Pre-training methods on proteins are recently gaining interest, leveraging either protein sequences or structures, while modeling their joint energy landscape is largely unexplored. In this work, inspired by the success of denoising diffusion models, we propose the DiffPreT approach to pre-train a protein encoder by sequence-structure multimodal diffusion modeling. DiffPreT guides the encoder to recover the native protein sequences and structures from the perturbed ones along the multimodal diffusion trajectory, which acquires the joint distribution of sequences and structures. Considering the essential protein conformational variations, we enhance DiffPreT by a physics-inspired method called Siamese Diffusion Trajectory Prediction (SiamDiff) to capture the correlation between different conformers of a protein. SiamDiff attains this goal by maximizing the mutual information between representations of diffusion trajectories of structurally-correlated conformers. We study the effectiveness of DiffPreT and SiamDiff on both atom- and residue-level structure-based protein understanding tasks. Experimental results show that the performance of DiffPreT is consistently competitive on all tasks, and SiamDiff achieves new state-of-the-art performance, considering the mean ranks on all tasks. The source code will be released upon acceptance.