Contribution
A process family interpolating hot and cold diffusion, a parameterization that splits the reverse step into denoising and deblurring, and an account of the trade-off between them in terms of the data manifold.
Key insight
Noise and blur remove different things, and only noise fills the gaps. Blur deletes high frequencies deterministically, so many clean images share one blurry image. The deblurring target is their mean, and stepping toward it leaves the manifold unless noise has already made those samples indistinguishable. Noise that dominates a band before blur removes it keeps the process on the data manifold.
Assumptions
- EDM architectures, training and Heun sampler, modified for two inputs and doubled outputs
- CIFAR-10 32², FFHQ 64², LSUN-church 128²
- Natural image spectra close to
1/f², for the BNR choice
Key results
- Table 3 (CIFAR-10, NFE 35): FID 1.97 (BNR 0) → 1.85 (0.5) → 2.01 (1) → 2.57 (2) → 11.97 (10)
- Figure 5: higher BNR needs more sampling steps to recover quality
- Table 1: improvements over EDM on CIFAR-10 and FFHQ. Best of three sampling rounds
Claims
| id | claim | strength | support |
|---|---|---|---|
| C1 | Removing noise from the process (high BNR) degrades generation | moderate | Table 3 sweep, one dataset |
| C2 | The degradation is caused by leaving the data manifold | weak | argued with an illustration, not measured |
| C3 | A moderate blur component improves on pure noise | weak | 0.12 FID, best of three, no variance |
| C4 | BNR = 0.5 can be chosen from spectra | weak | matches the sweep’s best, but the sweep is coarse and on one dataset |
Concepts
- BNR — blur level over noise level. 0 is hot diffusion, ∞ is cold
- Spectral dependency — the predictability of high-frequency detail from low-frequency structure in natural images
Connections
It extends Cold Diffusion (LIT-553) and compares against EDM (LIT-075), Blurring Diffusion and inverse heat dissipation. Table 1’s Cold Diffusion entry quotes a deblurring FID as a generation FID (see the LIT note).
Bearing on the record
- THEORY-080 files its account, which corrects THEORY-079
- No practice filed. The gain over EDM is too small and too thinly reported to recommend mixing in blur
Limitations
- Manifold departure is asserted from a diagram, not measured (for example by a density or classifier score of intermediate states)
- Best-of-three reporting, no seeds
- Small images only
Open questions
- Whether the cold-side degradation persists at higher resolution and in latent space, where spectra differ