  Diffusion generative models have achieved remarkable success in generating
images with a fixed resolution. However, existing models have limited ability
to generalize to different resolutions when training data at those resolutions
are not available. Leveraging techniques from operator learning, we present a
novel deep-learning architecture, Dual-FNO UNet (DFU), which approximates the
score operator by combining both spatial and spectral information at multiple
resolutions. Comparisons of DFU to baselines demonstrate its scalability: 1)
simultaneously training on multiple resolutions improves FID over training at
any single fixed resolution; 2) DFU generalizes beyond its training
resolutions, allowing for coherent, high-fidelity generation at
higher-resolutions with the same model, i.e. zero-shot super-resolution
image-generation; 3) we propose a fine-tuning strategy to further enhance the
zero-shot super-resolution image-generation capability of our model, leading to
a FID of 11.3 at 1.66 times the maximum training resolution on FFHQ, which no
other method can come close to achieving.
