k-means forces every point into exactly one cluster, with no notion of confidence. A Gaussian mixture model asks a softer question: what's the probability this point belongs to each cluster? Answering it requires an algorithm — expectation-maximisation — that recurs throughout probabilistic ML wherever there are hidden variables to infer.
Naive Bayes assumes something that is almost never true — that every feature is independent given the class — and yet remains a strong baseline for text classification decades after more sophisticated methods appeared. Understanding why a false assumption still produces a useful classifier is the real lesson of this page.
Autoencoders ended on an unsolved problem: the latent space has no known structure, so there's no principled way to pick a point to decode into a new sample. The variational autoencoder's fix is direct — force the latent space to match a known distribution during training, and sampling becomes as simple as drawing from that known distribution and decoding.