This paper proposes a beamforming inferring scheme for holographic antenna arrays using conditional Wasserstein GAN with gradient penalty (WGAN-GP). The scheme aims to reduce the overhead of channel estimation and beamforming by inferring high-dimensional beamforming matrices from low-dimensional channel information. Traditional beamforming methods require full channel information and matrix inversion, which increases computational complexity and resource overhead. In contrast, the proposed method uses a generator and discriminator trained adversarially to infer the high-dimensional beamforming matrix from low-dimensional data, achieving comparable performance to the weighted minimum mean-square error (WMMSE) algorithm while reducing overhead by over 50%. The system model considers a downlink millimeter wave communication system with a base station equipped with a large antenna array and multiple radio frequency chains. The channel model is based on the WAIR-D dataset, which provides realistic channel information for simulation. The proposed method uses a conditional WGAN-GP architecture, where the generator learns the distribution of the target beamforming matrices through adversarial training, and the discriminator evaluates the generated data against the real data distribution. The generator is trained to produce high-dimensional beamforming matrices from low-dimensional channel and beamforming information, while the discriminator ensures the generated data is close to the real data distribution. The training process involves estimating the high-dimensional channel information and using WMMSE to obtain the respective beamforming matrices. The low-dimensional matrices are then combined with stochastic noise to generate the high-dimensional beamforming matrices. The loss function combines the Wasserstein distance and the L2 norm to optimize the generator and discriminator. The prediction stage requires only a small amount of channel information from a few antennas, significantly reducing the overhead of channel estimation and beamforming. Simulation results show that the proposed method achieves a significant reduction in computational time compared to the traditional WMMSE algorithm, with the running time reduced by over 50%. The method also demonstrates improved spectral efficiency, especially with smaller antenna spacing, due to the high spatial correlation between adjacent antennas. The proposed scheme outperforms traditional methods in terms of spectral efficiency and resource overhead, highlighting the potential of holographic antenna arrays in future wireless communication systems. Future work will focus on extending the method to wideband MIMO scenarios and incorporating reconfigurable intelligent surfaces to broaden its application.This paper proposes a beamforming inferring scheme for holographic antenna arrays using conditional Wasserstein GAN with gradient penalty (WGAN-GP). The scheme aims to reduce the overhead of channel estimation and beamforming by inferring high-dimensional beamforming matrices from low-dimensional channel information. Traditional beamforming methods require full channel information and matrix inversion, which increases computational complexity and resource overhead. In contrast, the proposed method uses a generator and discriminator trained adversarially to infer the high-dimensional beamforming matrix from low-dimensional data, achieving comparable performance to the weighted minimum mean-square error (WMMSE) algorithm while reducing overhead by over 50%. The system model considers a downlink millimeter wave communication system with a base station equipped with a large antenna array and multiple radio frequency chains. The channel model is based on the WAIR-D dataset, which provides realistic channel information for simulation. The proposed method uses a conditional WGAN-GP architecture, where the generator learns the distribution of the target beamforming matrices through adversarial training, and the discriminator evaluates the generated data against the real data distribution. The generator is trained to produce high-dimensional beamforming matrices from low-dimensional channel and beamforming information, while the discriminator ensures the generated data is close to the real data distribution. The training process involves estimating the high-dimensional channel information and using WMMSE to obtain the respective beamforming matrices. The low-dimensional matrices are then combined with stochastic noise to generate the high-dimensional beamforming matrices. The loss function combines the Wasserstein distance and the L2 norm to optimize the generator and discriminator. The prediction stage requires only a small amount of channel information from a few antennas, significantly reducing the overhead of channel estimation and beamforming. Simulation results show that the proposed method achieves a significant reduction in computational time compared to the traditional WMMSE algorithm, with the running time reduced by over 50%. The method also demonstrates improved spectral efficiency, especially with smaller antenna spacing, due to the high spatial correlation between adjacent antennas. The proposed scheme outperforms traditional methods in terms of spectral efficiency and resource overhead, highlighting the potential of holographic antenna arrays in future wireless communication systems. Future work will focus on extending the method to wideband MIMO scenarios and incorporating reconfigurable intelligent surfaces to broaden its application.