Electroencephalography (EEG) is a promising, non-invasive, and cost-effective modality for Alzheimer's disease (AD) detection, but deep learning methods are limited by small and imbalanced clinical datasets. Generative augmentation offers a solution, yet existing approaches rely on inefficient class-specific models or fail to capture complex spatial and temporal brain dynamics. To address this, we propose GraM-Diff, a unified classifier-guided Graph-Mamba diffusion framework for EEG synthesis. It embeds Graph Convolutional Networks within a diffusion U-Net to model inter-electrode connectivity and Bidirectional Mamba state-space blocks for linear-complexity long-range temporal modeling. Latent-space classifier guidance lets a single model generate both healthy and pathological EEG within a shared representation, avoiding fragmented per-cohort pipelines. Across four EEG-based AD benchmarks, synthetic augmentation improves classification, yields superior Context-FID and correlation scores over strong generative baselines, and enhances robustness in data-scarce settings.

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