A normal distribution models continuous values with a bell-shaped density. Its mean locates the center, while its variance controls spread; the standard normal distribution has mean zero and unit variance. section 5.1.1 section 9.1.1
In generative image systems, normal distributions provide tractable representations and noise processes:
- Diffusion models add noise tensors drawn from a standard normal distribution to images over many time steps, gradually approaching standard-normal noise. section 5.1.1
- Weighted combinations of image values and noise preserve a zero mean and unit variance under the stated normalization assumptions. section 5.1.1
- VAE encoders output the parameters of a normal distribution rather than mapping each image to one latent-space point. section 9.1.1
From an image to noise
Start with a normalized dog image x₀, add a standard-normal noise tensor at each diffusion step, and obtain xₜ through a weighted image-noise combination. At the final step, xₜ approximates standard-normal noise. section 5.1.1
Figure 5.2 The forward diffusion process
Trace how a clean image becomes progressively noisier across the forward diffusion process. section 5.1.1
