Deformable object manipulation is a key capability in many robotic applications. A promising paradigm for this problem is shape servoing, which aims to control deformable objects toward desired goal shapes. However, existing approaches typically rely on impractical goal-shape acquisition methods, such as domain-knowledge engineering or manual manipulation. Moreover, prior methods generally assume a single deterministic goal and fail to handle multimodal goal settings, a common scenario in many real-world tasks where multiple distinct goal shapes can all lead to successful task completion. In this paper, we introduce DiffDef, a novel neural network that uses a diffusion model to learn a distribution of feasible goal shapes rather than predicting a single deterministic outcome. This allows DiffDef to generate diverse goal configurations while avoiding the mode-averaging artifacts common in deterministic predictors. We evaluate our method on several deformable manipulation tasks inspired by manufacturing and surgical applications, both in simulation and on two physical robotic platforms: the da Vinci Research Kit (dVRK) and a bimanual KUKA-based robotic system. The results demonstrate that DiffDef effectively captures multimodal goal distributions and significantly improves task performance in practical robotic settings. Website: sites.google.com/view/diffdef.

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