  Probability models have been proposed in the literature to account for
"intelligent" behavior in many contexts. In this paper, probability propagation
is applied to model agent's motion in potentially complex scenarios that
include goals and obstacles. The backward flow provides precious background
information to the agent's behavior, viz., inferences coming from the future
determine the agent's actions. Probability tensors are layered in time in both
directions in a manner similar to convolutional neural networks. The discussion
is carried out with reference to a set of simulated grids where, despite the
apparent task complexity, a solution, if feasible, is always found. The
original model proposed by Attias has been extended to include non-absorbing
obstacles, multiple goals and multiple agents. The emerging behaviors are very
realistic and demonstrate great potentials of the application of this framework
to real environments.
