Multi-modal Sequential Recommendation (SR) incorporates rich side information (e.g., textual and visual features) to enhance dynamic user preference modeling. However, existing frameworks inevitably suffer from a Dual-Noise Dilemma: (1) Feature-level redundancy stemming from the semantic gap between generic pre-trained representations and fine-grained recommendation intent; and (2) Sequence-level stochasticity induced by spurious interactions such as accidental clicks. To break this bottleneck, we propose DDMSR, a novel Dual-level Denoising Multi-modal Sequential Recommendation framework that systematically purifies signals from both feature-topological and sequence-frequency perspectives. Specifically, we first design a graph-based feature denoising module that leverages Laplacian smoothing on item semantic graphs as a structural low-pass filter, effectively suppressing high-frequency semantic noise while preserving salient features. For sequence purification, we introduce a frequency-domain sequence denoising module, utilizing the Fast Fourier Transform and a learnable frequency filter to adaptively modulate the interaction spectrum and attenuate anomalous signals. Furthermore, a multi-modal contrastive alignment objective is incorporated to bridge the heterogeneity gap and enforce cross-modal semantic consistency. Extensive experiments on four public benchmark datasets demonstrate that DDMSR consistently outperforms state-of-the-art baselines, providing a highly robust and efficient solution for multi-modal sequential recommendation. The source code is available at: https://github.com/jluo00/DDMSR.

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