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Torsion-Space Diffusion for Protein Backbone Generation with Geometric Refinement

Lakshaditya Singh, Adwait Shelke, Divyansh Agrawal

TL;DR

This work tackles the challenge of generating physically valid protein backbones by shifting diffusion from Cartesian space to torsion angles, ensuring local geometry by construction. It introduces a Transformer-based denoiser operating on torsion angles $(\phi,\psi,\omega)$, a differentiable forward-kinematics module that fixes backbone bond lengths at $b=3.8$Å, and an iterative Radius of Gyration refinement to improve global compactness. On standard PDB backbones, the method achieves 100% bond-length accuracy and substantially improves global structure, reducing Rg error from 70% to 18.6% relative to Cartesian baselines. The result is a scalable, efficient framework for geometrically valid backbone generation that provides a promising path toward full-atom protein design.

Abstract

Designing new protein structures is fundamental to computational biology, enabling advances in therapeutic molecule discovery and enzyme engineering. Existing diffusion-based generative models typically operate in Cartesian coordinate space, where adding noise disrupts strict geometric constraints such as fixed bond lengths and angles, often producing physically invalid structures. To address this limitation, we propose a Torsion-Space Diffusion Model that generates protein backbones by denoising torsion angles, ensuring perfect local geometry by construction. A differentiable forward-kinematics module reconstructs 3D coordinates with fixed 3.8 Angstrom backbone bond lengths while a constrained post-processing refinement optimizes global compactness via Radius of Gyration (Rg) correction, without violating bond constraints. Experiments on standard PDB proteins demonstrate 100% bond-length accuracy and significantly improved structural compactness, reducing Rg error from 70% to 18.6% compared to Cartesian diffusion baselines. Overall, this hybrid torsion-diffusion plus geometric-refinement framework generates physically valid and compact protein backbones, providing a promising path toward full-atom protein generation.

Torsion-Space Diffusion for Protein Backbone Generation with Geometric Refinement

TL;DR

This work tackles the challenge of generating physically valid protein backbones by shifting diffusion from Cartesian space to torsion angles, ensuring local geometry by construction. It introduces a Transformer-based denoiser operating on torsion angles , a differentiable forward-kinematics module that fixes backbone bond lengths at Å, and an iterative Radius of Gyration refinement to improve global compactness. On standard PDB backbones, the method achieves 100% bond-length accuracy and substantially improves global structure, reducing Rg error from 70% to 18.6% relative to Cartesian baselines. The result is a scalable, efficient framework for geometrically valid backbone generation that provides a promising path toward full-atom protein design.

Abstract

Designing new protein structures is fundamental to computational biology, enabling advances in therapeutic molecule discovery and enzyme engineering. Existing diffusion-based generative models typically operate in Cartesian coordinate space, where adding noise disrupts strict geometric constraints such as fixed bond lengths and angles, often producing physically invalid structures. To address this limitation, we propose a Torsion-Space Diffusion Model that generates protein backbones by denoising torsion angles, ensuring perfect local geometry by construction. A differentiable forward-kinematics module reconstructs 3D coordinates with fixed 3.8 Angstrom backbone bond lengths while a constrained post-processing refinement optimizes global compactness via Radius of Gyration (Rg) correction, without violating bond constraints. Experiments on standard PDB proteins demonstrate 100% bond-length accuracy and significantly improved structural compactness, reducing Rg error from 70% to 18.6% compared to Cartesian diffusion baselines. Overall, this hybrid torsion-diffusion plus geometric-refinement framework generates physically valid and compact protein backbones, providing a promising path toward full-atom protein generation.

Paper Structure

This paper contains 24 sections, 2 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Generative Models for Proteins
  4. Diffusion Models
  5. Methodology
  6. Data Preparation
  7. Torsion-Space Diffusion Model
  8. Forward Process
  9. Denoising Network Architecture
  10. Geometric Reconstruction
  11. Constrained Refinement Algorithm
  12. Experiments and Results
  13. Experimental Setup
  14. Dataset
  15. Training Hyperparameters
  16. ...and 9 more sections

Figures (4)

  • Figure 1: Comparison between the baseline Cartesian model and our proposed Torsion-Space model. The top row looks at Radius of Gyration (Rg), Bond Lengths, and Quality Scores. The bottom row shows bond length distributions and error reduction. Our model hits 100% bond accuracy and matches Rg much better.
  • Figure 2: Training loss curves showing the convergence of the model. Both the total loss (blue) and physics-based loss (green) drop, which tells us the model is successfully learning the torsion distribution.
  • Figure 3: Detailed bond length analysis. Note how tightly the bond lengths cluster around the target 3.8Å, indicating perfect geometric validity.
  • Figure 4: 3D visualization of the generated protein backbones. The structures show coherent folding patterns and valid local geometry, with visible secondary structure elements.