Fault detection has been extensively studied in both academia and industry. The rareness of faulty samples in the real world restricts the use of many supervised models, and the reliance on domain expertise for feature engineering raises Other barriers. For this reason, this paper proposes an unsupervised, end-to-end approach to fault detection based on a flow-based model, the Nonlinear Independent Components Estimation (NICE) model. A NICE model models a target distribution via a sequence of invertible transformations to a prior distribution in the latent space. We prove that, under certain conditions, the L2-norm of normal samples’ latent codes in a trained NICE model is Chi-distributed. This facilitates the use of hypothesis testing for fault detection purpose. Concretely, we first apply Zero-phase Component Analysis to decorrelate the data of normal states. The whitened data are fed to a NICE model for training, in a maximum likelihood sense. At the testing stage, samples whose L2-norm of latent codes fail in the hypothesis testing are suspected of being generated by different mechanisms and hence regarded as potential faults. The proposed approach was validated on two datasets of vibration signals; it proved superior to several alternatives. We also show the use of NICE, a type of generative model, can produce real-like vibration signals because of the model's bijective nature.