3-D pose estimation of instruments is a crucial step towards automatic scene understanding in robotic minimally invasive surgery. Although robotic systems can potentially directly provide joint values, this information is not commonly exploited inside the operating room, due to its possible unreliability, limited access and the time-consuming calibration required, especially for continuum robots. For this reason, standard approaches for 3-D pose estimation involve the use of external tracking systems. Recently, image-based methods have emerged as promising, non-invasive alternatives. While many image-based approaches in the literature have shown accurate results, they generally require either a complex iterative optimization for each processed image, making them unsuitable for real-time applications, or a large number of manually-annotated images for efficient learning. In this paper we propose a self-supervised image-based method, exploiting, at training time only, the imprecise kinematic information provided by the robot. In order to avoid introducing time-consuming manual annotations, the problem is formulated as an auto-encoder, smartly bottlenecked by the presence of a physical model of the robotic instruments and surgical camera, forcing a separation between image background and kinematic content. Validation of the method was performed on semi-synthetic, phantom and in-vivo datasets, obtained using a flexible robotized endoscope, showing promising results for real-time image-based 3-D pose estimation of surgical instruments.