Diffusion models now give the best perceptual quality in super-resolution (SR), but their architecture and training confine them to small fixed crops. Operational remote sensing needs seamless scenes orders of magnitude larger. Joint denoising fuses overlapping tiles at every reverse step and lets text-to-image diffusion generate beyond its training crop, but it assumes deterministic ODE samplers. With the stochastic sampler of SR models such as SR3, the averaging also partly cancels independent per-tile noise. This known variance erosion blurs the detail SR should recover and must be corrected. We carry variance-corrected fusion to conditional SR and derive Spatially-Decoupled Variance Correction (SDVC), an exact reformulation that replaces per-step global normalization with independent per-tile contributions accumulated in one additive pass. SDVC turns the coupled per-step computation into independent tile-local work, so the resulting pipeline, InfScene-SR, runs in parallel across GPUs and makes SR of arbitrarily large scenes feasible. On a 5$\times$ SR task built from NAIP aerial imagery, we evaluate whole scenes with fidelity, perceptual, seam-continuity, and faithfulness metrics. Under one backbone, InfScene-SR is the only fusion strategy that is seamless and sharp at once, the closest to the low-resolution observation among those that synthesize detail, and within 0.003 IoU of native high-resolution imagery on downstream invasive-plant segmentation. Code is available at https://github.com/TitorX/infscene-sr.

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