Diffusion Models — Noise Process & Denoising
Forward: q(xₜ|x₀) = N(√ᾱₜ x₀, (1-ᾱₜ)I) · Reverse: score matching
Controls
Timestep t / T:
0
T (total steps):
100
β schedule:
Linear
Cosine
Quadratic
Data distribution:
2D Mixture
Ring
Two Moons
Forward pass →
Reverse (denoise) ←
Reset to x₀
Forward:
Gradually add Gaussian noise over T steps. At t=T: pure noise N(0,I).
Reverse:
A neural network predicts the score ∇logp(xₜ) to denoise step-by-step.
DDPM:
xₜ₋₁ = (xₜ - β̃ₜ·ε̂)/√(1-βₜ) + σₜz