Recently, various methods have been introduced to address the OOD detection problem with training outlier exposure. These methods usually count on discriminative softmax metric or energy method to screen OOD samples. In this paper, we probe an alternative hypothesis on OOD detection by constructing a novel latent variable model based on independent component analysis (ICA) techniques. This novel method named Conditional-i builds upon the probabilistic formulation, and applies the Hilbert-Schmidt Independence Criteria that offers a convenient solution for optimizing variable dependencies. Conditional-i exclusively encodes the useful class condition into the probabilistic model, which provides the desired convenience in delivering theoretical support for the OOD detection task. To facilitate the implementation of the Conditional-i model, we construct unique memory bank architectures that allow for convenient end-to-end training within a tractable budget. Empirical results demonstrate an evident performance boost on benchmarks against SOTA methods. We also provide valuable theoretical justifications that our training strategy is guaranteed to bound the error in the context of OOD detection. Code is available at: https://github.com/OODHSIC/conditional-i.