Computed Tomography (CT) is a widely utilized imaging modality in clinical settings. Using densely acquired rotational X-ray arrays, CT can capture 3D spatial features. However, it is confronted with challenged such as significant time consumption and high radiation exposure. CT reconstruction methods based on sparse-view X-ray images have garnered substantial attention from researchers as they present a means to mitigate costs and risks. In recent years, diffusion models, particularly the Latent Diffusion Model (LDM), have demonstrated promising potential in the domain of 3D CT reconstruction. Nonetheless, due to the substantial differences between the 2D latent representation of X-ray modalities and the 3D latent representation of CT modalities, the vanilla LDM is incapable of achieving effective alignment within the latent space. To address this issue, we propose the Consistent Latent Space Diffusion Model (CLS-DM), which incorporates cross-modal feature contrastive learning to efficiently extract latent 3D information from 2D X-ray images and achieve latent space alignment between modalities. Experimental results indicate that CLS-DM outperforms classical and state-of-the-art generative models in terms of standard voxel-level metrics (PSNR, SSIM) on the LIDC-IDRI and CTSpine1K datasets. This methodology not only aids in enhancing the effectiveness and economic viability of sparse X-ray reconstructed CT but can also be generalized to other cross-modal transformation tasks, such as text-to-image synthesis. We have made our code publicly available at https://anonymous.4open.science/r/CLS-DM-50D6/ to facilitate further research and applications in other domains.