# Free energy Estimation on Any State Space

arXiv: https://arxiv.org/abs/2605.31063 · HTML: https://mlsanity.com/paper/2605.31063/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 57 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 17 of 17)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [NETS: A Non-Equilibrium Transport Sampler](https://mlsanity.com/paper/2410.02711/) (2024)
- [Learning Interpolations between Boltzmann Densities](https://mlsanity.com/paper/2301.07388/) (2023)
- [LEAPS: A discrete neural sampler via locally equivariant networks](https://mlsanity.com/paper/2502.10843/) (2025)
- [Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions](https://mlsanity.com/paper/2302.07261/) (2023)
- [Underdamped Diffusion Bridges with Applications to Sampling](https://mlsanity.com/paper/2503.01006/) (2025)
- [Generative Modeling with Phase Stochastic Bridges](https://mlsanity.com/paper/2310.07805/) (2023)
- [Diffuse Everything: Multimodal Diffusion Models on Arbitrary State Spaces](https://mlsanity.com/paper/2506.07903/) (2025)
- [Accelerated Parallel Tempering via Neural Transports](https://mlsanity.com/paper/2502.10328/) (2025)
- [A Unified Approach to Analysis and Design of Denoising Markov Models](https://mlsanity.com/paper/2504.01938/) (2025)
- [Momentum Multi-Marginal Schr"odinger Bridge Matching](https://mlsanity.com/paper/2506.10168/) (2025)
- [Solvation Free Energies from Neural Thermodynamic Integration](https://mlsanity.com/paper/2410.15815/) (2024)
- [Assessing generative modeling approaches for free energy estimates in condensed matter](https://mlsanity.com/paper/2512.23930/) (2025)

## Built on by (most cited first, 1 of 1)

- [Fixed-point neural samplers on discrete spaces](https://mlsanity.com/paper/2610.01739/) (2026)

## Abstract (arXiv)

Free energy estimation is a fundamental yet challenging problem, from physics to statistics. Classical approaches rely on thermodynamic transformations, ranging from direct estimation, quasistatic integration, to finite-time averaging. Recent work [He and Du et al., 2025] learns neural transports to significantly accelerate the efficiency in the finite-time regime. In this paper, we generalize this framework to arbitrary state spaces. Building on this view, we develop a generalized neural transport learning approach for efficient estimation. Experiments validate the effectiveness and efficiency of the proposed method beyond continuous settings, extending to discrete and multimodal spaces as well as autoregressive settings. Beyond free energy estimation, we establish algebraic identities and reveal a group-theoretic structure linking infinitesimal time reversal and generalized Doob's h-transforms, showing that their compositions form a generalized dihedral group.