The generation of indoor furniture layouts has significant applications in augmented reality, smart homes, and architectural design. Successful furniture arrangement requires proper physical relationships (e.g., collision avoidance) and spacing relationships between furniture and their functional zones to be respected. However, manually defined relationships are almost always incomplete and can produce unrealistic layouts. This work instead extracts spacing relationships automatically based on a hierarchical analysis and adopts the Delaunay Triangulation to produce important triple relationships. Compared to pairwise relationship modeling, triple relationships account for interactions and space utilization among multiple objects. To this end, we introduce RelTriple, a novel approach that enhances furniture distribution by learning spacing relationships between objects and regions. We formulate triple relationships as object-to-object (O2O) losses and object-to-region (O2R) losses and integrate them directly into the training process of generative diffusion. Our approach consistently improves over existing state-of-the-art methods in visual results evaluation metrics on unconditional layout generation, floorplan-conditioned layout generation, and scene rearrangement, achieving at least 12% on the introduced spatial relationship metric and superior spatial coherence and practical usability.