Source
Hsueh et al. (2025), LIT-555 — read as NOTE-297. The cold end of
the evidence is Bansal et al. (2022), LIT-553. Filed for #163’s
“[theory] warm diffusion”.
The account
It replaces THEORY-079, which read Cold Diffusion as showing that noise is incidental and any degradation, iterated, generates. This account keeps the restore-and-redegrade procedure and gives noise the job that one denied it: keeping the reverse process where the forward process went.
Two degradations, two effects. Noise hides information randomly and isotropically, and its forward marginals cover the space between data points. Blur deletes high frequencies deterministically, and its forward marginals collapse many data points onto one.
Why the cold side fails. When many clean images map to one blurry image, the deblurring prediction is their mean, which is not itself a natural image. A reverse step toward it lands somewhere the forward process never went, so the network sees an input unlike its training data and its prediction is unreliable. Noise prevents this by making the collapsed images indistinguishable before blur merges them, so the reverse process never has to choose deterministically between them.
Why some blur helps. Fine detail in natural images is predictable from
coarse structure. A deblurring head can use that dependency, while a pure
denoiser has to rebuild detail as if it were independent of the coarse
structure. Natural spectra fall roughly as 1/f² and noise is flat, so in
high bands noise dominates early. Blur applied to a band only after noise
has swamped it keeps the manifold intact and still hands work to the
deblurrer. On CIFAR-10 that is about BNR = 0.5.
What was actually shown
- The degradation curve. At fixed model, sampler and 35 steps, FID 1.97 → 1.85 → 2.01 → 2.57 → 11.97 as BNR goes 0 → 0.5 → 1 → 2 → 10 (LIT-555, Table 3). Higher BNR also needs more steps to recover (Figure 5)
- The cold end, independently. Cold Diffusion’s noiseless generation is FID 97.00 on CelebA, and σ = 0.002 of noise halves it (LIT-553, Table 5)
What this does not say
The manifold departure is inferred, not observed. Nothing measures where reverse-process states sit relative to forward-process states. The FID curve is the thing to be explained, and it is consistent with other explanations: for example that a two-headed model at high BNR simply learns a harder deblurring problem.
The “blur helps” half is thin. 1.97 → 1.85 FID, best of three sampling rounds, one dataset, no variance.
Nothing about latent diffusion. Latent spectra are not 1/f² image
spectra, and the BNR rule is derived from pixel statistics.
Why Proposed
It replaces an account the record has rejected and fits both papers’ numbers, but its mechanism has not been measured, and the half about blur helping rests on a margin smaller than the unreported variance plausibly is.