Flow Transformation: z ~ N(0,I) → x ~ Target

z ~ N(0,I)
Layer 1
Layer 2
Layer 3
Layer 4 (Final)

Jacobian Log-Determinant per Layer

Inverse Flow: x → z (Sampling Backward)

Target Distribution
Transformed Samples
Base Gaussian
4 layers
s = 1.0
t = 1.0
100%

Coupling Layer

y₁ = x₁
y₂ = x₂ ⊙ exp(s(x₁)) + t(x₁)

Invertible!
x₂ = (y₂ - t(x₁)) ⊙ exp(-s(x₁))

Jacobian

J = [I, 0; ∂y₂/∂x₁, diag(exp(s))]

log|det(J)| = Σᵢ s(x₁)ᵢ

Triangular → Easy determinant!

Metrics

Total log|det J|: -
Base log-prob: -
Final log-prob: -