Minimizing the Kullback–Leibler divergence from a fixed normal distribution with mean 4 and standard deviation 2 to a parametrized normal distribution.

Equipotential curves in black; flow fields generated by gradient descent in blue with (A) Euclidean metric in mean μ and standard deviation σ, displayed in μ−σ–plane (left) and μ−σ²–plane (right); (B) Euclidean metric in mean μ and variance s = σ², displayed in μ−σ–plane (left) and μ−σ²–plane (right); and (C) Euclidean metric in mean μ and precision τ = 1/σ², displayed in μ−σ–plane (left) and μ−σ²–plane (right).