CLUE: Correlated Latent Uncertainty for Single-Pass Deep Uncertainty Estimation

We present Correlated Latent Uncertainty Estimation (CLUE), a single-pass deep uncertainty quantification framework that combines efficient amortized neural prediction with Bayesian-style information propagation across inputs. CLUE introduces a kernel-based prior, allowing cross-input dependence over latent variables while preserving test-time inference efficiency. CLUE requires neither posterior sampling nor ensembles, and avoids matrix inversion during inference, yet recovers posterior contraction behavior analogous to conventional Bayesian models. In the white-noise limit of the kernel, CLUE reduces to standard evidential deep learning (EDL). This limiting case reveals standard EDL as amortized variational inference with an independent latent structure, providing a probabilistic explanation for several pathologies of EDL identified in prior work. Empirically, CLUE exhibits consistent Bayesian-like uncertainty contraction and improved uncertainty quality across synthetic and real-world benchmarks, while maintaining competitive predictive accuracy and fast single-pass inference.