Derek Frost

Derek Frost

Computational Art and Science

Blog posts

2025

DDPMs: Statistical Foundations

53 minute read

Published:

Learning data distribution involves identifying ‘key factors’, which inherently ‘control’ the characteristics of our observations. The controlling relationship can either be statistical, or based on physical laws, where we understand precisely how these factors manifest in data. We discuss these ‘key factors’, commonly referred to as latent variables, in detail below. First, we discuss their estimation from data using Variational Inference (VI). Then, we describe the opposite direction - data reconstruction and generation from latent variables.

DDPMs: Introduction

13 minute read

Published:

By this point, you most probably have heard that Stable Diffusion gradually noises the image until it becomes not recognizable. After that, you reverse the process and create images. Let’s say, you are interested in creating schematic Swiss-roll images (I mean… everyone likes cute cats but how about a variety?). In this case, forward and reverse diffusion processes could look like below:

2024

DDPMs: Appendix A - Notations

10 minute read

Published:

Here, notations used in the DDPM blog series are defined. Please keep in mind, some notations are introduced later in text and it’s OK to not understand them all right away (e.g., when you just start reading).