Google recently demonstrated that we can do style interpolation by squeezing multiple styles into one deep neural net model. However, I personally found this approach to be not flexible because you have to squeeze a pre-defined amount of styles into one model, and you can only do style interpolation within those pre-defined styles. However, style interpolation using deep neural net is quite easy. I was able to simply use linearly weight models that is used in photopaint.us to achieve style interpolation. Here is an example. The style Van Gogh Night Market and Carribean are linearly interpolated to stylize the image Chicago, and the interpolation seems quite smooth.
Style1: Van Gogh Night Market
Carribean: 0, Night Market: 1