# Scalable Energy-Based Models via Adversarial Training: Unifying Discrimination and Generation

arXiv: https://arxiv.org/abs/2510.13872 · HTML: https://mlsanity.com/paper/2510.13872/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 67 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Builds on (most cited first, 30 of 47)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [Do Adversarially Robust ImageNet Models Transfer Better?](https://mlsanity.com/paper/2007.08489/) (2020)
- [Uncovering the Limits of Adversarial Training against Norm-Bounded Adversarial Examples](https://mlsanity.com/paper/2010.03593/) (2020)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Fixing Data Augmentation to Improve Adversarial Robustness](https://mlsanity.com/paper/2103.01946/) (2021)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)

## Built on by (most cited first, 1 of 1)

- [Comparing SGLD and a fixed-noise predictor-corrector adaptation in canonical joint energy-based models on CIFAR-10](https://mlsanity.com/paper/2608.05025/) (2026)

## Abstract (arXiv)

Simultaneously achieving robust classification and high-fidelity generative modeling within a single framework presents a significant challenge. Hybrid approaches, such as Joint Energy-Based Models (JEM), interpret classifiers as EBMs but are often limited by the instability and poor sample quality inherent in training based on Stochastic Gradient Langevin Dynamics (SGLD). We address these limitations by proposing a novel training framework that integrates adversarial training (AT) principles for both discriminative robustness and stable generative learning. The proposed method introduces three key innovations: (1) the replacement of SGLD-based JEM learning with a stable, AT-based approach that optimizes the energy function through a Binary Cross-Entropy (BCE) loss that discriminates between real data and contrastive samples generated via Projected Gradient Descent (PGD); (2) adversarial training for the discriminative component that enhances classification robustness while implicitly providing the gradient regularization needed for stable EBM training; and (3) a two-stage training strategy that addresses normalization-related instabilities and enables leveraging pretrained robust classifiers, generalizing effectively across architectures. Experiments on CIFAR-10/100 and ImageNet demonstrate that our approach: (1) is the first EBM-based hybrid to scale to high-resolution datasets with high training stability, simultaneously achieving state-of-the-art discriminative and generative performance on ImageNet 256x256; (2) uniquely combines generative quality with adversarial robustness, enabling faithful counterfactual explanations; and (3) functions as a competitive standalone generative model, matching autoregressive models and surpassing diffusion models while offering additional versatility.