Data to 7 Oct 2026

A Theory of Generative ConvNet

arXiv 1602.03264 ↗First posted 10 Feb 2016stat.ML cs.LGcited by 174

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Abstract (arXiv)

We show that a generative random field model, which we call generative ConvNet, can be derived from the commonly used discriminative ConvNet, by assuming a ConvNet for multi-category classification and assuming one of the categories is a base category generated by a reference distribution. If we further assume that the non-linearity in the ConvNet is Rectified Linear Unit (ReLU) and the reference distribution is Gaussian white noise, then we obtain a generative ConvNet model that is unique among energy-based models: The model is piecewise Gaussian, and the means of the Gaussian pieces are defined by an auto-encoder, where the filters in the bottom-up encoding become the basis functions in the top-down decoding, and the binary activation variables detected by the filters in the bottom-up convolution process become the coefficients of the basis functions in the top-down deconvolution process. The Langevin dynamics for sampling the generative ConvNet is driven by the reconstruction error of this auto-encoder. The contrastive divergence learning of the generative ConvNet reconstructs the training images by the auto-encoder. The maximum likelihood learning algorithm can synthesize realistic natural image patterns.

Key facts. Cited by 174 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Feb 2016.

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Citing papers per year: 2020: 1; 2021: 39; 2022: 29; 2023: 57; 2024: 31; 2025: 10; 2026: 7.

174 papers.

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2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,903
2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
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2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMCcited by 216
2021Spatio-temporal Self-Supervised Representation Learning for 3D Point Cloudscited by 180
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2021Can multi-label classification networks know what they don't know?cited by 100
20223DILG: Irregular Latent Grids for 3D Generative Modelingcited by 92
2022SDF-StyleGAN: Implicit SDF-Based StyleGAN for 3D Shape Generationcited by 92

38 more

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2021Learning to Compose Visual Relationscited by 72
2021Unsupervised Learning of Compositional Energy Conceptscited by 71
2022Latent Diffusion Energy-Based Model for Interpretable Text Modelingcited by 67
2023Energy-based Out-of-Distribution Detection for Graph Neural Networkscited by 67
2021Controllable and Compositional Generation with Latent-Space Energy-Based Modelscited by 64
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2024EM Distillation for One-step Diffusion Modelscited by 60
2021Learning Generative Vision Transformer with Energy-Based Latent Space for Saliency Predictioncited by 57
2020Strictly Batch Imitation Learning by Energy-based Distribution Matchingcited by 54
2022Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learningcited by 54
2023Joint-MAE: 2D-3D Joint Masked Autoencoders for 3D Point Cloud Pre-trainingcited by 52
2024Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matchingcited by 50
2024Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connectionscited by 47
2022Object Representations as Fixed Points: Training Iterative Refinement Algorithms with Implicit Differentiationcited by 46
2022A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Modelcited by 44
2022Isolation and Impartial Aggregation: A Paradigm of Incremental Learning without Interferencecited by 44
2021Abstract Spatial-Temporal Reasoning via Probabilistic Abduction and Executioncited by 43
2022Energy-based Latent Aligner for Incremental Learningcited by 37
2024Learning Iterative Reasoning through Energy Diffusioncited by 36
2024Energy-Based Concept Bottleneck Models: Unifying Prediction, Concept Intervention, and Probabilistic Interpretationscited by 33
2023Energy-based Models are Zero-Shot Planners for Compositional Scene Rearrangementcited by 30
2021JEM++: Improved Techniques for Training JEMcited by 28
2021Autoencoding Under Normalization Constraintscited by 26
2024TabPFGen -- Tabular Data Generation with TabPFNcited by 26
2023Energy-guided Entropic Neural Optimal Transportcited by 25
2024A Geometric Explanation of the Likelihood OOD Detection Paradoxcited by 22
2024Watermarking Techniques for Large Language Models: A Surveycited by 20
2023Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihoodcited by 19
2023Binary Latent Diffusioncited by 18
2024Object-Conditioned Energy-Based Attention Map Alignment in Text-to-Image Diffusion Modelscited by 18
2024S2AC: Energy-Based Reinforcement Learning with Stein Soft Actor Criticcited by 18
2025Equilibrium Matching: Generative Modeling with Implicit Energy-Based Modelscited by 18
2021Energy-constrained Self-training for Unsupervised Domain Adaptationcited by 16
2023EGC: Image Generation and Classification via a Diffusion Energy-Based Modelcited by 16
2024Energy-based Automated Model Evaluationcited by 16

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