Thanks to the rapid development of diffusion models, unprecedented progress has been witnessed in image synthesis. Prior works mostly rely on pre-trained linguistic models, but a text is often too abstract to properly specify all the spatial properties of an image, e.g., the layout configuration of a scene, leading to the sub-optimal results of complex scene generation. In this paper, we achieve accurate complex scene generation by proposing a semantically controllable Layout-AWare diffusion model, termed LAW-Diffusion. Distinct from the previous Layout-to-Image generation (L2I) methods that only explore category-aware relationships, LAW-Diffusion introduces a spatial dependency parser to encode the location-aware semantic coherence across objects as a layout embedding and produces a scene with perceptually harmonious object styles and contextual relations. To be specific, we delicately instantiate each object's regional semantics as an object region map and leverage a location-aware cross-object attention module to capture the spatial dependencies among those disentangled representations. We further propose an adaptive guidance schedule for our layout guidance to mitigate the trade-off between the regional semantic alignment and the texture fidelity of generated objects. Moreover, LAW-Diffusion allows for instance reconfiguration while maintaining the other regions in a synthesized image by introducing a layout-aware latent grafting mechanism to recompose its local regional semantics. To better verify the plausibility of generated scenes, we propose a new evaluation metric for the L2I task, dubbed Scene Relation Score (SRS) to measure how the images preserve the rational and harmonious relations among contextual objects. Comprehensive experiments demonstrate that our LAW-Diffusion yields the state-of-the-art generative performance, especially with coherent object relations.