# Balanced Training of Energy-Based Models with Adaptive Flow Sampling

arXiv: https://arxiv.org/abs/2306.00684 · HTML: https://mlsanity.com/paper/2306.00684/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 53 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 29 of 29)

- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model](https://mlsanity.com/paper/1904.09770/) (2019)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Models](https://mlsanity.com/paper/1903.12370/) (2019)
- [VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Models](https://mlsanity.com/paper/2010.00654/) (2020)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)
- [Generalized Energy Based Models](https://mlsanity.com/paper/2003.05033/) (2020)
- [No MCMC for me: Amortized sampling for fast and stable training of energy-based models](https://mlsanity.com/paper/2010.04230/) (2020)
- [Markovian Score Climbing: Variational Inference with KL(p||q)](https://mlsanity.com/paper/2003.10374/) (2020)
- [A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Model](https://mlsanity.com/paper/2205.06924/) (2022)
- [Learning Energy-Based Model with Variational Auto-Encoder as Amortized Sampler](https://mlsanity.com/paper/2012.14936/) (2020)
- [Can Push-forward Generative Models Fit Multimodal Distributions?](https://mlsanity.com/paper/2206.14476/) (2022)
- [Exponential Family Estimation via Adversarial Dynamics Embedding](https://mlsanity.com/paper/1904.12083/) (2019)
- [Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence](https://mlsanity.com/paper/2106.15980/) (2021)
- [MCMC Should Mix: Learning Energy-Based Model with Neural Transport Latent Space MCMC](https://mlsanity.com/paper/2006.06897/) (2020)
- [Flow-based sampling for multimodal and extended-mode distributions in lattice field theory](https://mlsanity.com/paper/2107.00734/) (2021)
- [Local-Global MCMC kernels: the best of both worlds](https://mlsanity.com/paper/2111.02702/) (2021)
- [On Sampling with Approximate Transport Maps](https://mlsanity.com/paper/2302.04763/) (2023)
- [Learning a Restricted Boltzmann Machine using biased Monte Carlo sampling](https://mlsanity.com/paper/2206.01310/) (2022)
- [Exponential Tilting of Generative Models: Improving Sample Quality by Training and Sampling from Latent Energy](https://mlsanity.com/paper/2006.08100/) (2020)
- [Training Restricted Boltzmann Machines via the Thouless-Anderson-Palmer Free Energy](https://mlsanity.com/paper/1506.02914/) (2015)

## Built on by (most cited first, 4 of 4)

- [Stochastic Localization via Iterative Posterior Sampling](https://mlsanity.com/paper/2402.10758/) (2024)
- [Fast training and sampling of Restricted Boltzmann Machines](https://mlsanity.com/paper/2405.15376/) (2024)
- [Learning Energy-based Model via Dual-MCMC Teaching](https://mlsanity.com/paper/2312.02469/) (2023)
- [Total Variation Guarantees for Sampling with Stochastic Localization](https://mlsanity.com/paper/2603.29555/) (2026)

## Abstract (arXiv)

Energy-based models (EBMs) are versatile density estimation models that directly parameterize an unnormalized log density. Although very flexible, EBMs lack a specified normalization constant of the model, making the likelihood of the model computationally intractable. Several approximate samplers and variational inference techniques have been proposed to estimate the likelihood gradients for training. These techniques have shown promising results in generating samples, but little attention has been paid to the statistical accuracy of the estimated density, such as determining the relative importance of different classes in a dataset. In this work, we propose a new maximum likelihood training algorithm for EBMs that uses a different type of generative model, normalizing flows (NF), which have recently been proposed to facilitate sampling. Our method fits an NF to an EBM during training so that an NF-assisted sampling scheme provides an accurate gradient for the EBMs at all times, ultimately leading to a fast sampler for generating new data.