Learning goal: the squared-error optimum is not necessarily one original image; it is E[x₀ | x_t], a posterior-weighted average of possible clean sources. Greater noise can broaden uncertainty and make that average less detailed.

On the plot, click to place x _t, shown as a white circle. Bright points have larger posterior weights; the arrow points toward E[x₀ | x _t]

At small t, often only a few nearby candidates have large weights in this empirical toy. Increasing t spreads the weights and directs the estimate toward their weighted mean, possibly between modes rather than on a likely clean observation. This is the squared-error optimum: the conditional expectation, not a guaranteed recovery of the particular source.