Session-based Social Recommendation (SSR) enhances item recommendations by incorporating both session interactions and social network data. Despite recent progress, existing SSR methods-primarily based on Graph Neural Networks-are highly susceptible to session noise (irrelevant or unintentional interactions) and social noise (misleading signals from connected users). Prior denoising strategies often rely on heuristic resampling or reweighting techniques, which lack generalizability and robustness across diverse datasets. In this work, we explore a novel direction by introducing diffusion models for denoising in SSR. However, applying diffusion to SSR presents unique challenges due to heterogeneous data modalities, incompatible noise patterns, and the absence of semantic guidance during the reverse process. To overcome these challenges, we propose D3MRec, a Dual Denoising Diffusion Model specifically designed for SSR. D3MRec employs a dual-branch architecture that independently models session sequences and social graphs, applying denoising diffusion in their respective hidden representation spaces. This decoupled design preserves the structural integrity of each modality while enabling modality-specific denoising. Moreover, we introduce cross-modal guidance by leveraging collaborative signals from the other branch during the reverse diffusion process, enhancing alignment between session intents and social preferences. The dual denoising processes not only mitigate noise within each modality but also serve as mutual priors, facilitating robust and consistent representation learning across modalities. Extensive experiments on multiple benchmarks show that D3MRec significantly outperforms state-of-the-art models, particularly under noisy conditions, demonstrating its effectiveness and robustness.