Exact Recovery of Lipschitz Orthogonal Coordinate Transformations via Constrained Normalizing Flows

Nonlinear independent component analysis (nICA) is generally unidentifiable due in part to measure-preserving automorphisms (MPAs), which induce indistinguishable latent representations. We show that for non-Gaussian sources with mild regularity assumptions, such MPAs are not Lipschitz, motivating Lipschitz continuity as a structural assumption. Under this condition, we prove global identifiability of nICA within the class of Orthogonal Coordinate Transformations (OCTs) with bounded sources, recovering the true components up to permutation and scaling. Our analysis reduces the learning problem to a linear program over the Birkhoff polytope, and extends to functions with symmetric Jacobians, revealing connections to optimal transport. We introduce OCTNet and SYMNet, normalizing flow architectures that enforce these constraints in practice. Experiments demonstrate strong recovery performance and robustness to model misspecification, outperforming existing approaches.