Multimodal change detection (MCD) is a crucial technology for applications in natural resource monitoring, disaster assessment, and urban planning. To address the reliance on labeled data and enhance the robustness of structural features in the existing methods, we propose a structure difference compensation graph autoencoder (SDC-GAE) for unsupervised MCD. It is recognized that the registered multimodal images exhibit consistency in structural features in unchanged areas, while the structural features in changed areas are distinct. SDC-GAE utilizes a graph convolutional network (GCN) to extract deep structural features from multimodal images. It uses the structural features of one time-phase image to reconstruct its spectral features in the spectral feature space of the target image. Through structural difference compensation, SDC-GAE learns the structural disparities between different images, with the compensation value directly reflecting the intensity of the changes. The SDC-GAE loss function consists of three components: image reconstruction loss, which evaluates the spectral feature discrepancy between the reconstructed and target images, guiding the model to reduce these differences via structural difference compensation; sparse constraint loss, which accounts for the fact that changes are typically confined to a few areas, ensuring the sparsity of the detected changes; and structural consistency loss, which aligns the structural features of the reconstructed image closely with those of the target image. The efficacy of our method is validated through experiments on eight multimodal datasets, where it is compared with the state-of-the-art methods.