The motion of fatty acid vesicles driven by adhesion gradients of a liquid substrate (Langmuir monolayer) has been investigated. Trajectories of the vesicle motion reveal not only heterogeneity among vesicles in different regions of the monolayer but also heterogeneity within single-vesicle trajectories. Trajectories often exhibit complex behaviors such as circular and oscillating ones. Some vesicles exhibit intermittent dynamics that results in jump diffusion trajectories. In many vesicles their mean square displacements and effective diffusion coefficients exhibit a wide range of behaviors: (i) simple Brownian, (ii) subdiffusive, (iii) superdiffusive, and (iv) their combined motions. Even in the resting regime that the vesicle does not move substantially it exhibits active fluctuations due to spatio-temporal variations of the adhesion gradients of the monolayer. The results are compared with those in motor protein-driven transport of micrometer-sized particles bound to the cytoskeletal network and polymerization motor transport in. the cell previously reported.