Title: Stable cognitive maps for Path Integration emerge from fusing visual and proprioceptive sensors. Abstract: Spatial navigation in biological agents relies on the interplay between external (visual, olfactory, auditory, $\dots$) and proprioceptive (motor commands, linear and angular velocity, $\dots$) signals. How to combine and exploit these two streams of information, which vastly differ in terms of availability and reliability is a crucial issue. In the context of a new two--dimensional continuous environment we developed, we propose a direct-inverse model of environment dynamics to fuse image and action related signals, allowing reconstruction of the action relating the two successive images, as well as prediction of the new image from its current value and the action. The definition of those models naturally leads to the proposal of a minimalistic recurrent architecture, called Resetting Path Integrator (RPI), that can easily and reliably be trained to keep track of its position relative to its starting point during a sequence of movements. RPI updates its internal state using the (possibly noisy) proprioceptive signal, and occasionally resets it when the image signal is present.  Notably, the internal state of this minimal model exhibits strong correlation with position in the environment due to the direct-inverse models, is stable across long trajectories through resetting, and allows for disambiguation of visually confusing positions in the environment through integration of past movement, making it a prime candidate for a \textbf{cognitive map}. Our architecture is compared to state-of-the-art LSTM networks on identical tasks, and consistently shows better performance while also offering more interpretable internal dynamics and higher-quality representations.