  Classical diffusion models have shown superior generative results. Exploring
them in the quantum domain can advance the field of quantum generative
learning. This work introduces Quantum Generative Diffusion Model (QGDM) as
their simple and elegant quantum counterpart. Through a non-unitary forward
process, any target quantum state can be transformed into a completely mixed
state that has the highest entropy and maximum uncertainty about the system. A
trainable backward process is used to recover the former from the latter. The
design requirements for its backward process includes non-unitarity and small
parameter count. We introduce partial trace operations to enforce non-unitary
and reduce the number of trainable parameters by using a parameter-sharing
strategy and incorporating temporal information as an input in the backward
process. We present QGDM's resource-efficient version to reduce auxiliary
qubits while preserving generative capabilities. QGDM exhibits faster
convergence than Quantum Generative Adversarial Network (QGAN) because its
adopted convex-based optimization can result in better convergence. The results
of comparing it with QGAN demonstrate its effectiveness in generating both pure
and mixed quantum states. It can achieve 53.02% higher fidelity in mixed-state
generation than QGAN. The results highlight its great potential to tackle
challenging quantum generation tasks.
