What are the limitations of standard autoencoders that variational autoencoders aim to solve?

Standard autoencoders have limitations in sampling from the latent space due to undefined distributions, large gaps, and local discontinuities. Variational autoencoders address these issues by mapping inputs to a distribution rather than a single point, ensuring a continuous and more structured latent space.

Standard autoencoders face challenges in generating new data because the latent space they create is not well-defined or continuous. This results in difficulties when sampling new points, as the distribution of encoded points is uneven and contains large gaps. Additionally, there is no guarantee that small changes in the latent space will result in small changes in the output, leading to local discontinuities. Variational autoencoders solve these problems by encoding inputs into a multivariate normal distribution rather than a single point. This approach ensures that the latent space is continuous and more evenly distributed, allowing for more reliable sampling and generation of new data.