# Jeffreys Flow: Robust Boltzmann Generators for Rare Event Sampling via Parallel Tempering Distillation

arXiv: https://arxiv.org/abs/2604.05303 · HTML: https://mlsanity.com/paper/2604.05303/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 68 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 23 of 23)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
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- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Conditional Image Generation with Score-Based Diffusion Models](https://mlsanity.com/paper/2111.13606/) (2021)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Stochastic Variance Reduction for Nonconvex Optimization](https://mlsanity.com/paper/1603.06160/) (2016)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [Continual Repeated Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2201.13117/) (2022)
- [EM Distillation for One-step Diffusion Models](https://mlsanity.com/paper/2405.16852/) (2024)
- [Simple and Fast Distillation of Diffusion Models](https://mlsanity.com/paper/2409.19681/) (2024)
- [MoFlow: One-Step Flow Matching for Human Trajectory Forecasting via Implicit Maximum Likelihood Estimation based Distillation](https://mlsanity.com/paper/2503.09950/) (2025)
- [Normalizing flows for lattice gauge theory in arbitrary space-time dimension](https://mlsanity.com/paper/2305.02402/) (2023)
- [Scalable Boltzmann Generators for equilibrium sampling of large-scale materials](https://mlsanity.com/paper/2509.25486/) (2025)
- [Accelerating Convergence of Replica Exchange Stochastic Gradient MCMC via Variance Reduction](https://mlsanity.com/paper/2010.01084/) (2020)
- [Non-reversible Parallel Tempering for Deep Posterior Approximation](https://mlsanity.com/paper/2211.10837/) (2022)
- [Mitigating mode collapse in normalizing flows by annealing with an adaptive schedule: Application to parameter estimation](https://mlsanity.com/paper/2505.03652/) (2025)
- [Efficient Multimodal Sampling via Tempered Distribution Flow](https://mlsanity.com/paper/2304.03933/) (2023)
- [Flow to Rare Events: An Application of Normalizing Flow in Temporal Importance Sampling for Automated Vehicle Validation](https://mlsanity.com/paper/2407.07320/) (2024)

## Abstract (arXiv)

Sampling physical systems with rough energy landscapes is hindered by rare events and metastable trapping. While Boltzmann generators already offer a solution, their reliance on the reverse Kullback--Leibler divergence frequently induces catastrophic mode collapse, missing specific modes in multi-modal distributions. Here, we introduce the Jeffreys Flow, a robust generative framework that mitigates this failure by distilling empirical sampling data from Parallel Tempering trajectories using the symmetric Jeffreys divergence. This formulation effectively balances local target-seeking precision with global modes coverage. We show that minimizing Jeffreys divergence suppresses mode collapse and structurally corrects inherent inaccuracies via distillation of the empirical reference data. We demonstrate the framework's scalability and accuracy on highly non-convex multidimensional benchmarks, including the systematic correction of stochastic gradient biases in Replica Exchange Stochastic Gradient Langevin Dynamics and the massive acceleration of exact importance sampling in Path Integral Monte Carlo for quantum thermal states.