This paper introduces an energy‑adaptive noise schedule together with a spectral whitening strategy for transform‑domain diffusion models. Existing spectral diffusion approaches handle the non‑uniform statistics of transform coefficients by scaling, normalizing, or prioritizing frequencies, yet the forward diffusion noise schedule is typically independent of the underlying spectral energy distribution. We investigate whether the temporal evolution of the forward diffusion should also follow the spectral organization of natural images.
The proposed formulation combines global spectral whitening with an energy‑conditioned noise allocation. The injected noise is modulated jointly by the energy of each transform coefficient and an image‑dependent energy trajectory over diffusion time. The resulting forward process preserves Gaussian transitions, admits closed‑form marginals, and remains compatible with standard DDPM and DDIM samplers without altering the diffusion architecture.
Experiments on CIFAR‑10 demonstrate that adding the energy‑conditioned noise schedule and spectral whitening reduces the Fréchet Inception Distance of a compact DCT‑diff U‑Net variant from 142.48 to 100.45, confirming the contribution of both components.
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