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Placement migration is the movement of cells within an existing placement to address a variety of postplacement design-closure issues, such as timing, routing congestion, signal integrity, and heat distribution. To fix a design problem, one would like to perturb the design as little as possible while preserving the integrity of the original placement. This paper presents a new diffusion-based placement method based on a discrete approximation to the closed-form solution of the continuous diffusion equation. It has the advantage of smooth spreading, which helps preserve neighborhood characteristics of the original placement. Applying this technique to placement legalization demonstrates significant improvements in wire length and timing compared with other commonly used techniques.