Generative models realized with machine learning techniques are powerful
tools to infer complex and unknown data distributions from a finite number of
training samples in order to produce new synthetic data. Diffusion models are
an emerging framework that have recently overcome the performance of the
generative adversarial networks in creating synthetic text and high-quality
images. Here, we propose and discuss the quantum generalization of diffusion
models, i.e., three quantum-noise-driven generative diffusion models that could
be experimentally tested on real quantum systems. The idea is to harness unique
quantum features, in particular the non-trivial interplay among coherence,
entanglement and noise that the currently available noisy quantum processors do
unavoidably suffer from, in order to overcome the main computational burdens of
classical diffusion models during inference. Hence, we suggest to exploit
quantum noise not as an issue to be detected and solved but instead as a very
remarkably beneficial key ingredient to generate much more complex probability
distributions that would be difficult or even impossible to express
classically, and from which a quantum processor might sample more efficiently
than a classical one. Therefore, our results are expected to pave the way for
new quantum-inspired or quantum-based generative diffusion algorithms
addressing more powerfully classical tasks as data generation/prediction with
widespread real-world applications ranging from climate forecasting to
neuroscience, from traffic flow analysis to financial forecasting.

量子驱动扩散模型的量子泛化被提出，并讨论了可在实际量子系统上进行实验测试的三种量子噪声驱动的生成扩散模型。通过利用量子噪声作为生成更复杂的概率分布的重要成分，我们的结果有望为处理从气候预测到神经科学、交通流分析到金融预测等广泛的实际应用任务的新型量子驱动生成扩散算法铺平道路。