# Latent Diffusion Energy-Based Model for Interpretable Text Modeling

arXiv: https://arxiv.org/abs/2206.05895 · HTML: https://mlsanity.com/paper/2206.05895/

## Key facts

- Cited by 67 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 58 of its 80 references that are in the map.
- First posted on arXiv 13 Jun 2022.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 30 of 58)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [DailyDialog: A Manually Labelled Multi-turn Dialogue Dataset](https://mlsanity.com/paper/1710.03957/) (2017)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Learning Discourse-level Diversity for Neural Dialog Models using Conditional Variational Autoencoders](https://mlsanity.com/paper/1703.10960/) (2017)
- [Building End-To-End Dialogue Systems Using Generative Hierarchical Neural Network Models](https://mlsanity.com/paper/1507.04808/) (2015)
- [Regularizing and Optimizing LSTM Language Models](https://mlsanity.com/paper/1708.02182/) (2017)
- [Delete, Retrieve, Generate: A Simple Approach to Sentiment and Style Transfer](https://mlsanity.com/paper/1804.06437/) (2018)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [A Theory of Generative ConvNet](https://mlsanity.com/paper/1602.03264/) (2016)
- [A Hierarchical Latent Variable Encoder-Decoder Model for Generating Dialogues](https://mlsanity.com/paper/1605.06069/) (2016)
- [Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model](https://mlsanity.com/paper/1904.09770/) (2019)
- [Key-Value Retrieval Networks for Task-Oriented Dialogue](https://mlsanity.com/paper/1705.05414/) (2017)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [Lagging Inference Networks and Posterior Collapse in Variational Autoencoders](https://mlsanity.com/paper/1901.05534/) (2019)

## Built on by (most cited first, 30 of 67)

- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Diffusion-based Generation, Optimization, and Planning in 3D Scenes](https://mlsanity.com/paper/2301.06015/) (2023)
- [PhyScene: Physically Interactable 3D Scene Synthesis for Embodied AI](https://mlsanity.com/paper/2404.09465/) (2024)
- [A Survey on Diffusion Language Models](https://mlsanity.com/paper/2508.10875/) (2025)
- [Diffusion models for missing value imputation in tabular data](https://mlsanity.com/paper/2210.17128/) (2022)
- [Diffusion Action Segmentation](https://mlsanity.com/paper/2303.17959/) (2023)
- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [SeqDiffuSeq: Text Diffusion with Encoder-Decoder Transformers](https://mlsanity.com/paper/2212.10325/) (2022)
- [Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimization](https://mlsanity.com/paper/2308.05384/) (2023)
- [Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching](https://mlsanity.com/paper/2405.18816/) (2024)
- [DINOISER: Diffused Conditional Sequence Learning by Manipulating Noises](https://mlsanity.com/paper/2302.10025/) (2023)
- [DiffusionInst: Diffusion Model for Instance Segmentation](https://mlsanity.com/paper/2212.02773/) (2022)
- [RenAIssance: A Survey into AI Text-to-Image Generation in the Era of Large Model](https://mlsanity.com/paper/2309.00810/) (2023)
- [Diffusion Models for Robotic Manipulation: A Survey](https://mlsanity.com/paper/2504.08438/) (2025)
- [An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems](https://mlsanity.com/paper/2309.00983/) (2023)
- [Attacks and Defenses for Generative Diffusion Models: A Comprehensive Survey](https://mlsanity.com/paper/2408.03400/) (2024)
- [Composable Text Controls in Latent Space with ODEs](https://mlsanity.com/paper/2208.00638/) (2022)
- [The Rise of Diffusion Models in Time-Series Forecasting](https://mlsanity.com/paper/2401.03006/) (2024)
- [Latent Thought Models with Variational Bayes Inference-Time Computation](https://mlsanity.com/paper/2502.01567/) (2025)
- [Distribution Shift Inversion for Out-of-Distribution Prediction](https://mlsanity.com/paper/2306.08328/) (2023)
- [Quantum-Noise-Driven Generative Diffusion Models](https://mlsanity.com/paper/2308.12013/) (2023)
- [A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems](https://mlsanity.com/paper/2410.03108/) (2024)
- [Adaptive Multi-stage Density Ratio Estimation for Learning Latent Space Energy-based Model](https://mlsanity.com/paper/2209.08739/) (2022)
- [Object-Conditioned Energy-Based Attention Map Alignment in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2404.07389/) (2024)
- [Diffusion Models in NLP: A Survey](https://mlsanity.com/paper/2303.07576/) (2023)
- [Diffusion Models in Bioinformatics: A New Wave of Deep Learning Revolution in Action](https://mlsanity.com/paper/2302.10907/) (2023)
- [Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradients](https://mlsanity.com/paper/2505.03432/) (2025)
- [Diffusion-SS3D: Diffusion Model for Semi-supervised 3D Object Detection](https://mlsanity.com/paper/2312.02966/) (2023)

## Abstract (arXiv)

Latent space Energy-Based Models (EBMs), also known as energy-based priors, have drawn growing interests in generative modeling. Fueled by its flexibility in the formulation and strong modeling power of the latent space, recent works built upon it have made interesting attempts aiming at the interpretability of text modeling. However, latent space EBMs also inherit some flaws from EBMs in data space; the degenerate MCMC sampling quality in practice can lead to poor generation quality and instability in training, especially on data with complex latent structures. Inspired by the recent efforts that leverage diffusion recovery likelihood learning as a cure for the sampling issue, we introduce a novel symbiosis between the diffusion models and latent space EBMs in a variational learning framework, coined as the latent diffusion energy-based model. We develop a geometric clustering-based regularization jointly with the information bottleneck to further improve the quality of the learned latent space. Experiments on several challenging tasks demonstrate the superior performance of our model on interpretable text modeling over strong counterparts.