Diffusion Models

A Glimpse of Differential Equations Flow Models Example: Linear ODE If Adding Stochasticity to the Differential Equations A $dX_t$ Notation Constructing Training Targets for Flow & Diffusion Models from DE View Conditional and Marginal Distribution Path Conditional and Marginal Vector Field Side Note: Continuity Equation Extending to Stochastic Differential Equations Theorem: SDE Extension Trick Actually Optimizing for the Target Constructed Flow Matching! Example: Gaussian Path Score Matching! More on Score Matching: What to learn and what not to learn A Summary on Both Models from Differential Equations View References A Glimpse of Differential Equations We can view the target objects as vectors $z\in \mathbb{R}^d$, which is reasonable this notation is enought for many cases like images, videos or robots’ actions....

References: Tutorial on Diffusion Models for Imaging and Vision by Stanley Chan Dr. Yang Song’s blog on Score Matching Basics of Langevin Dynamics Unlike DDPM, which models the generative model as a hidden variable model with $x_{1:T}$ as the hidden variables, score-matching models, while deeply linked to DDPM, starts from a sampling view and later concerns about the distribution we sampled from. Let’s start with an assumption that we have a distribution $p(x)$ that we can sample from, and this distribution is exactly the distribution we want (say, the image distribution of a cat)....

Implementation really matters when it comes to training Diffusion Models. In this post, we will discuss some tircks, some problems I encountered, coding details and model architectures that avoid awkward failure of noise in noise out. Our goal is to generate satisfying samples from 2 common datasets: MNIST (easier) and CIFAR-10 (harder). References: The Annotated Diffusion Model Diffusers Lil’Log What are Diffusion Models? UNet Architecture UNet is a common architecture for image generation....

In this blog we will try to understand the member of diffusion family, DDPM. Given the common structure shared by variational autoencoders (VAEs) and diffusion models, we will first discuss some important content in VAE, and then introduce the DDPM. The blog will try to be self-contained and mathematically clear, but some prior knowledge of VAEs and generative models is assumed. References: VAE on Wikipedia Lil’Log What are Diffusion Models?...