What Comes Out Of The Noise Schedule

You are training a DDPM with the simplified objective. For one example the sampler draws a timestep with $\bar\alpha_t = 0.36$ , a data point $x_0 = 0.8$ (a single scalar coordinate), and noise $\epsilon = -1.0$ , then forms $x_t = \sqrt{\bar\alpha_t},x_0 + \sqrt{1-\bar\alpha_t},\epsilon$ .

What is $x_t$ , and what does the mean-squared-error target for $\epsilon_\theta(x_t, t)$ equal on this example?

$x_t = -0.32$ , and the target is the score $1.25$

$x_t = -0.32$ , and the target is $x_0 = 0.8$

$x_t = -0.352$ , and the target is $\epsilon = -1.0$

$x_t = -0.32$ , and the target is $\epsilon = -1.0$