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

arXiv: https://arxiv.org/abs/2602.16634 · HTML: https://mlsanity.com/paper/2602.16634/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 20 of its 110 references that are in the map.
- First posted on arXiv 18 Feb 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, 20 of 20)

- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [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)
- [Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching](https://mlsanity.com/paper/2504.11713/) (2025)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamics](https://mlsanity.com/paper/2302.01170/) (2023)
- [Generative Modeling of Molecular Dynamics Trajectories](https://mlsanity.com/paper/2409.17808/) (2024)
- [Navigating protein landscapes with a machine-learned transferable coarse-grained model](https://mlsanity.com/paper/2310.18278/) (2023)
- [Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models](https://mlsanity.com/paper/2506.17139/) (2025)
- [DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2509.21655/) (2025)
- [GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Models](https://mlsanity.com/paper/2509.25170/) (2025)
- [Implicit Transfer Operator Learning: Multiple Time-Resolution Surrogates for Molecular Dynamics](https://mlsanity.com/paper/2305.18046/) (2023)
- [Enhancing Diffusion-Based Sampling with Molecular Collective Variables](https://mlsanity.com/paper/2510.11923/) (2025)
- [Unlocking hidden biomolecular conformational landscapes in diffusion models at inference time](https://mlsanity.com/paper/2512.03312/) (2025)
- [Combine Umbrella Sampling with Integrated Tempering Method for Efficient and Accurate Calculation of Free Energy Changes of Complex Energy Surface](https://mlsanity.com/paper/1307.1864/) (2013)

## Built on by (most cited first, 13 of 13)

- [Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps](https://mlsanity.com/paper/2606.29110/) (2026)
- [Differentiable free energy surface: a variational approach to directly observing rare events using generative deep-learning models](https://mlsanity.com/paper/2604.09769/) (2026)
- [Generative Pseudo-Force Fields for Molecular Generation](https://mlsanity.com/paper/2605.19050/) (2026)
- [Catastrophic Compositional Generation: Why Vanilla Diffusion Models Fail to Extrapolate](https://mlsanity.com/paper/2606.23920/) (2026)
- [METALICA: METAdynamics and repLICA exchange for enhanced diffusion sampling](https://mlsanity.com/paper/2609.17823/) (2026)
- [Learning Implicit Bias in Generative Spaces for Accelerating Protein Dynamics Emulation](https://mlsanity.com/paper/2606.01833/) (2026)
- [Guided Discovery of New Behaviors using Diffusion Policies](https://mlsanity.com/paper/2606.08743/) (2026)
- [Unsupervised Thermodynamics of Molecular Diffusion Models: Action-Operator Semantics and Auditable Free-Energy Readout](https://mlsanity.com/paper/2606.30687/) (2026)
- [Diffeomorphic Optimization](https://mlsanity.com/paper/2607.00947/) (2026)
- [Stochastic Control Policies for Robust Molecular Transition Path Sampling](https://mlsanity.com/paper/2608.13800/) (2026)
- [Error-Corrected Inference-Time Scaling for Imperfect Diffusion Models](https://mlsanity.com/paper/2610.01933/) (2026)
- [ENCORE: Exact Non-equilibrium COntrol with Replica Exchange for Diffusion Generation](https://mlsanity.com/paper/2610.02538/) (2026)
- [Steering Diffusion Models to Rare Events with Sequential Monte Carlo](https://mlsanity.com/paper/2610.08652/) (2026)

## Abstract (arXiv)

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 DeltaG-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.