What do generative models aim to approximate using latent variables?

Generative models fundamentally focus on learning and approximating the underlying probability distribution of the training data. By doing so, they can generate new samples that resemble the training data. Latent variables play a crucial role in this process, as they capture the hidden structures or factors that influence the observed data. By modeling the data in terms of these latent variables, generative models can identify complex patterns and relationships within the data, ultimately allowing them to produce realistic and novel outputs.

This ability to approximate the distribution enables these models to perform a variety of tasks, such as generating images, creating text, or synthesizing other types of data that are similar to the original inputs. The emphasis on learning the probability distribution is what distinguishes generative models from other types of machine learning models, such as discriminative models, which focus directly on predicting labels based on features without inherently modeling the data's distribution.