The article provides an introduction to variational autoencoders (VAEs), a principled framework for learning deep latent-variable models and their corresponding inference models. VAEs combine probabilistic models with neural networks to approximate complex posterior distributions over latent variables. The authors motivate the use of VAEs by discussing the advantages of generative modeling over discriminative modeling, emphasizing the importance of understanding the data generation process. They explain the basic components of VAEs, including the encoder (or approximate posterior), the generative model, and the evidence lower bound (ELBO) objective. The ELBO is derived using Jensen's inequality and provides a lower bound on the log-likelihood of the data, which can be optimized using stochastic gradient descent (SGD). The reparameterization trick is introduced to enable efficient computation of gradients through the ELBO, allowing for joint optimization of both the generative and inference models. The article also covers advanced topics such as factorized Gaussian posteriors, the marginal likelihood, and related work in variational inference and deep learning.The article provides an introduction to variational autoencoders (VAEs), a principled framework for learning deep latent-variable models and their corresponding inference models. VAEs combine probabilistic models with neural networks to approximate complex posterior distributions over latent variables. The authors motivate the use of VAEs by discussing the advantages of generative modeling over discriminative modeling, emphasizing the importance of understanding the data generation process. They explain the basic components of VAEs, including the encoder (or approximate posterior), the generative model, and the evidence lower bound (ELBO) objective. The ELBO is derived using Jensen's inequality and provides a lower bound on the log-likelihood of the data, which can be optimized using stochastic gradient descent (SGD). The reparameterization trick is introduced to enable efficient computation of gradients through the ELBO, allowing for joint optimization of both the generative and inference models. The article also covers advanced topics such as factorized Gaussian posteriors, the marginal likelihood, and related work in variational inference and deep learning.