Diverse human motion prediction focuses on forecasting plausible future human motions based on past motion sequence, which has caused widespread attention. Note that there exists a discrepancy between the latent space dimension and the original human motion dimension. This discrepancy affects the generated human motion quality and accuracy. In this paper, we propose a novel method, called GAM, to innovatively map both the observed human motion sequence and the reconstructed human motion sequence into the latent space, and then minimize the divergence between these sequences in the latent space. Specifically, latent reconstruction losses are employed to ensure consistency across both the data space and the latent space. This operation can effectively align the human motion sequence with the latent representation, and mitigate the challenges between the uncertainty of human motion factors and inherent dimensionality differences. In addition, we employ the Mamba model to extract the spatio-temporal features of the dynamics of human motions. Through comprehensive experiments on two widely-used benchmarks, Human3.6M and HumanEva-I, our method is shown to outperform existing state-of-the-art approaches in both diversity and accuracy.