High-resolution sinogram completion is critical for computed tomography reconstruction, as missing projections can introduce severe artifacts. While diffusion models provide strong generative priors for this task, their inference cost grows prohibitively with resolution. We propose HRSino, a training-free and efficient diffusion inference approach for high-resolution sinogram completion. By explicitly accounting for spatial heterogeneity in signal characteristics, such as spectral sparsity and local complexity, HRSino allocates inference effort adaptively across spatial regions and resolutions, rather than applying uniform high-resolution diffusion steps. This enables global consistency to be captured at coarse scales while refining local details only where necessary. Experimental results show that HRSino reduces peak memory usage by up to 30.81% and inference time by up to 17.58% compared to the state-of-the-art framework, and maintains completion accuracy across datasets and resolutions.