提出可微碰撞监督的牙齿排列网络，解耦任务与特征建模，避免牙齿重叠。

Tooth arrangement is an essential step in the digital orthodontic planning process. Existing learning-based methods use hidden teeth features to directly regress teeth motions, which couples target pose perception and motion regression. It could lead to poor perceptions of three-dimensional transformation. They also ignore the possible overlaps or gaps between teeth of predicted dentition, which is generally unacceptable. Therefore, we propose DTAN, a differentiable collision-supervised tooth arrangement network, decoupling predicting tasks and feature modeling. DTAN decouples the tooth arrangement task by first predicting the hidden features of the final teeth poses and then using them to assist in regressing the motions between the beginning and target teeth. To learn the hidden features better, DTAN also decouples the teeth-hidden features into geometric and positional features, which are further supervised by feature consistency constraints. Furthermore, we propose a novel differentiable collision loss function for point cloud data to constrain the related gestures between teeth, which can be easily extended to other 3D point cloud tasks. We propose an arch-width guided tooth arrangement network, named C-DTAN, to make the results controllable. We construct three different tooth arrangement datasets and achieve drastically improved performance on accuracy and speed compared with existing methods.