Physically Valid Biomolecular Interaction Modeling with Gauss-Seidel Projection

Biomolecular interaction modeling has been substantially advanced by foundation models, yet they often produce all-atom structures that violate basic steric feasibility. We address this limitation by enforcing physical validity as a strict constraint during both training and inference with a unified module. At its core is a differentiable projection that maps the provisional atom coordinates from the diffusion model to the nearest physically valid configuration. This projection is achieved using a Gauss-Seidel scheme, which exploits the locality and sparsity of the constraints to ensure stable and fast convergence at scale. By implicit differentiation to obtain gradients, our module integrates seamlessly into existing frameworks for end-to-end finetuning. With our Gauss-Seidel projection module in place, two denoising steps are sufficient to produce biomolecular complexes that are both physically valid and structurally accurate. Across six benchmarks, our $2$-step model achieves the same structural accuracy as state-of-the-art $200$-step diffusion baselines, delivering ${\sim}10\times$ wall-clock speedups while guaranteeing physical validity. The code is available at https://github.com/chensiyuan030105/ProteinGS.git.