Enhanced Diffusion Sampling: Efficient Rare Event Sampling and Free Energy Calculation with Diffusion Models

Yu Xie, Ludwig Winkler, Lixin Sun, Sarah Lewis, Adam Foster, Jose Jimenez-Luna, Tim Hempel, Michael Gastegger, Yaoyi Chen, Iryna Zaporozhets, Cecilia Clementi, Christopher M. Bishop, Frank Noe

Keywords: Enhanced Sampling, Diffusion Models

TL;DR: We extend diffusion model equilibrium samplers with enhanced sampling algorithms for free energy estimations.

Abstract:

The rare-event sampling problem has long been the central limiting factor in molecular dynamics (MD), especially in biomolecular simulation. Recently, diffusion models such as BioEmu have emerged as powerful equilibrium samplers that generate independent samples from complex molecular distributions, eliminating the cost of sampling rare transition events. However, a sampling problem remains when computing observables that rely on states which are rare in equilibrium, for example folding free energies.
Here, we introduce enhanced diffusion sampling, enabling efficient exploration of rare‑event regions while preserving unbiased thermodynamic estimators. The key idea is to perform quantitatively accurate steering protocols to generate biased ensembles and subsequently recover equilibrium statistics via exact reweighting. We instantiate our framework in three algorithms: UmbrellaDiff (umbrella sampling with diffusion models), MetaDiff (a batchwise analogue for metadynamics), and $\Delta$G‑Diff (free‑energy differences via tilted ensembles).
Across toy systems, protein folding landscapes and folding free energies, our methods achieve fast, accurate, and scalable estimation of equilibrium properties within GPU-minutes to hours per system---closing the rare‑event sampling gap that remained after the advent of diffusion‑model equilibrium samplers.

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Submission Number: 55