  Learning probability distribution is an essential framework in classical
learning theory. As a counterpart, quantum state learning has spurred the
exploration of quantum machine learning theory. However, as dimensionality
increases, learning a high-dimensional unknown quantum state via conventional
quantum neural network approaches remains challenging due to trainability
issues. In this work, we devise the quantum sequential scattering model (QSSM),
inspired by the classical diffusion model, to overcome this scalability issue.
Training of our model could effectively circumvent the vanishing gradient
problem to a large class of high-dimensional target states possessing
polynomial-scaled Schmidt ranks. Theoretical analysis and numerical experiments
provide evidence for our model's effectiveness in learning both physical and
algorithmic meaningful quantum states and show an out-performance beating the
conventional approaches in training speed and learning accuracy. Our work has
indicated that an increasing entanglement, a property of quantum states, in the
target states, necessitates a larger scaled model, which could reduce our
model's learning performance and efficiency.
