The paper introduces a novel approach to specifying flexible and complex approximate posterior distributions in variational inference using normalizing flows. Normalizing flows transform a simple initial density through a sequence of invertible transformations, allowing for the construction of distributions that closely match the true posterior. The authors develop finite and infinitesimal flows, providing a unified view of methods for constructing rich posterior approximations. They demonstrate that normalizing flows can improve the performance and applicability of variational inference by better matching the true posterior distribution. The paper also discusses the theoretical advantages of normalizing flows and their scalability, showing that they can achieve better results on various datasets compared to other posterior approximation methods.The paper introduces a novel approach to specifying flexible and complex approximate posterior distributions in variational inference using normalizing flows. Normalizing flows transform a simple initial density through a sequence of invertible transformations, allowing for the construction of distributions that closely match the true posterior. The authors develop finite and infinitesimal flows, providing a unified view of methods for constructing rich posterior approximations. They demonstrate that normalizing flows can improve the performance and applicability of variational inference by better matching the true posterior distribution. The paper also discusses the theoretical advantages of normalizing flows and their scalability, showing that they can achieve better results on various datasets compared to other posterior approximation methods.