#score-function

Question 1: Single choice

Diffusion models work with the score of a density, $\mathbf{s}(\mathbf{x}) = \nabla_{\mathbf{x}} \log p(\mathbf{x})$ . For a single Gaussian $p = \mathcal{N}(\boldsymbol\mu, \sigma^2 I)$ , what do the direction and the length of the score tell you at a point $\mathbf{x}$ ?

Direction: toward the mode (uphill in density). Length: larger the farther $\mathbf{x}$ is from the mode1
Direction: away from the mode (downhill in density). Length: larger the closer $\mathbf{x}$ is to the mode2
Direction: toward the mode. Length: largest at the mode itself and shrinking with the distance3
Direction: along the contour lines of the density. Length: the same everywhere4

Timed test