# Prescribed Generative Adversarial Networks

arXiv: https://arxiv.org/abs/1910.04302 · HTML: https://mlsanity.com/paper/1910.04302/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2019.

## Built on by (most cited first, 23 of 23)

- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [Accelerating Diffusion Models via Early Stop of the Diffusion Process](https://mlsanity.com/paper/2205.12524/) (2022)
- [Autoregressive Conditional Neural Processes](https://mlsanity.com/paper/2303.14468/) (2023)
- [Studying Bias in GANs through the Lens of Race](https://mlsanity.com/paper/2209.02836/) (2022)
- [Diagnosing and Fixing Manifold Overfitting in Deep Generative Models](https://mlsanity.com/paper/2204.07172/) (2022)
- [Cousins Of The Vendi Score: A Family Of Similarity-Based Diversity Metrics For Science And Machine Learning](https://mlsanity.com/paper/2310.12952/) (2023)
- [Multiresolution Equivariant Graph Variational Autoencoder](https://mlsanity.com/paper/2106.00967/) (2021)
- [On Out-of-distribution Detection with Energy-based Models](https://mlsanity.com/paper/2107.08785/) (2021)
- [A Unified Contrastive Energy-based Model for Understanding the Generative Ability of Adversarial Training](https://mlsanity.com/paper/2203.13455/) (2022)
- [PAC-Bayesian Generalization Bounds for Adversarial Generative Models](https://mlsanity.com/paper/2302.08942/) (2023)
- [The Optimal Noise in Noise-Contrastive Learning Is Not What You Think](https://mlsanity.com/paper/2203.01110/) (2022)
- [Deep Time Series Forecasting with Shape and Temporal Criteria](https://mlsanity.com/paper/2104.04610/) (2021)
- [The Representation Jensen-Shannon Divergence](https://mlsanity.com/paper/2305.16446/) (2023)
- [Tail of Distribution GAN (TailGAN): Generative-Adversarial-Network-Based Boundary Formation](https://mlsanity.com/paper/2107.11658/) (2021)
- [DuelGAN: A Duel Between Two Discriminators Stabilizes the GAN Training](https://mlsanity.com/paper/2101.07524/) (2021)
- [Generative Adversarial Networks for Image Augmentation in Agriculture: A Systematic Review](https://mlsanity.com/paper/2204.04707/) (2022)
- [FROB: Few-shot ROBust Model for Classification and Out-of-Distribution Detection](https://mlsanity.com/paper/2111.15487/) (2021)
- [IID-GAN: an IID Sampling Perspective for Regularizing Mode Collapse](https://mlsanity.com/paper/2106.00563/) (2021)
- [Master's Thesis: Out-of-distribution Detection with Energy-based Models](https://mlsanity.com/paper/2302.12002/) (2023)
- [Generating Multi-type Temporal Sequences to Mitigate Class-imbalanced Problem](https://mlsanity.com/paper/2104.03428/) (2021)
- [Deep Probabilistic Graphical Modeling](https://mlsanity.com/paper/2104.12053/) (2021)
- [Exploring bidirectional bounds for minimax-training of Energy-based models](https://mlsanity.com/paper/2506.04609/) (2025)

## Abstract (arXiv)

Generative adversarial networks (GANs) are a powerful approach to unsupervised learning. They have achieved state-of-the-art performance in the image domain. However, GANs are limited in two ways. They often learn distributions with low support---a phenomenon known as mode collapse---and they do not guarantee the existence of a probability density, which makes evaluating generalization using predictive log-likelihood impossible. In this paper, we develop the prescribed GAN (PresGAN) to address these shortcomings. PresGANs add noise to the output of a density network and optimize an entropy-regularized adversarial loss. The added noise renders tractable approximations of the predictive log-likelihood and stabilizes the training procedure. The entropy regularizer encourages PresGANs to capture all the modes of the data distribution. Fitting PresGANs involves computing the intractable gradients of the entropy regularization term; PresGANs sidestep this intractability using unbiased stochastic estimates. We evaluate PresGANs on several datasets and found they mitigate mode collapse and generate samples with high perceptual quality. We further found that PresGANs reduce the gap in performance in terms of predictive log-likelihood between traditional GANs and variational autoencoders (VAEs).