Quantum generative models leverage the probabilistic structure of quantum mechan- ics to learn and reproduce complex data distributions beyond classical capabilities. Among these, Born machines encode probabilities via quantum amplitudes, offering efficient sampling and expressive power. However, their scalability is hindered by issues such as barren plateaus. In this thesis, we investigate Tensor Network Born Machines (TNBMs), which integrate tensor networks into the Born machine framework to overcome training obstacles while retaining expressive power. We examine their theoretical underpinnings and practical implementation for learning quantum data distributions