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The Variational Auto-Encoder (VAE) is one of the most used unsupervised machine learning models. But although the default choice of a Gaussian distribution for both the prior and posterior represents a mathematically convenient distribution…

Machine Learning · Statistics 2022-09-28 Tim R. Davidson , Luca Falorsi , Nicola De Cao , Thomas Kipf , Jakub M. Tomczak

Variational autoencoders (VAE) encode data into lower-dimensional latent vectors before decoding those vectors back to data. Once trained, decoding a random latent vector from the prior usually does not produce meaningful data, at least…

Machine Learning · Computer Science 2025-07-23 Alejandro Ascarate , Leo Lebrat , Rodrigo Santa Cruz , Clinton Fookes , Olivier Salvado

Variational autoencoders (VAE) encode data into lower-dimensional latent vectors before decoding those vectors back to data. Once trained, one can hope to detect out-of-distribution (abnormal) latent vectors, but several issues arise when…

Machine Learning · Computer Science 2026-05-12 Alejandro Ascarate , Leo Lebrat , Rodrigo Santa Cruz , Clinton Fookes , Olivier Salvado

Most visual generative models compress images into a latent space before applying diffusion or autoregressive modelling. Yet, existing approaches such as VAEs and foundation model aligned encoders implicitly constrain the latent space…

Computer Vision and Pattern Recognition · Computer Science 2025-12-09 Sen Ye , Jianning Pei , Mengde Xu , Shuyang Gu , Chunyu Wang , Liwei Wang , Han Hu

Variational Autoencoders (VAEs) have experienced recent success as data-generating models by using simple architectures that do not require significant fine-tuning of hyperparameters. However, VAEs are known to suffer from…

Machine Learning · Statistics 2020-07-22 Wei Cheng , Gregory Darnell , Sohini Ramachandran , Lorin Crawford

Variational autoencoder (VAE) has widely been utilized for modeling data distributions because it is theoretically elegant, easy to train, and has nice manifold representations. However, when applied to image reconstruction and synthesis…

Computer Vision and Pattern Recognition · Computer Science 2022-07-12 Dooseop Choi , KyoungWook Min

The key idea of variational auto-encoders (VAEs) resembles that of traditional auto-encoder models in which spatial information is supposed to be explicitly encoded in the latent space. However, the latent variables in VAEs are vectors,…

Machine Learning · Computer Science 2019-01-23 Zhengyang Wang , Hao Yuan , Shuiwang Ji

As a widely recognized approach to deep generative modeling, Variational Auto-Encoders (VAEs) still face challenges with the quality of generated images, often presenting noticeable blurriness. This issue stems from the unrealistic…

Machine Learning · Computer Science 2023-05-22 Georgios Batzolis , Jan Stanczuk , Carola-Bibiane Schönlieb

Generative modeling aims to generate new data samples that resemble a given dataset, with diffusion models recently becoming the most popular generative model. One of the main challenges of diffusion models is solving the problem in the…

Numerical Analysis · Mathematics 2025-10-08 Wonjun Lee , Riley C. W. O'Neill , Dongmian Zou , Jeff Calder , Gilad Lerman

Variational Autoencoders (VAEs) are well-established as a principled approach to probabilistic unsupervised learning with neural networks. Typically, an encoder network defines the parameters of a Gaussian distributed latent space from…

Machine Learning · Computer Science 2025-05-16 Alan Jeffares , Liyuan Liu

Recently, probabilistic predictive coding that directly models the conditional distribution of latent features across successive frames for temporal redundancy removal has yielded promising results. Existing methods using a single-scale…

Image and Video Processing · Electrical Eng. & Systems 2023-12-13 Ming Lu , Zhihao Duan , Fengqing Zhu , Zhan Ma

This tutorial focuses on the fundamental architectures of Variational Autoencoders (VAE) and Generative Adversarial Networks (GAN), disregarding their numerous variations, to highlight their core principles. Both VAE and GAN utilize simple…

Machine Learning · Computer Science 2025-03-05 Yuan-Hao Wei

We propose Tree Variational Autoencoder (TreeVAE), a new generative hierarchical clustering model that learns a flexible tree-based posterior distribution over latent variables. TreeVAE hierarchically divides samples according to their…

Machine Learning · Computer Science 2023-11-20 Laura Manduchi , Moritz Vandenhirtz , Alain Ryser , Julia Vogt

Semi-supervised learning is sought for leveraging the unlabelled data when labelled data is difficult or expensive to acquire. Deep generative models (e.g., Variational Autoencoder (VAE)) and semisupervised Generative Adversarial Networks…

Machine Learning · Computer Science 2019-05-09 Xiang Zhang , Lina Yao , Feng Yuan

We introduce the variational graph auto-encoder (VGAE), a framework for unsupervised learning on graph-structured data based on the variational auto-encoder (VAE). This model makes use of latent variables and is capable of learning…

Machine Learning · Statistics 2016-11-23 Thomas N. Kipf , Max Welling

Deep generative models are commonly used for generating images and text. Interpretability of these models is one important pursuit, other than the generation quality. Variational auto-encoder (VAE) with Gaussian distribution as prior has…

Machine Learning · Computer Science 2020-08-24 Wenxian Shi , Hao Zhou , Ning Miao , Lei Li

Variational autoencoders (VAEs) employ Bayesian inference to interpret sensory inputs, mirroring processes that occur in primate vision across both ventral (Higgins et al., 2021) and dorsal (Vafaii et al., 2023) pathways. Despite their…

Machine Learning · Computer Science 2024-12-10 Hadi Vafaii , Dekel Galor , Jacob L. Yates

Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatial statistical modelling. In this context they are used to encode…

Machine Learning · Computer Science 2023-04-11 Elizaveta Semenova , Yidan Xu , Adam Howes , Theo Rashid , Samir Bhatt , Swapnil Mishra , Seth Flaxman

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…

Machine Learning · Computer Science 2013-01-30 Hagai Attias

The Variational Autoencoder (VAE) has proven to be an effective model for producing semantically meaningful latent representations for natural data. However, it has thus far seen limited application to sequential data, and, as we…

Machine Learning · Computer Science 2019-11-12 Adam Roberts , Jesse Engel , Colin Raffel , Curtis Hawthorne , Douglas Eck
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