# Inference-time optimization for experiment-grounded protein ensemble generation

arXiv: https://arxiv.org/abs/2602.24007 · HTML: https://mlsanity.com/paper/2602.24007/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 66 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Builds on (most cited first, 11 of 11)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Iterated Denoising Energy Matching for Sampling from Boltzmann Densities](https://mlsanity.com/paper/2402.06121/) (2024)
- [AlphaFold Meets Flow Matching for Generating Protein Ensembles](https://mlsanity.com/paper/2402.04845/) (2024)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Stochastic Bias-Reduced Gradient Methods](https://mlsanity.com/paper/2106.09481/) (2021)
- [Multiscale guidance of protein structure prediction with heterogeneous cryo-EM data](https://mlsanity.com/paper/2506.04490/) (2025)
- [Generative modeling of protein ensembles guided by crystallographic electron densities](https://mlsanity.com/paper/2412.13223/) (2024)
- [Unlocking hidden biomolecular conformational landscapes in diffusion models at inference time](https://mlsanity.com/paper/2512.03312/) (2025)

## Built on by (most cited first, 2 of 2)

- [ConforNets: Latents-Based Conformational Control in OpenFold3](https://mlsanity.com/paper/2604.18559/) (2026)
- [Fold'EM: Direct atomic structure inference from Cryo-EM particles](https://mlsanity.com/paper/2610.01358/) (2026)

## Abstract (arXiv)

Protein function relies on dynamic conformational ensembles, yet current generative models like AlphaFold3 often fail to produce ensembles that match experimental data. Recent experiment-guided generators attempt to address this by steering the reverse diffusion process. However, these methods are limited by fixed sampling horizons and sensitivity to initialization, often yielding thermodynamically implausible results. We introduce a general inference-time optimization framework to solve these challenges. First, we optimize over latent representations to maximize ensemble log-likelihood, rather than perturbing structures post hoc. This approach eliminates dependence on diffusion length, removes initialization bias, and easily incorporates external constraints. Second, we present novel sampling schemes for drawing Boltzmann-weighted ensembles. By combining structural priors from AlphaFold3 with force-field-based priors, we sample from their product distribution while balancing experimental likelihoods. Our results show that this framework consistently outperforms state-of-the-art guidance, improving diversity, physical energy, and agreement with data in X-ray crystallography and NMR, often fitting the experimental data better than deposited PDB structures. Finally, inference-time optimization experiments maximizing ipTM scores reveal that perturbing AlphaFold3 embeddings can artificially inflate model confidence. This exposes a vulnerability in current design metrics, whose mitigation could offer a pathway to reduce false discovery rates in binder engineering.