<p>Sea surface temperature (SST) anomaly detection plays an important role in marine environmental monitoring. However, SST series usually show strong non-stationarity, multi-scale variability, and complex spatiotemporal evolution, which makes accurate anomaly detection difficult. To address these challenges, this study proposes a Multi-resolution Graph Diffusion Network (MGDN) for SST anomaly detection. The proposed method first decomposes SST series into multi-resolution representations to distinguish slowly varying background components from short-term local disturbances. Dynamic graph learning is then used to model spatial dependencies among different regions. A cross-resolution guided diffusion reconstruction module further reconstructs normal SST evolution patterns in a coarse-to-fine manner. Meanwhile, the Koopman operator is incorporated into the reverse denoising process to constrain latent temporal dynamics and improve reconstruction stability under nonlinear variations. Experiments are conducted in the South China Sea and the Bohai Sea using different input window lengths. MGDN is compared with multiple baseline methods and demonstrates stable and competitive detection performance. Ablation and visualization analyses further verify the effectiveness of the main modules. The results suggest that MGDN provides an effective framework for SST anomaly detection in complex marine environments.</p>