Navigating the labyrinth: How generative models tackle complex data sampling

The world of artificial intelligence (AI) has recently seen significant advancements in generative models, a type of machine-learning algorithms that "learn" patterns from sets of data in order to generate new, similar sets of data. Generative models are often used for things like drawing images and natural language generation – a famous example are the models used to develop chatGPT. Generative models have had remarkable success in various applications, from image and video generation to composing music and to language modeling. The problem is that we are lacking in theory when it comes to the capabilities and limitations of generative models; understandably, this gap can seriously affect how we develop and use them down the line. One of the main challenges has been the ability to effectively pick samples from complicated data patterns, especially given the limitations of traditional methods when dealing with the kind of high-dimensional and complex data commonly encountered in modern AI applications.