Optimal Extended Formulations from Optimal Dynamic Programming Algorithms

Abstract

While single-concept customization has been studied in 3D, multi-concept customization remains largely unexplored. To address this, we propose MultiDreamer3D that can generate coherent multi-concept 3D content in a divide-and-conquer manner. First, we generate 3D bounding boxes using an LLM-based layout controller. Next, a selective point cloud generator creates coarse point clouds for each concept. These point clouds are placed in the 3D bounding boxes and initialized into 3D Gaussian Splatting with concept labels, enabling precise identification of concept attributions in 2D projections. Finally, we refine 3D Gaussians via concept-aware interval score matching, guided by concept-aware diffusion. Our experimental results show that MultiDreamer3D not only ensures object presence and preserves the distinct identities of each concept but also successfully handles complex cases such as property change or interaction. To the best of our knowledge, we are the first to address the multi-concept customization in 3D.