This paper introduces an energy-adaptive noise scheduling and whitening strategy for transform-domain diffusion models. Existing spectral diffusion methods account for the non-uniform statistics of transform coefficients through coefficient scaling, normalization, or frequency prioritization, while the forward diffusion noise schedule remains largely independent of the underlying spectral-energy distribution. We investigate whether the temporal evolution of the forward diffusion process should also follow the spectral organization of natural images. The proposed formulation combines global spectral whitening with energy-conditioned noise allocation that jointly modulates the injected noise according to the energy of individual transform coefficients and an image-dependent energy path over diffusion time. The resulting forward process preserves Gaussian transitions with closed-form marginals and remains compatible with standard DDPM and DDIM procedures without modifying the diffusion architecture. Experiments on CIFAR-10 demonstrate the contribution of the proposed energy-conditioned noise schedule and spectral whitening, reducing Fréchet Inception Distance from 142.48 for a compact DCTdiff U-Net variant to 100.45.
Figures & tables
Figure 1: Radial DCT energy profile in the YCbCr and RGB domains for the full-spectrum representation.
Figure 2: Profile of YCbCr spectral coefficients after normalization ( 5 ) and spectral weighting ( 6 ) in the full-spectrum DCT representation.
Figure 3: Example of an image-dependent energy-conditioned noise path β~E(t) before mean normalization to the dimensionless modulation factor βE(t) , compared with the linear noise schedule βt .
Figure 4: FID evolution of DCTdiff, ECSdiff with ψk and ECSdiff during training, evaluated using 1000 generated samples at each checkpoint. The training-epoch axis is shown on a logarithmic scale.
Config.
50
100
150
250
350
500
1000
Pixel
107.19
106.81
100.30
98.23
98.41
95.26
86.69
USDM
233.89
226.44
182.36
213.54
166.80
188.30
192.24
DCTdiff
183.93
183.28
183.19
185.76
190.77
186.73
176.69
ECSdiff
171.92
147.61
140.85
138.59
136.46
132.61
136.68
Table 1: FID evolution during training.
Config.
500
1000
2500
5000
10000
DCTdiff
197.84
176.69
155.11
148.84
142.48
ECSdiff
157.78
136.68
114.39
104.58
100.45
Table 2: FID evaluation with different numbers of generated samples.
Figure 5: Sampling comparison after 1000 training epochs using the same seed from the test set for all methods. From left to right: USDM, DCTdiff, EAFW, and ECSdiff. Upper row: DDPM sampling. Lower row: DDIM sampling ( 14 ).
ECE & CSL University of Illinois Urbana-Champaign · Computer Science Department Carnegie Mellon University · ECE, CSL & NCSA University of Illinois Urbana-Champaign