Torsion-Space Diffusion for Protein Backbone Generation with Geometric Refinement

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.