The paper presents a novel beamforming inferring scheme for holographic antenna arrays using conditional Wasserstein generative adversarial networks (WGAN-GP). The proposed method aims to reduce the computational and resource overhead associated with traditional beamforming techniques, which often require full channel information and the inversion of large-dimensional matrices. By leveraging a small subset of channel information, the scheme can infer high-dimensional beamforming matrices with significant performance comparable to the weighted minimum mean-square error (WMMSE) algorithm, while reducing overhead by over 50%. The system model considers a downlink millimeter wave (mmWave) communication system with a base station (BS) equipped with an array of antenna elements and radio frequency chains. The target optimization problem involves inferring a high-dimensional beamforming matrix from low-dimensional channel and beamforming matrices. The proposed conditional WGAN-GP architecture consists of a generator and a discriminator, trained adversarially to provide an adaptive loss function. The generator learns to map low-dimensional beamforming matrices to high-dimensional ones, while the discriminator assesses the closeness of the generator's output to real data using the Wasserstein distance. Simulation results demonstrate that the proposed method achieves comparable performance to WMMSE while significantly reducing the time required for beamforming. The performance is evaluated using the WAIR-D dataset, showing that the proposed scheme can handle different antenna spacing and numbers, with better performance at smaller antenna spacing due to higher spatial correlation. The paper concludes by highlighting the potential of holographic antenna arrays and future work directions, including extending the method to MIMO wideband channels and incorporating reconfigurable intelligent surfaces.The paper presents a novel beamforming inferring scheme for holographic antenna arrays using conditional Wasserstein generative adversarial networks (WGAN-GP). The proposed method aims to reduce the computational and resource overhead associated with traditional beamforming techniques, which often require full channel information and the inversion of large-dimensional matrices. By leveraging a small subset of channel information, the scheme can infer high-dimensional beamforming matrices with significant performance comparable to the weighted minimum mean-square error (WMMSE) algorithm, while reducing overhead by over 50%. The system model considers a downlink millimeter wave (mmWave) communication system with a base station (BS) equipped with an array of antenna elements and radio frequency chains. The target optimization problem involves inferring a high-dimensional beamforming matrix from low-dimensional channel and beamforming matrices. The proposed conditional WGAN-GP architecture consists of a generator and a discriminator, trained adversarially to provide an adaptive loss function. The generator learns to map low-dimensional beamforming matrices to high-dimensional ones, while the discriminator assesses the closeness of the generator's output to real data using the Wasserstein distance. Simulation results demonstrate that the proposed method achieves comparable performance to WMMSE while significantly reducing the time required for beamforming. The performance is evaluated using the WAIR-D dataset, showing that the proposed scheme can handle different antenna spacing and numbers, with better performance at smaller antenna spacing due to higher spatial correlation. The paper concludes by highlighting the potential of holographic antenna arrays and future work directions, including extending the method to MIMO wideband channels and incorporating reconfigurable intelligent surfaces.