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. An example of numerical simulations for an hybrid classical-quantum generative diffusion model is also included. 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.

翻译：通过机器学习技术实现的生成模型是从有限训练样本中推断复杂未知数据分布、生成新合成数据的强大工具。扩散模型作为一种新兴框架，近期在生成合成文本与高质量图像方面已超越生成对抗网络的性能。本文提出并探讨了扩散模型的量子泛化，即三种可基于真实量子系统进行实验验证的量子噪声驱动生成扩散模型。其核心思想是利用量子特征（特别是当前可用噪声量子处理器难以避免的相干性、纠缠与噪声之间非平凡相互作用）来克服经典扩散模型在推理阶段的主要计算瓶颈。因此，我们建议将量子噪声视为一种极具价值的核心要素而非需要检测解决的问题，通过其生成更复杂的概率分布——这些分布难以甚至无法用经典方式表达，且量子处理器从中采样的效率可能优于经典处理器。文中还包含一个混合经典-量子生成扩散模型的数值模拟示例。预期我们的研究成果将为新型量子启发或量子基生成扩散算法铺平道路，使其能更强大地处理经典任务（如数据生成/预测），在气候预测、神经科学、交通流量分析及金融预测等广泛实际应用领域发挥重要作用。