A Reddit user Tommaso Romanò has created a procedural ivy generator in Unity. The work was shared via the author's Twitter account and in the r/Unity3D subreddit. The vines generate during runtime and their paths are evaluated using Raycasts and the Normal Vectors of the surface. The generator seems to be highly customizable and the colors and paths can be altered.
Tommaso also shared a tutorial on making the same generator for your Unity projects. The first part of the tutorial can be found on the artist's Twitter page and shows how the branches were generated.