Microsoft announce (July 2018) that Visio Visual for Power BI is generally available. This allows a user to use Visio Online and Power BI together to illustrate and compare data as both diagrams and visualisations in one place. From a licensing perspective, Office 365 subscribers can use five free trial instances of Visio Visual and after that, any user can view visuals, and users licensed with Visio Online Plan 1 or Plan 2 can edit a Visio Visual in Power BI.

Find the announcement here: http://bit.ly/2P9zTom.