mlsanityData to 7 Oct 2026

Bi-level Doubly Variational Learning for Energy-based Latent Variable Models

arXiv 2203.14702 ↗First posted 24 Mar 2022cs.CV cs.LG stat.MLcited by 6

Not on the map. Why?

Abstract (arXiv)

Energy-based latent variable models (EBLVMs) are more expressive than conventional energy-based models. However, its potential on visual tasks are limited by its training process based on maximum likelihood estimate that requires sampling from two intractable distributions. In this paper, we propose Bi-level doubly variational learning (BiDVL), which is based on a new bi-level optimization framework and two tractable variational distributions to facilitate learning EBLVMs. Particularly, we lead a decoupled EBLVM consisting of a marginal energy-based distribution and a structural posterior to handle the difficulties when learning deep EBLVMs on images. By choosing a symmetric KL divergence in the lower level of our framework, a compact BiDVL for visual tasks can be obtained. Our model achieves impressive image generation performance over related works. It also demonstrates the significant capacity of testing image reconstruction and out-of-distribution detection.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 32 of its 47 references that are in the map. First posted on arXiv 24 Mar 2022.

Builds on

32 of 47 references.

References · 32

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  3. 2013Auto-Encoding Variational Bayescited by 3,980
  4. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  5. 2015Variational Inference with Normalizing Flowscited by 2,161
  6. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  7. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  8. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  9. 2020Energy-based Out-of-distribution Detectioncited by 1,296
  10. 2019Your Classifier is Secretly an Energy Based Model and You Should Treat it Like Onecited by 402
  11. 2016Unrolled Generative Adversarial Networkscited by 208
  12. 2021Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyondcited by 151
20 more
  1. 2020Learning Latent Space Energy-Based Prior Modelcited by 104
  2. 2020VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Modelscited by 103
  3. 2020A Generic First-Order Algorithmic Framework for Bi-Level Programming Beyond Lower-Level Singletoncited by 78
  4. 2019Flow Contrastive Estimation of Energy-Based Modelscited by 75
  5. 2020Generalized Energy Based Modelscited by 73
  6. 2020Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Samplingcited by 71
  7. 2020No MCMC for me: Amortized sampling for fast and stable training of energy-based modelscited by 64
  8. 2020Learning Energy-Based Model with Variational Auto-Encoder as Amortized Samplercited by 43
  9. 2018Divergence Triangle for Joint Training of Generator Model, Energy-based Model, and Inference Modelcited by 34
  10. 2017ALICE: Towards Understanding Adversarial Learning for Joint Distribution Matchingcited by 32
  11. 2020Joint Training of Variational Auto-Encoder and Latent Energy-Based Modelcited by 30
  12. 2020Training Deep Energy-Based Models with f-Divergence Minimizationcited by 29
  13. 2019Learning Energy-Based Models in High-Dimensional Spaces with Multi-scale Denoising Score Matchingcited by 26
  14. 2017Symmetric Variational Autoencoder and Connections to Adversarial Learningcited by 14
  15. 2020Bi-level Score Matching for Learning Energy-based Latent Variable Modelscited by 10
  16. 2021Bounds all around: training energy-based models with bidirectional boundscited by 10
  17. 2020Variational (Gradient) Estimate of the Score Function in Energy-based Latent Variable Modelscited by 8
  18. 2020Discriminator Contrastive Divergence: Semi-Amortized Generative Modeling by Exploring Energy of the Discriminatorcited by 7
  19. 2020Exponential Tilting of Generative Models: Improving Sample Quality by Training and Sampling from Latent Energycited by 6
  20. 2019To Relieve Your Headache of Training an MRF, Take AdVILcited by 2

Built on by

Cited by year

Citing papers per year: 2023: 3; 2024: 1; 2025: 2.

6 papers.

  1. 2023Guiding Energy-based Models via Contrastive Latent Variablescited by 17
  2. 2023EGC: Image Generation and Classification via a Diffusion Energy-Based Modelcited by 16
  3. 2024Improving Adversarial Energy-Based Model via Diffusion Processcited by 7
  4. 2023How to Construct Energy for Images? Denoising Autoencoder Can Be Energy Based Modelcited by 1
  5. 2025Exploring bidirectional bounds for minimax-training of Energy-based modelscited by 0
  6. 2025From Data to Rewards: a Bilevel Optimization Perspective on Maximum Likelihood Estimationcited by 0