On Uniformly Scaling Flows: A Density-Aligned Approach to Deep One-Class Classification

Unsupervised anomaly detection is commonly approached through two major paradigms: deep one-class methods learn compact representations of nominal data, whereas deep density estimators such as normalizing flows model exact likelihoods. We show that uniformly scaling flows (USFs), normalizing flows with a constant Jacobian determinant, provide a principled bridge between these paradigms. Specifically, we prove that maximum-likelihood training of a USF reduces to a one-class objective whose inherent regularization mechanism prevents representational collapse and incentivizes density-aligned latent representations. This connection implies that USFs inherit both the density faithfulness of flows and the distance-based reasoning of one-class methods: their negative log-likelihood is monotonic in the latent norm, whereas in non-USFs the Jacobian term can entangle likelihood with local volume changes. Consequently, we advocate USFs as drop‑in replacements for non‑USFs in modern anomaly detection architectures and identify mechanisms that recover expressivity and enhance numerical stability. Across tabular and image benchmarks, this substitution simplifies optimization, markedly reduces run-to-run variability, and consistently matches or improves detection quality, while mitigating severe failure modes. Thus, our results unify two central perspectives on anomaly detection, indicating that normalizing flow-based methods benefit more from density-faithful geometry than from greater nominal expressivity.