Recent text-to-image (T2I) diffusion models have achieved remarkable progress in generating high-quality images given text-prompts as input. However, these models fail to convey appropriate spatial composition specified by a layout instruction. In this work, we probe into zero-shot grounded T2I generation with diffusion models, that is, generating images corresponding to the input layout information without training auxiliary modules or finetuning diffusion models. We propose a Region and Boundary (R&B) aware cross-attention guidance approach that gradually modulates the attention maps of diffusion model during generative process, and assists the model to synthesize images (1) with high fidelity, (2) highly compatible with textual input, and (3) interpreting layout instructions accurately. Specifically, we leverage the discrete sampling to bridge the gap between consecutive attention maps and discrete layout constraints, and design a region-aware loss to refine the generative layout during diffusion process. We further propose a boundary-aware loss to strengthen object discriminability within the corresponding regions. Experimental results show that our method outperforms existing state-of-the-art zero-shot grounded T2I generation methods by a large margin both qualitatively and quantitatively on several benchmarks. Project page: https://sagileo.github.io/Region-and-Boundary.