Diffusion Model — Step-by-Step Visualization

Algorithm Pattern

Gradual Gaussian Corruption

Key Idea

The diffusion forward process adds Gaussian noise at each step. After T steps, any data becomes pure N(0,1) noise. The model learns to REVERSE this process — denoising step by step to generate new data.

Step-by-Step Approach

1. Choose a noise schedule: β_1, β_2, …, β_T (small positive values).
2. x_t = √α_t · x_{t-1} + √(1−α_t) · ε where ε ~ N(0,1), α_t = 1−β_t.
3. Equivalently: x_t = √ᾱ_t · x_0 + √(1−ᾱ_t) · ε where ᾱ_t = Π α_i.
4. Signal component √ᾱ_t decreases; noise component √(1−ᾱ_t) increases.
5. Model learns to predict ε given x_t and t — then reverses to get x_0.

Common Gotchas

• DDPM uses T=1000 steps; DDIM achieves good quality in 50 steps.
• The model is trained to predict the NOISE ε, not the clean image directly.
• Stable Diffusion applies diffusion in a compressed latent space, not pixel space.