<p>In many physical systems, degrees of freedom are coupled <i>via</i> hydrodynamic forces, even in the absence of Hamiltonian interactions. A particularly important and widespread example concerns the transport of microscopic particles in fluids near deformable boundaries. In such a situation, the influence of elastohydrodynamic couplings on Brownian motion remains to be understood. Unfortunately, the temporal and spatial scales associated with the thermal fluctuations of usual surfaces are often so small that their deformations are difficult to monitor experimentally, together with the much slower and larger particle motion at stake. Here, we propose a minimal model describing the hydrodynamic coupling of a colloidal particle to a fluctuating elastic mode, in presence of an external periodic potential. We demonstrate that the late-time diffusion coefficient of the particle increases with the compliance of the elastic mode. Our results reveal and quantify two features: first, spontaneous microscopic transport in complex environments can be affected by soft boundaries – a situation with numerous practical implications in nanoscale and biological physics; and second, the effects of fast and tiny surface deformations are imprinted in long-term and large-distance colloidal mobility, and are therefore measurable in practice.</p>