## 3 Results
### Classification of Generative AI Models
#### 3.2.1 Variational Autoencoders (VAE)  
A variational autoencoder (VAE) is a type of autoencoder that combines variational inference with an encoder-decoder architecture. Autoencoders consist of an encoder network that maps high-dimensional data to a low-dimensional representation and a decoder network that reconstructs the original input from the representation [19]. However, traditional autoencoders lack the ability to generate new data points. In Figure 4, in a VAE, the encoder network maps the input data (x) to the parameters of a probability distribution in a latent space (z) using input layer and hidden layer composed of neural network units, such as dense or convolutional layers. This distribution is often modeled as a multivariate Gaussian with mean and covariance parameters [27] achieved in mean, variance layers. Samples are drawn from this latent space distribution in sampling layer, generated by the encoder, to produce new data points using the decoder network (y) with hidden and output layers. By sampling from the approximate posterior distribution in the latent space, VAEs can generate diverse outputs resembling the training data. Neural networks, such as fully connected networks or convolutional neural networks (CNNs), are commonly used as encoders and decoders in VAEs. The specific architecture \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Model** & **Architecture Components** & **Training Method** \\ \hline Variational Autoencoders & Encoder–Decoder & Variational Inference [19] \\ \hline Generative Adversarial Networks & Generator–Discriminator & Adversarial [44] \\ \hline Diffusion Models & Noising (Forward)–Denoising & Iterative Refinement [31] \\ \hline Transformers & Encoder–Decoder & Supervised [74] \\ \hline Language Models & Recurrent Neural Networks & Supervised [75] \\ \hline Normalizing Flow Models & Coupling Layers & Maximum-Likelihood Estimation [76] \\ \hline Hybrid Models & Combination of Different Models & Varied \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Architecture components and training methods used in generative AI models. Figure 3: Classification of the generative AI models based on the architecture. depends on the data and its complexity. For images or grid-like data, CNNs or deconvolutional neural networks (also known as convolutional transpose networks) are often employed as decoders. Training a VAE involves optimizing the model parameters by minimizing a loss function comprising a reconstruction loss and a regularization term. The reconstruction loss measures the discrepancy between the input data and the reconstructed output, while the regularization term computes the Kullback-Leibler (KL) divergence between the approximate posterior distribution and a chosen prior distribution in the latent space. This term promotes smoothness and regularization. The training process of a VAE includes selecting the network architecture, defining the loss function, and iterating through batches of input data. The encoder processes the data, latent space points are sampled, and the decoder reconstructs the input. The total loss, combining the reconstruction loss and regularization term, is computed, and gradients are used to update the model parameters through backpropagation. While VAEs offer generative modeling and capture complex latent representations, they may suffer from issues such as blurry reconstructions and challenges in evaluating the quality of generated samples.