting Equivariant Graph Neural Networks Across 3D Scientific Tasks](https://mlsanity.com/paper/2607.19083/) (2026)
- [Recovering molecules from coarse-grained beads: free-energy-conditioned generative backmapping across chemical space](https://mlsanity.com/paper/2609.04432/) (2026)

## Abstract (arXiv)

Coarse-grained molecular models of proteins permit access to length and time scales unattainable by all-atom models and the simulation of processes that occur on long-time scales such as aggregation and folding. The reduced resolution realizes computational accelerations but an atomistic representation can be vital for a complete understanding of mechanistic details. Backmapping is the process of restoring all-atom resolution to coarse-grained molecular models. In this work, we report DiAMoNDBack (Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping) as an autoregressive denoising diffusion probability model to restore all-atom details to coarse-grained protein representations retaining only Cα coordinates. The autoregressive generation process proceeds from the protein N-terminus to C-terminus in a residue-by-residue fashion conditioned on the Cα trace and previously backmapped backbone and side chain atoms within the local neighborhood. The local and autoregressive nature of our model makes it transferable between proteins. The stochastic nature of the denoising diffusion process means that the model generates a realistic ensemble of backbone and side chain all-atom configurations consistent with the coarse-grained Cα trace. We train DiAMoNDBack over 65k+ structures from Protein Data Bank (PDB) and validate it in applications to a hold-out PDB test set, intrinsically-disordered protein structures from the Protein Ensemble Database (PED), molecular dynamics simulations of fast-folding mini-proteins from DE Shaw Research, and coarse-grained simulation data. We achieve state-of-the-art reconstruction performance in terms of correct bond formation, avoidance of side chain clashes, and diversity of the generated side chain configurational states. We make DiAMoNDBack model publicly available as a free and open source Python package.