Fusion of a panchromatic (PAN) image and corresponding multispectral (MS) image is also known as pansharpening, which aims to combine abundant spatial details of PAN and spectral information of MS images. Due to the absence of high-resolution MS images, available deep-learning-based methods usually follow the paradigm of training at reduced resolution and testing at both reduced and full resolution. When taking original MS and PAN images as inputs, they always obtain sub-optimal results due to the scale variation. In this paper, we propose to explore the self-supervised representation for pansharpening by designing a cross-predictive diffusion model, named CrossDiff. It has two-stage training. In the first stage, we introduce a cross-predictive pretext task to pre-train the UNet structure based on conditional Denoising Diffusion Probabilistic Model (DDPM). While in the second stage, the encoders of the UNets are frozen to directly extract spatial and spectral features from PAN and MS images, and only the fusion head is trained to adapt for pansharpening task. Extensive experiments show the effectiveness and superiority of the proposed model compared with state-of-the-art supervised and unsupervised methods. Besides, the cross-sensor experiments also verify the generalization ability of proposed self-supervised representation learners for other satellite datasets. Code is available at https://github.com/codgodtao/CrossDiff.