ConjNorm: Tractable Density Estimation for Out-of-Distribution Detection
Existing post-hoc out-of-distribution (OOD) detection methods rely on logits, distance metrics, or strong distributional assumptions, limiting their ability to accurately model true data density. To address this, we propose a unified density modeling framework based on Bregman divergences, reformulating density estimation as a differentiable optimization problem for the optimal norm coefficient $ p $. We first uncover a novel paradigm for exponential-family density modeling under conjugate constraints, leading to ConjNorm—a method that achieves unbiased, analytically differentiable density estimation without restrictive distributional assumptions. ConjNorm integrates Bregman divergence theory, exponential-family modeling, and Monte Carlo importance sampling. On CIFAR-100 and ImageNet-1K, it reduces false positive rate at 95% true positive rate (FPR95) by 13.25% and 28.19%, respectively, over prior state-of-the-art methods, significantly improving both OOD detection accuracy and robustness.