Abstract: Generative artificial intelligence is reshaping computational physics by turning the construction of controllable mappings from simple priors to complex target distributions into a learnable and physically testable framework. Focusing on high-energy nuclear physics, this review discusses how normalizing flows, diffusion models and related generative methods can be interpreted as probability transporters and learnable dynamical surrogates, and how they can be combined with reweighting, Metropolis correction and nonequilibrium identities to remain scientifically reliable. We summarize recent progress in lattice field theory, heavy-ion collision simulation, detector fast simulation, inverse problems and equation-of-state inference, and further review how symmetry, conservation laws and geometric structure can be embedded into model design. Finally, we discuss connections to statistical physics, quantum many-body systems, materials design and automated scientific discovery, and outline open challenges in scalability, uncertainty quantification, interpretability and physics consistency.