xₜ = αₜ x₀ + σₜ ε is a vector sum in 2D.
The blue arrow is the signal component (toward x̂₀),
the red arrow is the noise component (toward ε̂).
Predicting one determines the other — they sit on opposite ends of the same decomposition through xₜ.
Drag xₜ to see how the decomposition changes near different data modes.