A normalizing flow is an invertible transformation that f Z (x) : R d → R d that maps high-dimensional data x ∼ P X (x) to a latent space representation z ∼ P Z (z), with inverse f -1 (i.e., f -1 • f (z) = z). The distribution P Z (called the "standard" or "base" distribution) is chosen to be one that is easy to sample from and whose density is easy to evaluate, typically an isotropic Gaussian.