The introduction of Variational Autoencoders (VAE) has been marked as a breakthrough in the history of representation learning models. Besides having several accolades of its own, VAE has successfully flagged off a series of inventions in the form of its immediate successors. Wasserstein Autoencoder (WAE), being an heir to that realm carries with it all of the goodness and heightened generative promises, matching even the generative adversarial networks (GANs). Needless to say, recent years have witnessed a remarkable resurgence in statistical analyses of the GANs. Similar examinations for Autoencoders however, despite their diverse applicability and notable empirical performance, remain largely absent. To close this gap, in this paper, we investigate the statistical properties of WAE. Firstly, we provide statistical guarantees that WAE achieves the target distribution in the latent space, utilizing the Vapnik-Chervonenkis (VC) theory. The main result, consequently ensures the regeneration of the input distribution, harnessing the potential offered by Optimal Transport of measures under the Wasserstein metric. This study, in turn, hints at the class of distributions WAE can reconstruct after suffering a compression in the form of a latent law.

Let, f,g P ( C). Observe that, sup Using Dudley's chaining argument coupled with symmetrization, it can be shown that (Corollary

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.

The introduction of Variational Autoencoders (VAE) has been marked as a breakthrough in the history of representation learning models. Besides having several accolades of its own, VAE has successfully flagged off a series of inventions in the form of its immediate successors. Wasserstein Autoencoder (WAE), being an heir to that realm carries with it all of the goodness and heightened generative promises, matching even the generative adversarial networks (GANs). Needless to say, recent years have witnessed a remarkable resurgence in statistical analyses of the GANs. Similar examinations for Autoencoders however, despite their diverse applicability and notable empirical performance, remain largely absent.

The introduction of Variational Autoencoders (VAE) has been marked as a breakthrough in the history of representation learning models. Besides having several accolades of its own, VAE has successfully flagged off a series of inventions in the form of its immediate successors. Wasserstein Autoencoder (WAE), being an heir to that realm carries with it all of the goodness and heightened generative promises, matching even the generative adversarial networks (GANs). Needless to say, recent years have witnessed a remarkable resurgence in statistical analyses of the GANs. Similar examinations for Autoencoders, however, despite their diverse applicability and notable empirical performance, remain largely absent. To close this gap, in this paper, we investigate the statistical properties of WAE. Firstly, we provide statistical guarantees that WAE achieves the target distribution in the latent space, utilizing the Vapnik Chervonenkis (VC) theory. The main result, consequently ensures the regeneration of the input distribution, harnessing the potential offered by Optimal Transport of measures under the Wasserstein metric. This study, in turn, hints at the class of distributions WAE can reconstruct after suffering a compression in the form of a latent law.