https://www.youtube.com/watch?v=_JQSMhqXw-4

Introduction

A diffusion model is trained using variational inference to generate data through a parameterized Markov chain. The diffusion model consists of two main processes: the forward diffusion process, which incrementally adds noise to the data until it assumes the form of a normal distribution, and the reverse process, where this transformation is learned in reverse.

• Variational inference: The process of approximating the posterior probability distribution p(z|x) with a more manageable probability distribution q(z).
• Parameterize: The act of re-expressing an expression using different parameters. In this process, the number of parameters is usually chosen to be fewer than the order of the expression (e.g., using 2 parameters for a cubic expression), thus creating a mapping function to a lower dimension (e.g., from 3D to 2D).
• Markov chain: A stochastic process in which the transition from one state to another depends only on the immediate previous state.

Background

Forward(diffusion) process

Process that adds the noise from gaussian distribution

• Gradual Transformation: This process incrementally adds noise to data samples, progressively transforming them from their original distribution to pure noise.
• Complexity Reduction: As noise is added step by step, the complexity of the data is reduced, ultimately leading to a distribution resembling normal noise.
• Markov Chain Dependency: The process follows a Markov chain, where each step depends solely on the immediate previous state, ensuring a controlled addition of noise.