# Physically Valid Biomolecular Interaction Modeling with Gauss-Seidel Projection

arXiv: https://arxiv.org/abs/2510.08946 · HTML: https://mlsanity.com/paper/2510.08946/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 47 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Builds on (most cited first, 12 of 12)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Directly Fine-Tuning Diffusion Models on Differentiable Rewards](https://mlsanity.com/paper/2309.17400/) (2023)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Riemannian Score-Based Generative Modelling](https://mlsanity.com/paper/2202.02763/) (2022)
- [Manifold Diffusion Fields](https://mlsanity.com/paper/2305.15586/) (2023)
- [Vertex Block Descent](https://mlsanity.com/paper/2403.06321/) (2024)

## Built on by (most cited first, 4 of 4)

- [SnareNet: Flexible Repair Layers for Neural Networks with Hard Constraints](https://mlsanity.com/paper/2602.09317/) (2026)
- [Learning Structure, Energy, and Dynamics: A Survey of Artificial Intelligence for Protein Dynamics](https://mlsanity.com/paper/2604.25244/) (2026)
- [Differentiate the Solver, Not the Equation: Reverse-Sweep Adjoints for Block Implicit Simulation](https://mlsanity.com/paper/2608.08559/) (2026)
- [Inference-Time Projection for Physically Valid Biomolecular Diffusion Models](https://mlsanity.com/paper/2610.07037/) (2026)

## Abstract (arXiv)

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 uniffed module. At its core is a differentiable projection that maps the provisional atom coordinates from the diffusion model to the nearest physically valid conffguration. 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 ffnetuning. With our Gauss-Seidel projection module in place, two denoising steps are sufffcient 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 approximately 10 times faster wall-clock speed while guaranteeing physical validity. The code is available at https://github.com/chensiyuan030105/ProteinGS.git.