Memory-enhanced diffusivity in walking droplets mediated by wave interference

The motion of particles subject to random perturbations is a ubiquitous problem across fields, including fluid mechanics, active matter, and statistical physics. Whether arising from temporal fluctuations or spatial heterogeneities, such stochastic forces typically lead to diffusive behavior in the long-time limit. A notable exception is Anderson localization, in which diffusion is suppressed due to the interplay between spatial disorder and the wavelike nature of quantum particles. A recent hydrodynamic analog of this phenomenon, observed in walking droplets -- which exhibit dual wave-particle behaviors by virtue of their guiding wave field -- raises fundamental questions about how path memory governs the emergent transport in wave-dressed active particles. Replacing spatial disorder with temporal fluctuations, here, we demonstrate that walking droplets exhibit an increased orientational persistence and, consequently, an amplified diffusion coefficient compared to inertial active particles lacking wave memory. By analyzing the nonlocal wave forces generated during sharp turns, we identify a wave-mediated restoring force that tends to drive the droplet back toward its previous direction of motion, thereby rationalizing the observed enhancement in diffusivity. Our results arise from generic wave interference effects and may thus extend to other wave-dressed active particle systems, suggesting new strategies for controlling transport via wave-mediated memory.