Beta is the diffusion coefficient that controls how much noise enters an image at one timestep. A noise schedule usually increases beta gradually, moving from a small amount of noise toward a larger amount. section 12.9
For example, a schedule can increase beta from 0.0001 near the first timestep to 0.02 near timestep 1000. Alpha is calculated as 1 − beta, so beta controls the portion of signal no longer preserved at that step. Alpha-bar multiplies the alpha values across timesteps to track the remaining original signal. section 12.9
Using beta in a schedule
A simple implementation creates evenly spaced beta values between 0.0001 and 0.02, calculates alpha as 1.0 minus beta, and computes alpha-bar with a cumulative product. Forward diffusion then uses alpha-bar to mix the original image with random noise. The same alpha and beta schedule is reused during denoising so the reverse process mirrors noising. section 12.9 section 12.25
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 |
|
Compare beta, alpha, and alpha-bar across timesteps to see how a small per-step change progressively reduces the remaining signal. section 12.9
