## 3 Results
### Classification of Generative AI Models
#### 3.2.4 Diffusion Models  
Diffusion models are a type of generative model that operates by progressively introducing noise into data until it conforms to a desired distribution. The main idea behind diffusion models is to learn the process of reversing this diffusion, enabling the generation of valid samples [31]. In Figure 8 the forward pass of a diffusion model, Gaussian noise is iteratively added to the data in a series of steps. This noise corrupts the original data, gradually degrading its quality. As the noise level increases with each step, the images become increasingly distorted or destroyed. The objective of the diffusion model is to learn the dynamics of this diffusion process. By observing the corrupted data and the corresponding noise levels, the model learns to estimate the conditional probability distribution that describes the relationship between the corrupted data and the noise levels. Once the diffusion process is learned, the model can then perform the reverse pass, starting from the corrupted data and progressively removing the noise in each step [32]. This process of denoising leads to the generation of valid and realistic samples that resemble the original data distribution. There are three sub-types that differ in their implementation of the forward and backward diffusion pass. These sub-types are denoising diffusion probabilistic models (DDPMs), score-based generative models (SGMs), and stochastic differential equations (SDEs) [29]. _Denoising Diffusion Probabilistic Models (DDPMs):_ DDPMs, also known as denoising score-matching models, incorporate a two-step process for diffusion [101]. They apply Markov chains to progressively corrupt data with Gaussian noise and then reverse the forward diffusion process by learning Markov transition kernels. DDPMs focus on modeling the diffusion process and its associated reversibility. _Score-based Generative Models (SGMs):_ SGMs, also referred to as score-matching models, work directly with the gradient of the log density (score function) of the data [32]. They perturb the data with noise at multiple scales and jointly estimate the score function of all noisy data distributions using a neural network conditioned on different noise levels. This decoupling of training and inference steps enables flexible sampling. _Stochastic Differential Equations (SDEs):_ SDEs generalize diffusion models into continuous settings. They formulate noise perturbations and denoising processes as solutions to stochastic differential equations [1]. By leveraging the probabilistic flow of these equations, the reverse generation process can be modeled. Probability flow ordinary differential equations (ODEs) can also be utilized to represent the reverse process. Figure 8: Typical structure of diffusion model. Diffusion models employ neural network architectures to capture the complex dependencies and patterns in the data. These architectures can consist of various layers, such as convolutional layers for image data or recurrent layers for sequential data. The network is trained to learn the conditional probability distribution that describes the relationship between the corrupted data and the noise levels. The training objective of diffusion models is typically based on maximum-likelihood estimation or other probabilistic frameworks. The model parameters are optimized to minimize the discrepancy between the generated samples and the original data distribution. Various techniques such as gradient descent and backpropagation are employed to train the model effectively. Diffusion models, such as the deep diffusion generative models (DDGM), have gained prominence as strong generative models in recent years. They take a novel technique to modeling complicated data distributions by diffusing a given input iteratively towards a target distribution. However, to address specific difficulties or increase performance in specific scenarios, variations in diffusion models are necessary. The latent diffusion model (LDM) [102] is a variant of the diffusion model that operates in latent space.