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This paper discusses how to derive multidimensional conformable diffusion equation from continuous time random walks process by employing fractional Laplace transform and the conformable fractional derivative defined by Khalil et al in [10]. The results show that there exists intimate relationship between the stretched exponential function and conformable diffusion equation involving the conformable fractional derivative. The relationship is analogous to the relationship between the exponential function and usual diffusion equation involving usual derivative and the relationship between the Mittag-Leffler function and subdiffusion or slow diffusion equation involving Caputo fractional derivative. Multidimensional conformable FokkerPlanck equation is also derived here. The equation describes diffusion process influenced by external force fields. Conformable semigroup associated with the solution to the conformable diffusion equation has similar properties to the properties of the semigroup associated with the solution to usual diffusion except the semigroup property. For sufficiently large time, the graphs of the solution to the conformable diffusion equation and the subdiffusion equation involving Caputo fractional derivative are sufficiently close. Especially, for, the graphs are sufficiently close for . In presence of nonzero constant external force fields, the particle involved in the diffusion process moves faster toward the directions of the external force fields. [ABSTRACT FROM AUTHOR]