Editing Diffusion Models (section)

== <span style="color: #FFFFFF;">Understanding</span> ==
Diffusion models learn by training on data that has been corrupted with noise. At each training step, the model is shown a noisy version of a real image (with a known noise level t) and must predict the original noise that was added. Over millions of training examples, the model learns: "given a partially noisy image at noise level t, here's how to denoise it."

'''The forward process''' is fixed and mathematically defined:
x''t = √(ᾱ''t) · x''0 + √(1-ᾱ''t) · ε, where ε ~ N(0,I)

This means any noisy version of an image can be computed in one step directly from the original.

'''The reverse process''' is what the model learns:
p''θ(x''{t-1} | x_t) — given a noisy image at step t, predict the slightly less noisy image at step t-1.

'''Why not just use a GAN?''' GANs (Generative Adversarial Networks) were the previous state-of-the-art for image generation. They train a generator and discriminator in adversarial competition. Diffusion models have several advantages: more stable training (no mode collapse), better coverage of the data distribution (more diverse samples), and more principled theoretical grounding. The trade-off is slower sampling.

'''Latent diffusion''' solves the speed problem: instead of working in pixel space (512×512×3 = 786,432 dimensions), the VAE encodes images into a much smaller latent space (64×64×4 = 16,384 dimensions). The diffusion process runs in this compressed space — 50× fewer dimensions — making training and inference dramatically faster.
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