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Objective of the Research The objective of this research is to prove that a prototypical deterministic model of microscopic chaos can lead to a stochastic diffusive process that is Gaussian distributed.Novelty of the work We give an alternative proof that the position process of a damped particle kicked by microscopic chaotic force describes a Gaussian process that is normal diffusive.The proof is based on the position probability distribution of the particle derived as an asymptotic series up till second-order employing "Feynman sums" on graphs of double binary forest.As in our earlier result obtained from the Salem-Zygmund approach [1],the time scale τ between kicks need not be small.