Working Principle of Diffusion Models
The core idea behind diffusion models is to train a neural network to reverse the diffusion process. During training, the model learns to predict the noise added at each step of the forward process. This is done by minimizing a loss function that measures the difference between the predicted and actual noise.
Forward Process (Diffusion)
The forward process involves gradually corrupting the data [Tex]x_0[/Tex] with Gaussian noise over a sequence of time steps. Let [Tex]x_t[/Tex] represent the noisy data at time step t. The process is defined as:
[Tex]x_t = \sqrt{1 – \beta_t} x_{t-1} + \sqrt{\beta_t} \epsilon[/Tex]
where:
- [Tex]\beta_t[/Tex] is the noise schedule, a small positive number that controls the amount of noise added at each step.
- [Tex]\epsilon[/Tex] is is Gaussian noise.
As t increases, [Tex]x_t[/Tex] becomes more noisy until it approximates a Gaussian distribution.
Reverse Process (Denoising)
The reverse process aims to reconstruct the original data [Tex]x_0[/Tex] from the noisy data [Tex]x_T[/Tex] at the final time step T. This process is modelled using a neural network to approximate the conditional probability [Tex]p_\theta(x_{t-1} | x_t)[/Tex]. The reverse process can be formulated as:
[Tex] x_{t-1} = \frac{1}{\sqrt{1 – \beta_t}} \left( x_t – \frac{\beta_t}{\sqrt{1 – \beta_t}} \epsilon_\theta(x_t, t) \right)[/Tex]
where,
- [Tex]\epsilon_\theta[/Tex] is a neural network parameterized by [Tex]\theta[/Tex] that predicts the noise.
What are Diffusion Models?
Diffusion models are a powerful class of generative models that have gained prominence in the field of machine learning and artificial intelligence. They offer a unique approach to generating data by simulating the diffusion process, which is inspired by physical processes such as heat diffusion. This article delves into the diffusion model, exploring its architecture, working principles, applications, and advantages.
Table of Content
- Understanding Diffusion Models
- Key Components of Diffusion Models
- Architecture of Diffusion Models
- Working Principle of Diffusion Models
- Training Diffusion Models
- Applications of Diffusion Models
- Advantages of Diffusion Models
- Limitations of Diffusion Models
- Conclusion