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Nanosized solid Pb inclusions in Al have fcc structure and perfect cuboctahedral shape. When the inclusions melt they attain a rounded equilibrium shape and due to the low miscibility between the two elements, the liquid inclusions are retained as individual nanosized droplets located inside the solid Al matrix. As the temperature is increased the smaller liquid Pb inclusions are observed to move in a three-dimensional random walk over distances that can be orders of magnitude larger than their size. Inclusions attached to dislocations exhibit a similar type of random walk confined to long-distance one-dimensional movement along the dislocation lines and short-range two-dimensional vibrations perpendicular to the dislocation lines. The diffusion coefficients of the moving inclusions can be obtained from an Einstein-Smoluchowski analysis of the inclusion traces providing input for information on the mechanisms responsible for the movements.