Holographic generative flows with AdS/CFT

Abstract Holography, in the form of the anti-de Sitter/conformal field theory 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 Generative AdS (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 modified National Institute of Standards and Technology, 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.