# Learning Joint Latent Space EBM Prior Model for Multi-layer Generator

arXiv: https://arxiv.org/abs/2306.06323 · HTML: https://mlsanity.com/paper/2306.06323/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 52 references that are in the map.
- First posted on arXiv 10 Jun 2023.

## Builds on (most cited first, 30 of 37)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [MoCoGAN: Decomposing Motion and Content for Video Generation](https://mlsanity.com/paper/1707.04993/) (2017)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model](https://mlsanity.com/paper/1904.09770/) (2019)
- [From Variational to Deterministic Autoencoders](https://mlsanity.com/paper/1903.12436/) (2019)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [Learning Energy-Based Models by Diffusion Recovery Likelihood](https://mlsanity.com/paper/2012.08125/) (2020)
- [Efficient GAN-Based Anomaly Detection](https://mlsanity.com/paper/1802.06222/) (2018)
- [Train Sparsely, Generate Densely: Memory-efficient Unsupervised Training of High-resolution Temporal GAN](https://mlsanity.com/paper/1811.09245/) (2018)
- [BIVA: A Very Deep Hierarchy of Latent Variables for Generative Modeling](https://mlsanity.com/paper/1902.02102/) (2019)
- [On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Models](https://mlsanity.com/paper/1903.12370/) (2019)
- [Learning Latent Space Energy-Based Prior Model](https://mlsanity.com/paper/2006.08205/) (2020)
- [VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Models](https://mlsanity.com/paper/2010.00654/) (2020)
- [A Contrastive Learning Approach for Training Variational Autoencoder Priors](https://mlsanity.com/paper/2010.02917/) (2020)
- [Hierarchical VAEs Know What They Don't Know](https://mlsanity.com/paper/2102.08248/) (2021)

## Built on by (most cited first, 8 of 8)

- [Learning Energy-based Model via Dual-MCMC Teaching](https://mlsanity.com/paper/2312.02469/) (2023)
- [Learning Multimodal Latent Generative Models with Energy-Based Prior](https://mlsanity.com/paper/2409.19862/) (2024)
- [Learning Hierarchical Features with Joint Latent Space Energy-Based Prior](https://mlsanity.com/paper/2310.09604/) (2023)
- [Learning Latent Space Hierarchical EBM Diffusion Models](https://mlsanity.com/paper/2405.13910/) (2024)
- [HypDAE: Hyperbolic Diffusion Autoencoders for Hierarchical Few-shot Image Generation](https://mlsanity.com/paper/2411.17784/) (2024)
- [Learning Energy-based Variational Latent Prior for VAEs](https://mlsanity.com/paper/2510.00260/) (2025)
- [Computationally Efficient Diffusion Models in Medical Imaging: A Comprehensive Review](https://mlsanity.com/paper/2505.07866/) (2025)
- [A Source-Free Approach for Domain Adaptation via Multiview Image Transformation and Latent Space Consistency](https://mlsanity.com/paper/2601.20284/) (2026)

## Abstract (arXiv)

This paper studies the fundamental problem of learning multi-layer generator models. The multi-layer generator model builds multiple layers of latent variables as a prior model on top of the generator, which benefits learning complex data distribution and hierarchical representations. However, such a prior model usually focuses on modeling inter-layer relations between latent variables by assuming non-informative (conditional) Gaussian distributions, which can be limited in model expressivity. To tackle this issue and learn more expressive prior models, we propose an energy-based model (EBM) on the joint latent space over all layers of latent variables with the multi-layer generator as its backbone. Such joint latent space EBM prior model captures the intra-layer contextual relations at each layer through layer-wise energy terms, and latent variables across different layers are jointly corrected. We develop a joint training scheme via maximum likelihood estimation (MLE), which involves Markov Chain Monte Carlo (MCMC) sampling for both prior and posterior distributions of the latent variables from different layers. To ensure efficient inference and learning, we further propose a variational training scheme where an inference model is used to amortize the costly posterior MCMC sampling. Our experiments demonstrate that the learned model can be expressive in generating high-quality images and capturing hierarchical features for better outlier detection.