Mathematical Principles of the DDPM Diffusion Model and PyTorch Implementation

A Diffusion Model is a generative model that transforms a simple noise distribution into data samples, and it has recently achieved innovative results in the fields of image, audio, and video generation.

The core mechanism of DDPM (Denoising Diffusion Probabilistic Models) consists of the following two processes.

• Forward Diffusion Process: A fixed process that gradually adds Gaussian noise to data until it becomes a fully noisy state.
• Reverse Denoising Process: A process that gradually restores data from noise through a trained neural network to produce an actual image.

Mathematically, a Gaussian distribution and a variance schedule are used to define the loss function that the model must optimize. Based on Phil Wang's implementation, this guide connects theory and practice by providing step-by-step code implementation using PyTorch.