<p>Although GNN-based multi-modal recommendation has proven effective in modeling user preferences, current approaches typically tackle issues in a fragmented manner, thereby failing to simultaneously mitigate the intricate noise found in both graph topologies and modal features. Specifically, current approaches face limitations in three aspects: the interference of noisy interactions within user feedback, the amplification of modal-specific noise during fusion, and the lack of semantic alignment between representations learned from heterogeneous sources. To systematically address these issues, this paper proposes PGS-Rec (Joint Learning of Principal Graphs and Spectral Representations), a unified framework that synergizes structural purification, feature denoising, and decision alignment. First, a Principal Graph Learning module is employed to adaptively extract core subgraphs from raw interactions, thereby purifying user feedback signals while preserving key collaborative information. Secondly, to mitigate content-related noise, multi-modal representations are transformed into the spectral domain, where trainable filters are employed to achieve adaptive denoising and robust fusion. Finally, a cross-view distribution alignment module, incorporating knowledge distillation, is designed to enforce alignment between the graph-derived behavioral view and the content-derived semantic view. By integrating these components, PGS-Rec ensures that the purified graph structure provides a reliable propagation path for the denoised features, while the alignment mechanism bridges the semantic gap, achieving a holistic improvement. Comprehensive empirical analysis conducted on diverse real-world datasets confirms that PGS-Rec surpasses existing state-of-the-art baselines, thereby verifying the efficacy of our proposed joint learning architecture. To facilitate reproducibility, the source code and datasets have been released at <a href="https://github.com/Zyh0815/PGS-Rec">https://github.com/Zyh0815/PGS-Rec</a>.</p>