Introduction to Diffusion Models for Generative AI
Chapter 1: Generative Modeling Fundamentals
Overview of Generative Models
Motivation for Diffusion Models
The Core Idea: Noise and Denoise
Probabilistic Framework Introduction
Quiz for Chapter 1
Chapter 2: The Forward Diffusion Process
Defining the Markov Chain
Gaussian Noise Schedule
Mathematical Formulation per Step
Sampling from Intermediate Steps
Properties of the Forward Process
Practice: Simulating Forward Diffusion
Quiz for Chapter 2
Chapter 3: The Reverse Diffusion Process
The Goal: Reversing the Markov Chain
Approximating the Reverse Transition
Parameterizing the Reverse Process with Neural Networks
Predicting the Noise Component
Mathematical Formulation of the Denoising Step
Quiz for Chapter 3
Chapter 4: Model Architecture and Training
The U-Net Architecture for Noise Prediction
Integrating Timestep Information
Defining the Training Objective
Simplified Training Loss Derivation
The Training Algorithm
Hands-on Practical: Setting up the U-Net
Quiz for Chapter 4
Chapter 5: Sampling and Generation Process
Generating Data from Noise
The DDPM Sampling Algorithm
Understanding Sampling Variance
Introduction to Faster Sampling: DDIM
The DDIM Sampling Algorithm
Trade-offs Between DDPM and DDIM
Practice: Implementing Sampling Loops
Quiz for Chapter 5
Chapter 6: Conditional Generation with Diffusion Models
Motivation for Conditional Generation
Classifier Guidance
Classifier-Free Guidance (CFG)
Implementing Classifier-Free Guidance
Text Conditioning Basics
Architecture Modifications for Conditioning
Hands-on Practical: Applying Guidance
Quiz for Chapter 6
Mathematical Formulation of the Denoising Step
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- Denoising Diffusion Probabilistic Models, Jonathan Ho, Ajay Jain, Pieter Abbeel, 2020 Advances in Neural Information Processing Systems (NeurIPS) DOI: 10.48550/arXiv.2006.11239 - This seminal paper introduced the Denoising Diffusion Probabilistic Models (DDPM) framework, providing the foundational mathematical formulation for the forward and reverse diffusion processes, including the derivation of the posterior q(x_{t-1}|x_t, x_0) discussed in the section.
- The Annotated Diffusion Model, Niels Rogge, Kashif Rasul, 2022 (Hugging Face) - This detailed tutorial, part of the Hugging Face Diffusers documentation, provides an annotated implementation and explanation of the DDPM mathematical steps, aligning closely with the content presented.
- Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole, 2020 International Conference on Learning Representations (ICLR) DOI: 10.48550/arXiv.2011.13456 - This paper unified DDPMs with score-based models and introduced the continuous-time framework for generative diffusion, offering a deeper theoretical understanding of the reverse process.