# Implicit Generation and Generalization in Energy-Based Models

arXiv: https://arxiv.org/abs/1903.08689 · HTML: https://mlsanity.com/paper/1903.08689/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2019.

## Built on by (most cited first, 22 of 22)

- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Restoring Vision in Adverse Weather Conditions with Patch-Based Denoising Diffusion Models](https://mlsanity.com/paper/2207.14626/) (2022)
- [Symbolic Music Generation with Diffusion Models](https://mlsanity.com/paper/2103.16091/) (2021)
- [DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latents](https://mlsanity.com/paper/2201.00308/) (2022)
- [Controllable and Compositional Generation with Latent-Space Energy-Based Models](https://mlsanity.com/paper/2110.10873/) (2021)
- [Trajectory Prediction with Latent Belief Energy-Based Model](https://mlsanity.com/paper/2104.03086/) (2021)
- [Strictly Batch Imitation Learning by Energy-based Distribution Matching](https://mlsanity.com/paper/2006.14154/) (2020)
- [Object Representations as Fixed Points: Training Iterative Refinement Algorithms with Implicit Differentiation](https://mlsanity.com/paper/2207.00787/) (2022)
- [Energy-Based Imitation Learning](https://mlsanity.com/paper/2004.09395/) (2020)
- [Learning Iterative Reasoning through Energy Minimization](https://mlsanity.com/paper/2206.15448/) (2022)
- [Towards Understanding the Generative Capability of Adversarially Robust Classifiers](https://mlsanity.com/paper/2108.09093/) (2021)
- [Entropic Issues in Likelihood-Based OOD Detection](https://mlsanity.com/paper/2109.10794/) (2021)
- [Ideas in Inference-time Scaling can Benefit Generative Pre-training Algorithms](https://mlsanity.com/paper/2503.07154/) (2025)
- [Molecule Design by Latent Space Energy-Based Modeling and Gradual Distribution Shifting](https://mlsanity.com/paper/2306.14902/) (2023)
- [Pitfalls of Gaussians as a noise distribution in NCE](https://mlsanity.com/paper/2210.00189/) (2022)
- [Preference Optimization for Molecule Synthesis with Conditional Residual Energy-based Models](https://mlsanity.com/paper/2406.02066/) (2024)
- [Progressive Test Time Energy Adaptation for Medical Image Segmentation](https://mlsanity.com/paper/2503.16616/) (2025)
- [No Shifted Augmentations (NSA): compact distributions for robust self-supervised Anomaly Detection](https://mlsanity.com/paper/2203.10344/) (2022)
- [Versatile Energy-Based Probabilistic Models for High Energy Physics](https://mlsanity.com/paper/2302.00695/) (2023)
- [Energy-Based Anomaly Detection and Localization](https://mlsanity.com/paper/2105.03270/) (2021)
- [Non-Generative Energy Based Models](https://mlsanity.com/paper/2304.01297/) (2023)
- [Learning Multimodal Energy-Based Model with Multimodal Variational Auto-Encoder via MCMC Revision](https://mlsanity.com/paper/2605.00644/) (2026)

## Abstract (arXiv)

Energy based models (EBMs) are appealing due to their generality and simplicity in likelihood modeling, but have been traditionally difficult to train. We present techniques to scale MCMC based EBM training on continuous neural networks, and we show its success on the high-dimensional data domains of ImageNet32x32, ImageNet128x128, CIFAR-10, and robotic hand trajectories, achieving better samples than other likelihood models and nearing the performance of contemporary GAN approaches, while covering all modes of the data. We highlight some unique capabilities of implicit generation such as compositionality and corrupt image reconstruction and inpainting. Finally, we show that EBMs are useful models across a wide variety of tasks, achieving state-of-the-art out-of-distribution classification, adversarially robust classification, state-of-the-art continual online class learning, and coherent long term predicted trajectory rollouts.