Pansharpening is a powerful technique for generating high-resolution multispectral (HRMS) images by fusing currently available image pairs of low-resolution multispectral (LRMS) and texture-rich panchromatic (PAN) data, effectively addressing the physical constraints of satellite sensors. While recent generative diffusion models have demonstrated impressive performance gains in this domain, their prohibitive computational demands and training costs hinder practicality in resource-constrained remote sensing satellite systems. In this work, we propose NODiff, a novel diffusion framework that replaces the conventional attention-based denoising backbone with a neural operator, seamlessly integrating operator learning and generative modeling into an efficient yet effective solution for pansharpening. In practice, we implement our approach through a two-stage learning paradigm: First, we pretrain the proposed Neural Operator-based diffusion model to learn the high-resolution texture priors essential for pansharpening. Afterward, we freeze the pretrained parameters, and design a lightweight conditional detail guidance adapter to enable efficient fine-tuning for generating desired HRMS images. Meanwhile, a time-aware low-rank adaptation is introduced to dynamically refine high-frequency details potentially affected by spectral mode truncation. Extensive experiments on multiple benchmark datasets demonstrate that NODiff achieves competitive pansharpening performance while significantly reducing training and inference costs. Beyond pansharpening, our method provides new insights into building resource-efficient generative models.