#linear-schedule

Question 1: Single choice

DDPM uses $T = 1000$ steps with $\beta_t$ increasing linearly from $\beta_1 = 10^{-4}$ to $\beta_T = 0.02$ . In $x_T = \sqrt{\bar\alpha_T}\,x_0 + \sqrt{1-\bar\alpha_T}\,\epsilon$ , roughly how large is the signal coefficient $\sqrt{\bar\alpha_T}$ ? Hint: $\ln \bar\alpha_T = \sum_t \ln(1-\beta_t) \approx -\sum_t \beta_t$ .

About $0.14$ : the noise level of the last step, $\sqrt{\beta_T}$ , sets the signal left1
About $0.006$ : $x_T$ is almost pure noise, with only a faint trace of $x_0$ 2
About $0.95$ : each step removes so little signal that most of $x_0$ survives3
Exactly $0$ : after $T$ steps no information at all about $x_0$ is left4

Timed test