Normalizing flows are a family of generative models that have emerged as a powerful framework for flexible density estimation, efficient sampling, and probabilistic inference. The key idea is to construct complex probability distributions by applying a sequence of invertible transformations to simple base distributions, such as a Gaussian. This approach allows one to model high-dimensional data with exact likelihood evaluation and tractable training via maximum likelihood.

In this talk, I will introduce the foundations of normalizing flows, beginning with the mathematical underpinnings of invertible transformations and the change-of-variables formula. I will then discuss several widely used architectures—including coupling flows, autoregressive flows, and continuous-time flows—highlighting their strengths, limitations, and use cases.