The goal of this thesis is to compare various methods used for solving inverse problems. While the forward mapping is typically well-defined and deterministic, the inverse mapping is most of the time more complicated, ambiguous and ill-posed. There is significant interest not only in accurately modeling both the forward and inverse mappings but also in obtaining reliable un- certainty estimates for the inverse predictions. In this thesis, we compare several approaches for inverse problem-solving, including Coupling Flows (CFs), Neural Spline Flows (NSFs), Invertible Neural Networks (INNs) and Conditional Flow Matching (CFM). The INN training framework is of particular interest and is extended with more complex Normalizing Flows. All these methods are evaluated on a range of datasets like synthetic nonlinear datasets (uniform cluster mixturedataset, sine-wave dataset, kinematics dataset) and real-world datasets (combined cycle power plant dataset and blast furnace dataset). Our results indicate that more expressive transformations do not always yield the best performance. The NSF does not continuously outperform simpler alternatives despite employing sophisticated spline transformations. For limited amount of data and noisy scenarios simpler flows such as CFs demonstrate comparable or occasionally better performance. The CFM emerges as an excellent alternative to NSF with largely equivalent results. In contrast, the INN approach, due to its specialized training procedure, struggled with stochastic tasks and proved challenging to fine-tune and train effectively.