Holographic generative flows with AdS/CFT

Holography, in the form of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, offers a natural setting for generative modelling. Data on a boundary manifold lifts into a higher-dimensional bulk through a propagator, and this extra dimension plays the role of a flow parameter. We exploit this structure to build GenAdS, an approach to generative flow matching in which the dynamics are represented by the evolution of fields in AdS, together with a residual correction learned by a neural network. Boundary samples are encoded as scalar sources, transported into the bulk along the flow, and decoded after numerical integration. Our paradigm combines a Fourier-space encoding scheme for the data as AdS sources, a normalised radial phase space in which to stage the flow-matching dynamics, and a Klein--Gordon backbone to guide the flow. On a two-dimensional checkerboard benchmark, our experiments show that most of the benefit of GenAdS comes from the Fourier representation and convolutional architecture. However, when we remove momentum-channel regularisation, our most physics-informed GenAdS variant rivals the strongest physics-free control on boundary violation. On MNIST, GenAdS models remain close to a convolutional baseline on fidelity while achieving significantly higher recall at comparable precision, suggesting a fidelity-coverage trade-off. Our findings establish GenAdS as a physically interpretable and experimentally controllable framework for generative modelling, with many avenues for future extension.