# Diffusion-based Annealed Boltzmann Generators : benefits, pitfalls and hopes

arXiv: https://arxiv.org/abs/2601.21026 · HTML: https://mlsanity.com/paper/2601.21026/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 118 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Builds on (most cited first, 6 of 6)

- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Review](https://mlsanity.com/paper/2407.13734/) (2024)
- [Blindness of score-based methods to isolated components and mixing proportions](https://mlsanity.com/paper/2008.10087/) (2020)
- [Diffusion-PINN Sampler](https://mlsanity.com/paper/2410.15336/) (2024)
- [Bootstrap Your Flow](https://mlsanity.com/paper/2111.11510/) (2021)

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

- [Markov Chain Monte Carlo with Diffusion Paths](https://mlsanity.com/paper/2607.11631/) (2026)
- [Error-Corrected Inference-Time Scaling for Imperfect Diffusion Models](https://mlsanity.com/paper/2610.01933/) (2026)

## Abstract (arXiv)

Sampling configurations at thermodynamic equilibrium is a central challenge in statistical physics. Boltzmann Generators (BGs) tackle it by combining a generative model with a Monte Carlo (MC) correction step to obtain asymptotically unbiased samples from an unnormalized target. Most current BGs use classic MC mechanisms such as importance sampling, which both require tractable likelihoods from the backbone model and scale poorly in high-dimensional, multi-modal targets. We study BGs built on annealed Monte Carlo (aMC), which is designed to overcome these limitations by bridging a simple reference to the target through a sequence of intermediate densities. Diffusion models (DMs) are powerful generative models and have already been incorporated into aMC-based recalibration schemes via the diffusion-induced density path, making them appealing backbones for aMC-BGs. We provide an empirical meta-analysis of DM-based aMC-BGs on controlled multi-modal Gaussian mixtures (varying mode separation, number of modes, and dimension), explicitly disentangling inference effects from learning effects by comparing (i) a perfectly learned DM and (ii) a DM trained from data. Even with a perfect DM, standard integrations using only first-order stochastic denoising kernels fail systematically, whereas second-order denoising kernels can substantially improve performance when covariance information is available. We further propose a deterministic aMC integration based on first-order transport maps derived from DMs, which outperforms the stochastic first-order variant at higher computational cost. Finally, in the learned-DM setting, all DM-aMC variants struggle to produce accurate BGs; we trace the main bottleneck to inaccurate DM log-density estimation. Code available at https://github.com/h2o64/dabg.