# Inference-Time Projection for Physically Valid Biomolecular Diffusion Models

arXiv: https://arxiv.org/abs/2610.07037 · HTML: https://mlsanity.com/paper/2610.07037/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## 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, 17 of 17)

- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [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)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [Protein structure generation via folding diffusion](https://mlsanity.com/paper/2209.15611/) (2022)
- [Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2205.15019/) (2022)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [Smoothed Energy Guidance: Guiding Diffusion Models with Reduced Energy Curvature of Attention](https://mlsanity.com/paper/2408.00760/) (2024)
- [OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials](https://mlsanity.com/paper/2310.03121/) (2023)
- [Constrained Diffusion with Trust Sampling](https://mlsanity.com/paper/2411.10932/) (2024)
- [Constrained Diffusion for Protein Design with Hard Structural Constraints](https://mlsanity.com/paper/2510.14989/) (2025)
- [Physically Valid Biomolecular Interaction Modeling with Gauss-Seidel Projection](https://mlsanity.com/paper/2510.08946/) (2025)
- [Predict-Project-Renoise: Sampling Diffusion Models under Hard Constraints](https://mlsanity.com/paper/2601.21033/) (2026)

## Abstract (arXiv)

AlphaFold 3-style cofolding models predict biomolecular complexes with high structural accuracy, yet a large fraction of their outputs are physically invalid: chains overlap at interfaces, ligand bond lengths and angles are distorted, rings are non-planar, and stereocentres are inverted. Current approaches either steer the sampler with physics-informed potentials, which multiplies sampling cost and memory overhead making inference impossible on large complexes, or finetune the model, costing time and tying the fix to one architecture. We observe that, unlike structural accuracy, physical validity is fully verifiable at inference time from quantities the sampler already holds. We therefore treat physical validity as a constrained inference problem and introduce two closed-form projection operators applied to the diffusion model's denoised clean-coordinate estimate, hatx0: an inter-chain van der Waals projection that pushes apart the most severely clashing atom pairs, and a ligand distance-geometry projection that restores bond lengths, angles, internal contacts, planarity and chirality. Both operators are local, sparse and displacement-capped, require no network evaluations, gradients or importance sampling, and leave the denoiser and its weights untouched, so they can be dropped into any AF3-style sampler without retraining. Applied to two independently developed models, Boltz-2 and OpenFold-3, across five benchmarks (CASP15, CASP16, the PoseBusters monomer and complex sets, and the Boltz physical-validity test set), our method recovers perfect physical validity while preserving structural-accuracy and ligand-placement metrics. These gains are achieved with negligible runtime and memory overhead, providing a practical, model-agnostic route to physically valid all-atom structure prediction.