Diffusion-based image compression has exhibited robust performance. However, most existing methods primarily emphasize spatial domain, causing frequency dependencies to be learned only implicitly. We revisit this problem from a frequency perspective, and observe pronounced heterogeneity between global and local frequency dependencies. Global frequency patterns describe the energy distribution over the entire image, whereas patch level frequency relations govern the coupling of local details. These two forms of dependency differ substantially in both scale and semantic level, yet most methods overlook this distinction. To address this issue, we propose a learning heterogeneous global local frequency dependencies in diffusion-based image compression which uses Fourier and Mamba jointly models both global and local frequency correlations(FMDiff). The core of FMDiff is the dual branch FMBlock. In the frequency branch, features are decomposed into magnitude and phase, then fed into Mamba separately. Its scanning mechanism captures cross frequency coupling within each patch while aggregating long range frequency context along the sequence. Magnitude phase interactive modulation is then used to explicitly restore spectral information corrupted by compression. The spatial branch provides high level semantic constraints and is fused with the frequency branch during diffusion reconstruction. Extensive experiments show that FMDiff consistently improves performance across multiple datasets.