In recent years, convolutional-neural-network-based methods have been introduced to the field of hyperspectral image super-resolution following their great success in the field of RGB image super-resolution. However, hyperspectral images appear different from RGB images in that they have high dimensionality, implying a redundancy in the high-dimensional space. Existing approaches struggle in learning the spectral correlation and spatial priors, leading to inferior performance. In this paper, we present a difference curvature multidimensional network for hyperspectral image super-resolution that exploits the spectral correlation to help improve the spatial resolution. Specifically, we introduce a multidimensional enhanced convolution (MEC) unit into the network to learn the spectral correlation through a self-attention mechanism. Meanwhile, it reduces the redundancy in the spectral dimension via a bottleneck projection to condense useful spectral features and reduce computations. To remove the unrelated information in high-dimensional space and extract the delicate texture features of a hyperspectral image, we design an additional difference curvature branch (DCB), which works as an edge indicator to fully preserve the texture information and eliminate the unwanted noise. Experiments on three publicly available datasets demonstrate that the proposed method can recover sharper images with minimal spectral distortion compared to state-of-the-art methods. PSNR/SAM is 0.3–0.5 dB/0.2–0.4 better than the second best methods. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.