Radiology Report Generation (RRG) aims to automatically generate diagnostic reports from radiology images. To achieve this, existing methods have leveraged the powerful cross-modal generation capabilities of Multimodal Large Language Models (MLLMs), primarily focusing on optimizing cross-modal alignment between radiographs and reports through Supervised Fine-Tuning (SFT). However, by only performing instance-level alignment with the image-text pairs, the standard SFT paradigm fails to establish anatomically-grounded alignment, where the templated nature of reports often leads to sub-optimal generation quality. To address this, we propose \textsc{S2D-Align}, a novel SFT paradigm that establishes anatomically-grounded alignment by leveraging auxiliary signals of varying granularities. \textsc{S2D-Align} implements a shallow-to-deep strategy, progressively enriching the alignment process: it begins with the coarse radiograph-report pairing, then introduces reference reports for instance-level guidance, and ultimately utilizes key phrases to ground the generation in specific anatomical details. To bridge the different alignment stages, we introduce a memory-based adapter that empowers feature sharing, thereby integrating coarse and fine-grained guidance. For evaluation, we conduct experiments on the public \textsc{MIMIC-CXR} and \textsc{IU X-Ray} benchmarks, where \textsc{S2D-Align} achieves state-of-the-art performance compared to existing methods. Ablation studies validate the effectiveness of our multi-stage, auxiliary-guided approach, highlighting a promising direction for enhancing grounding capabilities in complex, multi-modal generation tasks.