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Shape changes resulting from segmental flexibility are ubiquitous in molecular and biological systems, and are expected to affect both the diffusive motion and (biological) function of dispersed objects. The recent development of colloidal structures with freely-jointed bonds have now made a direct experimental investigation of diffusive shape-changing objects possible. Here, we show the effect of segmental flexibility on the simplest possible model system, a freely-jointed cluster of three spherical particles, and validate long-standing theoretical predictions. We find that in addition to the rotational diffusion time, an analogous conformational diffusion time governs the relaxation of the diffusive motion, unique to flexible assemblies, and that their translational diffusivity differs by a small but measurable amount. We also uncovered a Brownian quasiscallop mode, where diffusive motion is coupled to Brownian shape changes. Our findings could have implications for molecular and biological systems where diffusion plays an important role, such as functional site availability in lock-and-key protein interactions., Comment: Ruben W. Verweij and Pepijn G. Moerman contributed equally to this work. 22 pages, 11 figures