Orthodontic motion planning plays a crucial role in digital orthodontics by predicting tooth motion sequences to assist dentists in formulating treatment plans efficiently. Most prior work generates the entire intermediate tooth motion sequence given the initial and target tooth alignments. In practice, only the initial alignment of the patient is obtained. However, no existing method can predict the complete motion sequence using only the initial tooth alignment. To address this gap, we propose OrthoDiff, a novel target-free framework that uses only initial tooth alignment through a progressive generation strategy. This strategy generates tooth motion sequences by decomposing the entire motion sequence into multi-level motions, progressively constraining the inference space and reducing the complexity of target-free planning from coarse to fine. Moreover, we design a hierarchical diffusion transformer as the backbone of OrthoDiff, which treats tooth alignment as a sequence of tooth tokens and fully leverages the topological prior knowledge of the dental model. Through extensive evaluations, we demonstrate that our method significantly outperforms state-of-the-art techniques in target-free tooth motion generation. Ablation studies further confirm the efficacy of key components in our network design. Meanwhile, we also achieve state-of-the-art results in tooth target alignment prediction, benefiting from our framework. The code and data will be publicly available at https://github.com/Intelligent-Orthodontics/OrthoDiff.github.io.

Tooth motion generation is an essential task in digital orthodontic treatment for precise and quick dental healthcare, which aims to generate the whole intermediate tooth motion process given the initial pathological and target ideal tooth alignments. Most prior works for multi-agent motion planning problems usually result in complex solutions. Moreover, the occlusal relationship between upper and lower teeth is often overlooked. In this paper, we propose a collaborative tooth motion diffusion model. The critical insight is to remodel the problem as a diffusion process. In this sense, we model the whole tooth motion distribution with a diffusion model and transform the planning problem into a sampling process from this distribution. We design a tooth latent representation to provide accurate conditional guides consisting of two key components: the tooth frame represents the position and posture, and the tooth latent shape code represents the geometric morphology. Subsequently, we present a collaborative diffusion model to learn the multi-tooth motion distribution based on inter-tooth and occlusal constraints, which are implemented by graph structure and new loss functions, respectively. Extensive qualitative and quantitative experiments demonstrate the superiority of our framework in the application of orthodontics compared with state-of-the-art methods.