# No MCMC for me: Amortized sampling for fast and stable training of energy-based models

arXiv: https://arxiv.org/abs/2010.04230 · HTML: https://mlsanity.com/paper/2010.04230/

## Key facts

- Cited by 64 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2020.

## Built on by (most cited first, 30 of 64)

- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics](https://mlsanity.com/paper/2202.11705/) (2022)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Generative Flow Networks for Discrete Probabilistic Modeling](https://mlsanity.com/paper/2202.01361/) (2022)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [Your ViT is Secretly a Hybrid Discriminative-Generative Diffusion Model](https://mlsanity.com/paper/2208.07791/) (2022)
- [Energy-Based Open-World Uncertainty Modeling for Confidence Calibration](https://mlsanity.com/paper/2107.12628/) (2021)
- [A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Model](https://mlsanity.com/paper/2205.06924/) (2022)
- [JEM++: Improved Techniques for Training JEM](https://mlsanity.com/paper/2109.09032/) (2021)
- [Learning Data Representations with Joint Diffusion Models](https://mlsanity.com/paper/2301.13622/) (2023)
- [Learning Implicit Priors for Motion Optimization](https://mlsanity.com/paper/2204.05369/) (2022)
- [Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood](https://mlsanity.com/paper/2309.05153/) (2023)
- [Guiding Energy-based Models via Contrastive Latent Variables](https://mlsanity.com/paper/2303.03023/) (2023)
- [Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approach](https://mlsanity.com/paper/2310.18677/) (2023)
- [On Out-of-distribution Detection with Energy-based Models](https://mlsanity.com/paper/2107.08785/) (2021)
- [Towards Bridging the Performance Gaps of Joint Energy-based Models](https://mlsanity.com/paper/2209.07959/) (2022)
- [Energy-Based Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2202.04933/) (2022)
- [Learning Probabilistic Models from Generator Latent Spaces with Hat EBM](https://mlsanity.com/paper/2210.16486/) (2022)
- [Bounds all around: training energy-based models with bidirectional bounds](https://mlsanity.com/paper/2111.00929/) (2021)
- [Revisiting Energy Based Models as Policies: Ranking Noise Contrastive Estimation and Interpolating Energy Models](https://mlsanity.com/paper/2309.05803/) (2023)
- [Hamiltonian Dynamics with Non-Newtonian Momentum for Rapid Sampling](https://mlsanity.com/paper/2111.02434/) (2021)
- [Training Energy-Based Models with Diffusion Contrastive Divergences](https://mlsanity.com/paper/2307.01668/) (2023)
- [Learning Energy Networks with Generalized Fenchel-Young Losses](https://mlsanity.com/paper/2205.09589/) (2022)
- [Learning Symbolic Representations Through Joint GEnerative and DIscriminative Training](https://mlsanity.com/paper/2304.11357/) (2023)
- [Pseudo-Spherical Contrastive Divergence](https://mlsanity.com/paper/2111.00780/) (2021)
- [Learning Energy-based Model via Dual-MCMC Teaching](https://mlsanity.com/paper/2312.02469/) (2023)
- [Improving Adversarial Energy-Based Model via Diffusion Process](https://mlsanity.com/paper/2403.01666/) (2024)
- [Follow the Energy, Find the Path: Riemannian Metrics from Energy-Based Models](https://mlsanity.com/paper/2505.18230/) (2025)

## Abstract (arXiv)

Energy-Based Models (EBMs) present a flexible and appealing way to represent uncertainty. Despite recent advances, training EBMs on high-dimensional data remains a challenging problem as the state-of-the-art approaches are costly, unstable, and require considerable tuning and domain expertise to apply successfully. In this work, we present a simple method for training EBMs at scale which uses an entropy-regularized generator to amortize the MCMC sampling typically used in EBM training. We improve upon prior MCMC-based entropy regularization methods with a fast variational approximation. We demonstrate the effectiveness of our approach by using it to train tractable likelihood models. Next, we apply our estimator to the recently proposed Joint Energy Model (JEM), where we match the original performance with faster and stable training. This allows us to extend JEM models to semi-supervised classification on tabular data from a variety of continuous domains.