  Diffusion models generate high-resolution images through iterative stochastic
processes. In particular, the denoising method is one of the most popular
approaches that predicts the noise in samples and denoises it at each time
step. It has been commonly observed that the resolution of generated samples
changes over time, starting off blurry and coarse, and becoming sharper and
finer. In this paper, we introduce "resolution chromatography" that indicates
the signal generation rate of each resolution, which is very helpful concept to
mathematically explain this coarse-to-fine behavior in generation process, to
understand the role of noise schedule, and to design time-dependent modulation.
Using resolution chromatography, we determine which resolution level becomes
dominant at a specific time step, and experimentally verify our theory with
text-to-image diffusion models. We also propose some direct applications
utilizing the concept: upscaling pre-trained models to higher resolutions and
time-dependent prompt composing. Our theory not only enables a better
understanding of numerous pre-existing techniques for manipulating image
generation, but also suggests the potential for designing better noise
schedules.
