Quantum Diffusion Models and Phase Transitions

Inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided by score functions. In a recent work [1], we show that the Petz recovery map under continuous-time evolution is exactly a quantum analogue of the diffusion model. If the quantum conditional mutual information (CMI) along the diffusion noise path always decays fast, such quantum diffusion models can always locally learn and generate new data. To test this insight under realistic conditions, we develop an efficient numerical simulation method that incorporates the natural noise in neutral atom platforms. The quantum-classical correspondence also inspires a new perspective on the phases of classical data distributions that are classified through mutual accessibility via local operations. Through numerical experiments, we demonstrate that the classical distributions in diffusion models also exhibit phases and phase transitions. This result also opens up new directions for studying phases of data distributions, the broader science of generative artificial intelligence, and guiding the design of neural networks inspired by physics concepts.