Hi Arnaud ,
Essential Diagram does not support import/export of Visio diagrams. Essential Diagram's Visio Import feature extends only to the import and reuse of shapes from Visio stencil files (*.vss) files. However I have logged a feature request in this regard. You can trace the status of this feature request from the following link.
Feature Request #1404 - To add support for import/export diagram to Excel, Word and Visio file.We will implement this feature at the earliest and keep you informed.
Thanks for using Syncfusion product.
Regards,
Nagaraj