# Learning Latent Space Energy-Based Prior Model

arXiv: https://arxiv.org/abs/2006.08205 · HTML: https://mlsanity.com/paper/2006.08205/

## Key facts

- Cited by 104 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 30 of 104)

- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics](https://mlsanity.com/paper/2202.11705/) (2022)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Unleashing Transformers: Parallel Token Prediction with Discrete Absorbing Diffusion for Fast High-Resolution Image Generation from Vector-Quantized Codes](https://mlsanity.com/paper/2111.12701/) (2021)
- [Latent Diffusion Energy-Based Model for Interpretable Text Modeling](https://mlsanity.com/paper/2206.05895/) (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)
- [Your ViT is Secretly a Hybrid Discriminative-Generative Diffusion Model](https://mlsanity.com/paper/2208.07791/) (2022)
- [Learning Generative Vision Transformer with Energy-Based Latent Space for Saliency Prediction](https://mlsanity.com/paper/2112.13528/) (2021)
- [Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections](https://mlsanity.com/paper/2404.02954/) (2024)
- [A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Model](https://mlsanity.com/paper/2205.06924/) (2022)
- [Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder](https://mlsanity.com/paper/2105.00026/) (2021)
- [Unsupervised Foreground Extraction via Deep Region Competition](https://mlsanity.com/paper/2110.15497/) (2021)
- [Particle algorithms for maximum likelihood training of latent variable models](https://mlsanity.com/paper/2204.12965/) (2022)
- [Pythae: Unifying Generative Autoencoders in Python -- A Benchmarking Use Case](https://mlsanity.com/paper/2206.08309/) (2022)
- [A Geometric Perspective on Variational Autoencoders](https://mlsanity.com/paper/2209.07370/) (2022)
- [Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood](https://mlsanity.com/paper/2309.05153/) (2023)
- [Adaptive Multi-stage Density Ratio Estimation for Learning Latent Space Energy-based Model](https://mlsanity.com/paper/2209.08739/) (2022)
- [Diverse 3D Hand Gesture Prediction from Body Dynamics by Bilateral Hand Disentanglement](https://mlsanity.com/paper/2303.01765/) (2023)
- [Binary Latent Diffusion](https://mlsanity.com/paper/2304.04820/) (2023)
- [Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approach](https://mlsanity.com/paper/2310.18677/) (2023)
- [Deep Generative model with Hierarchical Latent Factors for Time Series Anomaly Detection](https://mlsanity.com/paper/2202.07586/) (2022)
- [Latent Space Energy-Based Model of Symbol-Vector Coupling for Text Generation and Classification](https://mlsanity.com/paper/2108.11556/) (2021)
- [Latent Plan Transformer for Trajectory Abstraction: Planning as Latent Space Inference](https://mlsanity.com/paper/2402.04647/) (2024)
- [A Review of Change of Variable Formulas for Generative Modeling](https://mlsanity.com/paper/2308.02652/) (2023)
- [Learning Energy-Based Prior Model with Diffusion-Amortized MCMC](https://mlsanity.com/paper/2310.03218/) (2023)
- [Weakly-supervised Contrastive Learning for Unsupervised Object Discovery](https://mlsanity.com/paper/2307.03376/) (2023)
- [Momentum Particle Maximum Likelihood](https://mlsanity.com/paper/2312.07335/) (2023)
- [A prior-based approximate latent Riemannian metric](https://mlsanity.com/paper/2103.05290/) (2021)

## Abstract (arXiv)

We propose to learn energy-based model (EBM) in the latent space of a generator model, so that the EBM serves as a prior model that stands on the top-down network of the generator model. Both the latent space EBM and the top-down network can be learned jointly by maximum likelihood, which involves short-run MCMC sampling from both the prior and posterior distributions of the latent vector. Due to the low dimensionality of the latent space and the expressiveness of the top-down network, a simple EBM in latent space can capture regularities in the data effectively, and MCMC sampling in latent space is efficient and mixes well. We show that the learned model exhibits strong performances in terms of image and text generation and anomaly detection. The one-page code can be found in supplementary materials.