Knowledge graphs mostly exhibit a mixture of branching relations, e.g., hasFriend, and complex structures, e.g., hierarchy and loop. Most knowledge graph embeddings have problems expressing them, because they model a specific relation r from a head h to tails by starting at the node embedding of h and transitioning deterministically to exactly one other point in the embedding space. We overcome this issue in our novel framework ItCAREToE by modeling relations between nodes by relation-specific, stochastic transitions. Our framework is based on stochastic ItCARETo processes, which operate on low-dimensional manifolds. ItCAREToE is highly expressive and generic subsuming various state-of-the-art models operating on different, also non-Euclidean, manifolds. Experimental results show the superiority of ItCAREToE over other deterministic embedding models with regard to the KG completion task.