Estimating ego-pose from cameras is an important problem in robotics with applications ranging from mobile robotics to augmented reality. While SOTA models are becoming increasingly accurate, they can still be unwieldy due to high computational costs. In this paper, we propose to solve the problem by using invertible neural networks (INN) to find the mapping between the latent space of images and poses for a given scene. Our model achieves similar performance to the SOTA while being faster to train and only requiring offline rendering of low-resolution synthetic data. By using normalizing flows, the proposed method also provides uncertainty estimation for the output. We also demonstrated the efficiency of this method by deploying the model on a mobile robot.