CONJNORM: Tractable Density Estimation for Out-of-Distribution Detection This paper proposes a novel theoretical framework for out-of-distribution (OOD) detection based on Bregman divergence, which extends distribution considerations to an exponential family of distributions. The framework reframes density function design as a search for the optimal norm coefficient p against the given dataset. The method, called CONJNORM, leverages a Monte Carlo-based importance sampling technique to estimate the partition function, enabling tractable density estimation. Extensive experiments on OOD detection benchmarks demonstrate that CONJNORM outperforms existing methods by up to 13.25% and 28.19% on CIFAR-100 and ImageNet-1K, respectively. The framework provides a unified perspective for designing density functions and addresses the challenge of normalization in density estimation. The method is evaluated on various datasets and protocols, including hard OOD detection and long-tailed OOD settings, showing its effectiveness and robustness. The results highlight the importance of selecting an appropriate norm coefficient and the benefits of using conjugate functions in Bregman divergence for OOD detection.CONJNORM: Tractable Density Estimation for Out-of-Distribution Detection This paper proposes a novel theoretical framework for out-of-distribution (OOD) detection based on Bregman divergence, which extends distribution considerations to an exponential family of distributions. The framework reframes density function design as a search for the optimal norm coefficient p against the given dataset. The method, called CONJNORM, leverages a Monte Carlo-based importance sampling technique to estimate the partition function, enabling tractable density estimation. Extensive experiments on OOD detection benchmarks demonstrate that CONJNORM outperforms existing methods by up to 13.25% and 28.19% on CIFAR-100 and ImageNet-1K, respectively. The framework provides a unified perspective for designing density functions and addresses the challenge of normalization in density estimation. The method is evaluated on various datasets and protocols, including hard OOD detection and long-tailed OOD settings, showing its effectiveness and robustness. The results highlight the importance of selecting an appropriate norm coefficient and the benefits of using conjugate functions in Bregman divergence for OOD detection.