Learning goal: ∇log p_t, the score, points up the log-density landscape; √ᾱ_t E[x₀|x_t] − x_t, the denoising displacement, has the same direction with scale factor σ _t ² under the Gaussian-noise Tweedie identity.

Pale points: samples at t; √ᾱ _t x₀ marks the scaled clean location before noise. Arrows show normalized field directions.

Overlay both fields: their normalized arrows coincide up to numerical precision because the denoising displacement equals σ _t ² times the score. At large t, arrows become approximately directed toward the origin because p _t approaches a standard Gaussian, whose score is −x. At smaller noise they reflect the target's finer geometry.