We introduce CHOrD, a novel framework for scalable synthesis of 3D indoor scenes, designed to create house-scale, collision-free, and hierarchically structured indoor digital twins. In contrast to existing methods that directly synthesize the scene layout as a scene graph or object list, CHOrD incorporates a 2D image-based intermediate layout representation, enabling effective prevention of collision artifacts by successfully capturing them as out-of-distribution (OOD) scenarios during generation. Furthermore, unlike existing methods, CHOrD is capable of generating scene layouts that adhere to complex floor plans with multi-modal controls, enabling the creation of coherent, house-wide layouts robust to both geometric and semantic variations in room structures. Additionally, we propose a novel dataset with expanded coverage of household items and room configurations, as well as significantly improved data quality. CHOrD demonstrates state-of-the-art performance on both the 3D-FRONT and our proposed datasets, delivering photorealistic, spatially coherent indoor scene synthesis adaptable to arbitrary floor plan variations.

While deep learning techniques have become extremely popular for solving a broad range of optimization problems, methods to enforce hard constraints during optimization, particularly on deep neural networks, remain underdeveloped. Inspired by the rich literature on meshless interpolation and its extension to spectral collocation methods in scientific computing, we develop a series of approaches for enforcing hard constraints on neural fields, which we refer to as Constrained Neural Fields (CNF). The constraints can be specified as a linear operator applied to the neural field and its derivatives. We also design specific model representations and training strategies for problems where standard models may encounter difficulties, such as conditioning of the system, memory consumption, and capacity of the network when being constrained. Our approaches are demonstrated in a wide range of real-world applications. Additionally, we develop a framework that enables highly efficient model and constraint specification, which can be readily applied to any downstream task where hard constraints need to be explicitly satisfied during optimization.