Inverse problems seek to recover an unknown source signal X for which we have indirect, partial, or noisy measurements Y. Most real-world inverse problems are ill-posed and the conventional line of attack has been to assume some structure (or prior) on X. Unfortunately, priors are not always available and often challenging to model mathematically. Generative models are powerful tools that learn patterns from data, hence a new opportunity to obtain samples from the priors of X. Given such a prior sample, it may be possible to compute how well the sample explains the measurement Y, and iteratively guide the denoising process to generate samples from the posterior p(X|Y). This paradigm of posterior sampling is unlocking a wide range of applications that—before the deep learning era—were facing performance walls. This talk will introduce the core ideas in this paradigm, generalize the framework, and show how this framework can be applied to multiple applications, including unsupervised speech separation, zero-shot human pose tracking, and inverse path planning.