ShapeMorph: 3D Shape Completion via Blockwise Discrete Diffusion

We introduce ShapeMorph, a diffusion-based method specifically designed for generating precise and diverse 3D shape completions. By integrating an irregular dis-crete representation with a novel blockwise discrete dif-fusion model, ShapeMorph can produce multiple, high-quality shape completions while maintaining fidelity to the input. In particular, each 3D shape is encoded into a com-pact sequence of irregularly distributed discrete variables, ensuring an accurate capture of the object's topological de-tails. We then propose a blockwise discrete diffusion model to precisely learn the shape completion distribution based on various incompleteness. We also introduce a Flow trans-former into our diffusion process, serving as a denoising network, to enhance the modeling adaptability and flexibil-ity. ShapeMorph addresses common challenges in existing methods, such as poor completion, limited diversity, and misalignment with the input. Results show ShapeMorph outperforms state-of-the-art methods and effectively pro-cesses a variety of input types and levels of incompleteness.