Brain tumors are among the most clinically significant neurological diseases and remain a major cause of morbidity and mortality due to their aggressive growth and structural heterogeneity. As tumors expand, they induce substantial anatomical deformation that disrupts both local tissue organization and global brain architecture, complicating diagnosis, treatment planning, and surgical navigation. Yet a subject-specific reference of how the brain would appear without tumor-induced changes is fundamentally unobtainable in clinical practice. We present BrainNormalizer, an anatomy-informed diffusion framework that reconstructs pseudo-healthy MRIs directly from tumorous scans by conditioning the generative process on boundary cues extracted from the subject's own anatomy. This boundary-guided conditioning enables anatomically plausible pseudo-healthy reconstruction without requiring paired non-tumorous and tumorous scans. BrainNormalizer employs a two-stage training strategy. The pretrained diffusion model is first adapted through inpainting-based fine-tuning on tumorous and non-tumorous scans. Next, an edge-map-guided ControlNet branch is trained to inject fine-grained anatomical contours into the frozen decoder while preserving learned priors. During inference, a deliberate misalignment strategy pairs tumorous inputs with non-tumorous prompts and mirrored contralateral edge maps, leveraging hemispheric correspondence to guide reconstruction. On the BraTS2020 dataset, BrainNormalizer achieves strong quantitative performance and qualitatively produces anatomically plausible reconstructions in tumor-affected regions while retaining overall structural coherence. BrainNormalizer provides clinically reliable anatomical references for treatment planning and supports new research directions in counterfactual modeling and tumor-induced deformation analysis.