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‘Universal distribution approximation for probability distribution’
25 min readNov 1, 2024
On the Universality of Coupling based Normalizing Flows 2402.06578v1 Universality of Coupling based Normalizing Flows
The insights in this section indicate that existing constructions rely on pathological normalized flows and do not converge under KL divergence, which prompts us to introduce new universal theorems.
Theorem 4.6. Coupling-based normalizing flows with affine couplings are distributional universal approximator under the convergence metric ∆affineas given in Section 4.4.
Corollary 4.7. Coupling-based normalizing flows with coupling functions at least as expressive as affine couplings are distributional universal approximator under the convergence metric ∆affineas given in Section 4.4.
