# A survey on Variational Autoencoders from a GreenAI perspective

arXiv: https://arxiv.org/abs/2103.01071 · HTML: https://mlsanity.com/paper/2103.01071/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 72 references that are in the map.
- First posted on arXiv 1 Mar 2021.

## Builds on (most cited first, 30 of 41)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Green AI](https://mlsanity.com/paper/1907.10597/) (2019)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Quantifying the Carbon Emissions of Machine Learning](https://mlsanity.com/paper/1910.09700/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Generating Images with Perceptual Similarity Metrics based on Deep Networks](https://mlsanity.com/paper/1602.02644/) (2016)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [DRAW: A Recurrent Neural Network For Image Generation](https://mlsanity.com/paper/1502.04623/) (2015)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [f-VAEGAN-D2: A Feature Generating Framework for Any-Shot Learning](https://mlsanity.com/paper/1903.10132/) (2019)
- [From Variational to Deterministic Autoencoders](https://mlsanity.com/paper/1903.12436/) (2019)
- [An Analysis of Deep Neural Network Models for Practical Applications](https://mlsanity.com/paper/1605.07678/) (2016)
- [Preventing Posterior Collapse with delta-VAEs](https://mlsanity.com/paper/1901.03416/) (2019)

## Built on by (most cited first, 22 of 22)

- [A Systematic Review of Green AI](https://mlsanity.com/paper/2301.11047/) (2023)
- [Precipitation nowcasting with generative diffusion models](https://mlsanity.com/paper/2308.06733/) (2023)
- [Wind speed super-resolution and validation: from ERA5 to CERRA via diffusion models](https://mlsanity.com/paper/2401.15469/) (2024)
- [Comparing the latent space of generative models](https://mlsanity.com/paper/2207.06812/) (2022)
- [Dissecting FLOPs along input dimensions for GreenAI cost estimations](https://mlsanity.com/paper/2107.11949/) (2021)
- [An Overview on Generative AI at Scale with Edge-Cloud Computing](https://mlsanity.com/paper/2306.17170/) (2023)
- [Image Embedding for Denoising Generative Models](https://mlsanity.com/paper/2301.07485/) (2022)
- [GuardDoor: Safeguarding Against Malicious Diffusion Editing via Protective Backdoors](https://mlsanity.com/paper/2503.03944/) (2025)
- [Estimating Deep Learning energy consumption based on model architecture and training environment](https://mlsanity.com/paper/2307.05520/) (2023)
- [Small is Sufficient: Reducing the World AI Energy Consumption Through Model Selection](https://mlsanity.com/paper/2510.01889/) (2025)
- [Generative Adversarial Network based Voice Conversion: Techniques, Challenges, and Recent Advancements](https://mlsanity.com/paper/2504.19197/) (2025)
- [Enhancing variational generation through self-decomposition](https://mlsanity.com/paper/2202.02738/) (2022)
- [MaSkel: A Model for Human Whole-body X-rays Generation from Human Masking Images](https://mlsanity.com/paper/2404.09000/) (2024)
- [Uniform Transformation: Refining Latent Representation in Variational Autoencoders](https://mlsanity.com/paper/2407.02681/) (2024)
- [A Diffusion-Based Generative Prior Approach to Sparse-view Computed Tomography](https://mlsanity.com/paper/2602.10722/) (2026)
- [Deep Fake Detection, Deterrence and Response: Challenges and Opportunities](https://mlsanity.com/paper/2211.14667/) (2022)
- [Can Perturbations Help Reduce Investment Risks? Risk-Aware Stock Recommendation via Split Variational Adversarial Training](https://mlsanity.com/paper/2304.11043/) (2023)
- [Illumination and Shadows in Head Rotation: experiments with Denoising Diffusion Models](https://mlsanity.com/paper/2308.06057/) (2023)
- [Prime Convolutional Model: Breaking the Ground for Theoretical Explainability](https://mlsanity.com/paper/2503.02773/) (2025)
- [Adventurer: Exploration with BiGAN for Deep Reinforcement Learning](https://mlsanity.com/paper/2503.18612/) (2025)
- [On the flow matching interpretability](https://mlsanity.com/paper/2510.21210/) (2025)
- [Soft-Constrained Optimization of Latent Space in Variational Autoencoders](https://mlsanity.com/paper/2607.23751/) (2026)

## Abstract (arXiv)

Variational AutoEncoders (VAEs) are powerful generative models that merge elements from statistics and information theory with the flexibility offered by deep neural networks to efficiently solve the generation problem for high dimensional data. The key insight of VAEs is to learn the latent distribution of data in such a way that new meaningful samples can be generated from it. This approach led to tremendous research and variations in the architectural design of VAEs, nourishing the recent field of research known as unsupervised representation learning. In this article, we provide a comparative evaluation of some of the most successful, recent variations of VAEs. We particularly focus the analysis on the energetic efficiency of the different models, in the spirit of the so called Green AI, aiming both to reduce the carbon footprint and the financial cost of generative techniques. For each architecture we provide its mathematical formulation, the ideas underlying its design, a detailed model description, a running implementation and quantitative results.