Tutorial on Diffusion Models for Imaging and Vision

Authors: Stanley H. Chan

What

This tutorial provides a comprehensive overview of diffusion models for imaging and vision, focusing on the core concepts and mathematical foundations behind these models, such as Variational Autoencoders (VAEs), Denoising Diffusion Probabilistic Models (DDPMs), Score-Matching Langevin Dynamics (SMLDs), and Stochastic Differential Equations (SDEs).

Why

Diffusion models have revolutionized generative AI, enabling remarkable applications in text-to-image and text-to-video generation. This tutorial is crucial for understanding the inner workings of these models and for researchers and students aiming to contribute to this burgeoning field or apply diffusion models in various domains.

How

The paper employs a step-by-step approach, beginning with the fundamentals of VAEs and progressively introducing more sophisticated concepts like DDPMs, SMLDs, and SDEs. Each section offers clear explanations, illustrative examples, mathematical derivations, and connections between different perspectives. The paper also discusses training and inference procedures for each model, highlighting the role of denoisers, score functions, and noise schedules.

Result

The tutorial effectively elucidates that diffusion models achieve their remarkable performance through incremental updates, gradually transforming noise into coherent data samples. The equivalence between denoising score matching and explicit score matching is a key result, justifying the use of denoisers in diffusion models. The connection between discrete-time diffusion iterations and continuous-time SDEs provides a unifying framework for analyzing and comparing different diffusion models.

LF

The tutorial points out that while iterative denoising is currently dominant, it may not be the definitive solution for image generation. Future research could explore more biologically plausible generative processes and address the computational cost associated with diffusion models. The justification for using non-Gaussian noise distributions is also a potential area for investigation.

Abstract

The astonishing growth of generative tools in recent years has empowered many exciting applications in text-to-image generation and text-to-video generation. The underlying principle behind these generative tools is the concept of diffusion, a particular sampling mechanism that has overcome some shortcomings that were deemed difficult in the previous approaches. The goal of this tutorial is to discuss the essential ideas underlying the diffusion models. The target audience of this tutorial includes undergraduate and graduate students who are interested in doing research on diffusion models or applying these models to solve other problems.