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Alpha

As explained in Grokking AI Algorithms, Second Edition

An alpha is a diffusion-schedule coefficient that controls the retained signal or corresponding denoising contribution at a timestep.

Alpha is the part of the signal retained at a diffusion timestep. Calculate it as 1 − beta: a larger alpha preserves more of the original image, while a smaller alpha permits more noise. section 12.9

Use alpha to understand how diffusion schedules control image changes:

  • Pair alpha with beta: beta specifies the noise added at a timestep, and alpha specifies the retained signal through 1 − beta. section 12.9
  • Distinguish alpha from alpha-bar: alpha describes one timestep, whereas alpha-bar multiplies earlier alpha values to represent the total signal remaining after t steps. section 12.9
  • Reuse the same alpha values during denoising so the reverse process mirrors the forward noising process. section 12.25

Reading a small schedule

At timestep 1, beta is 0.00010, so alpha is 0.99990: nearly all signal is retained. At timestep 3, beta is 0.00014 and alpha is 0.99986. The corresponding alpha-bar multiplies the alpha values from timesteps 1 through 3, giving 0.99964. section 12.9

Table 12.1 A subset of values for the noise schedule

Timestep (t)

Beta

Alpha calculation (1 - beta)

Alpha

Alpha-Bar calculation

Alpha-Bar

1

0.00010

1 - 0.00010

0.99990

0.99990

0.99990

2

0.00012

1 - 0.00012

0.99988

0.99990 × 0.99988

0.99978

3

0.00014

1 - 0.00014

0.99986

0.99990 × 0.99988 × 0.99986

0.99964

…

1000

0.02000

1 - 0.02000

0.98000

0.00004

Inspect the schedule table to compare beta, alpha, and alpha-bar across timesteps. section 12.9

How Grokking AI Algorithms, Second Edition covers it

How deep it goes
Defines alpha as 1 − beta, contrasts it with cumulative alpha-bar, and demonstrates schedule values without deriving deeper theory.
Examples
Uses timestep tables, a happy-face noise progression, pixel calculations, and NumPy schedule code.
What it assumes
Assumes basic arithmetic and introduces beta, alpha-bar, and timestep schedules alongside alpha.
What you can do after
Apply it via NumPy to calculate diffusion schedules and support matched forward-noising and reverse-denoising steps.
How it connects
Connects alpha with beta, alpha-bar, noise schedules, forward diffusion, and denoising.
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