Visualisation

The forward diffusion process: adding noise step by step

Last reviewed 5 May 2026

An image gradually corrupted by Gaussian noise becomes pure static.

From the chapter: Chapter 14: Generative Models

Glossary: diffusion model

Transcript

A clean image. Sharp edges, recognisable content.

Add a small amount of Gaussian noise. The image becomes slightly grainier. Most details intact.

Add more noise. The image starts to look hazy.

Continue. Each step adds a fixed-variance noise increment. The image degrades visibly.

After many steps, typically a thousand, the image is pure noise. The original signal is gone. The result is a sample from a standard Gaussian.

This is the forward diffusion process. A Markov chain that gradually destroys structure.

Crucially, the process is fixed and known. We can write down, exactly, the distribution at any intermediate step. Apply a closed-form formula directly: the noised image is a scaled version of the original plus scaled noise. No sequential simulation required.

This forward chain is the easy half of diffusion. The interesting half is the reverse: starting from pure noise and progressively removing it to recover an image.

Train a neural network to predict the noise at each step. To sample, start from noise, apply the network repeatedly, and an image appears.

The forward process tells you what the network must learn to undo. The reverse process is generation.

Stable Diffusion, DALL-E, Sora, Veo. All built on this two-step framing.

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