This paper presents two methods using training over multidimensional sequences for automatic improvisation. We consider as dimensions musical features such as melody, harmony, timbre, etc. We first present a system combining interpolated probabilistic models with a factor oracle. The probabilistic models are trained on a corpus to learn the correlation between dimensions and are used to guide the navigation in the factor oracle that ensure a logical improvisation. Improvisations are therefore created in a way where the intuition of a context is enriched with multidimensional knowledge. We then introduce a system creating multidimensional improvisations based on communication between dimensions via probabilistc message passing. The communication infers some anticipatory behaviour on each dimension now influenced by the others, creating a consistent multidimensional improvisation. Both systems are evaluated by professional improvisers during listening sessions. Overall, they receive good feedback and show encouraging results, first on how multidimensional knowledge can help performing better navigation in the factor oracle and second on how communication through message passing can emulate the interactivity between dimensions or musicians.