Variational Autoencoders (VAEs) Explained: From Theory to ELBO and the Reparameterization Trick

Variational Autoencoders (VAEs) are generative models that improve upon standard autoencoders by creating a more structured latent space suitable for generating new data. They work by approximating the intractable posterior distribution p(z|x) with a learned normal distribution q(z|x) using an encoder. The model is trained by maximizing the Evidence Lower Bound (ELBO), which balances two competing objectives. One objective is a reconstruction loss that ensures the decoder can accurately rebuild the input from the latent space. The other objective is a KL divergence regularization term that forces the latent space to conform to a prior distribution, such as a standard normal, which enables smooth interpolation and generation.