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arxiv: 2604.09436 · v1 · submitted 2026-04-10 · 💻 cs.CV

SCoRe: Clean Image Generation from Diffusion Models Trained on Noisy Images

Yuta Matsuzaki , Seiichi Uchida , Shumpei Takezaki This is my paper

Pith reviewed 2026-05-10 18:09 UTC · model grok-4.3

classification 💻 cs.CV
keywords diffusion modelsimage generationnoisy training dataspectral cutofffrequency domainSDEdittraining-freehigh-frequency artifacts
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The pith

A frequency cutoff plus SDEdit regeneration removes high-frequency noise artifacts from diffusion models trained on noisy images.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Diffusion models trained on noisy data tend to reproduce those high-frequency corruptions in their outputs. SCoRe counters this at generation time by cutting off the corrupted frequencies in a partially denoised image and then regenerating the missing high frequencies with SDEdit. A mapping derived from radially averaged power spectral density selects the exact SDEdit starting timestep so that the injected noise level matches the cutoff without adding fresh artifacts. The entire procedure requires no retraining or fine-tuning of the original model. On both synthetic CIFAR-10 and real SIDD noisy datasets the resulting images lie measurably closer to clean distributions than those produced by post-processing or noise-robust baselines.

Core claim

By suppressing corrupted high-frequency components through a spectral cutoff and then regenerating them via SDEdit initialized at a timestep obtained from a RAPSD-based mapping, a diffusion model trained on noisy images can produce samples whose distribution more closely matches that of clean images.

What carries the argument

Spectral Cutoff Regeneration (SCoRe): a training-free procedure that applies a frequency cutoff to remove noisy high-frequency content and regenerates it with SDEdit whose starting timestep is fixed by a closed-form RAPSD-derived mapping between cutoff frequency and diffusion noise level.

If this is right

  • Clean-looking samples can be obtained from existing diffusion models without collecting or training on new clean data.
  • The same model can be used for both noisy and clean generation by toggling the SCoRe post-step.
  • High-frequency artifacts introduced by noisy training data are isolated to the upper part of the spectrum and can be targeted independently of low-frequency structure.
  • The RAPSD mapping provides a parameter-free way to choose SDEdit strength once the cutoff frequency is set.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the spectral bias holds for other generative models, similar cutoff-and-regenerate strategies could be adapted beyond diffusion.
  • The approach may lower the barrier to using real-world noisy datasets for training large generative models by shifting cleanup to inference time.
  • Testing SCoRe on progressively stronger noise levels could reveal the maximum noise the mapping can still correct before regeneration fails.

Load-bearing premise

The diffusion model must reliably infer plausible high-frequency details from the remaining low-frequency cues once the cutoff is applied, and the RAPSD mapping must set the SDEdit noise level so that regeneration neither under- nor over-corrects.

What would settle it

Generate a large set of images with SCoRe on a model trained on known noisy data and measure whether their radially averaged power spectra above the cutoff frequency match the clean data distribution or instead remain statistically closer to the noisy training distribution.

Figures

Figures reproduced from arXiv: 2604.09436 by Seiichi Uchida, Shumpei Takezaki, Yuta Matsuzaki.

Figure 1
Figure 1. Figure 1: Impact of a dataset containing noisy training images on the generated [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Overview of the diffusion and reverse processes in terms of frequency components. (b) [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The generation process of a diffusion model trained on noisy images. (a) Standard generation process: produces noisy generated images. (b) SDEdit: [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Generated images under CIFAR-10 with Gaussian noise: (a) Training examples, (b) standard diffusion sampling, (c) generated images post-processed [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Effect of the noisy-data ratio in training on FID (x-axis: percentage [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Generated Results : (a) training examples, (b) standard diffusion sampling, (c) generated images post-processed with a bilateral filter, (d) generated [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
read the original abstract

Diffusion models trained on noisy datasets often reproduce high-frequency training artifacts, significantly degrading generation quality. To address this, we propose SCoRe (Spectral Cutoff Regeneration), a training-free, generation-time spectral regeneration method for clean image generation from diffusion models trained on noisy images. Leveraging the spectral bias of diffusion models, which infer high-frequency details from low-frequency cues, SCoRe suppresses corrupted high-frequency components of a generated image via a frequency cutoff and regenerates them via SDEdit. Crucially, we derive a theoretical mapping between the cutoff frequency and the SDEdit initialization timestep based on Radially Averaged Power Spectral Density (RAPSD), which prevents excessive noise injection during regeneration. Experiments on synthetic (CIFAR-10) and real-world (SIDD) noisy datasets demonstrate that SCoRe substantially outperforms post-processing and noise-robust baselines, restoring samples closer to clean image distributions without any retraining or fine-tuning.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes SCoRe, a training-free method for clean image generation from diffusion models trained on noisy data. It suppresses high-frequency components above a cutoff frequency (derived via Radially Averaged Power Spectral Density, RAPSD) in an initial generation and regenerates them using SDEdit initialized at a theoretically mapped timestep, leveraging the model's spectral bias to infer clean high frequencies from low-frequency cues. Experiments on CIFAR-10 (synthetic noise) and SIDD (real camera noise) report substantial outperformance over post-processing and noise-robust baselines without retraining.

Significance. If the RAPSD-to-timestep mapping is rigorously validated and the outperformance holds under controlled ablations, the result would be significant for practical use of diffusion models on imperfect real-world data, as it avoids the need for clean training sets or fine-tuning. The training-free design and explicit use of spectral properties represent a useful contribution to generation and restoration pipelines.

major comments (3)
  1. [§3] §3 (Theoretical mapping derivation): The central RAPSD-derived equivalence between cutoff frequency and SDEdit timestep assumes that the radially averaged power spectrum of the noisy training distribution directly inverts to the forward diffusion noise variance schedule at that t. This equivalence is load-bearing for the claim of artifact-free regeneration but is not shown to hold exactly for either synthetic Gaussian noise (CIFAR-10) or structured camera noise (SIDD); without an explicit derivation or matching to the variance schedule in Eq. (forward process), the mapping risks either residual artifacts or over-smoothing.
  2. [§4.1–4.2] §4.1–4.2 (Quantitative experiments): The reported gains over baselines rest on the mapping's accuracy, yet no ablation compares the RAPSD-derived timestep against an oracle or grid-searched timestep; if the improvement is comparable under a simple fixed-timestep SDEdit, the specific contribution of the RAPSD mapping is not isolated and the central claim is weakened.
  3. [§4.2] §4.2 (SIDD results): Real-world noise spectra are not guaranteed to be radially symmetric or to match the assumed power-law decay used for the cutoff; the paper should quantify failure cases where the mapping injects structured noise that the model has memorized from the noisy training distribution, as this directly tests the skeptic's concern about unverified equivalence.
minor comments (2)
  1. [Abstract] The acronym RAPSD should be expanded on first use in the abstract and introduction for clarity.
  2. [Figures] Figure captions should explicitly state the number of diffusion steps used for both the initial generation and the SDEdit regeneration phase to allow direct reproduction.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback. We address each major comment below and describe the revisions we will incorporate to improve the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (Theoretical mapping derivation): The central RAPSD-derived equivalence between cutoff frequency and SDEdit timestep assumes that the radially averaged power spectrum of the noisy training distribution directly inverts to the forward diffusion noise variance schedule at that t. This equivalence is load-bearing for the claim of artifact-free regeneration but is not shown to hold exactly for either synthetic Gaussian noise (CIFAR-10) or structured camera noise (SIDD); without an explicit derivation or matching to the variance schedule in Eq. (forward process), the mapping risks either residual artifacts or over-smoothing.

    Authors: We thank the referee for this observation. Section 3 derives the mapping by equating the RAPSD of the noisy training distribution to the expected high-frequency power introduced by the forward diffusion process at timestep t, using the variance schedule to determine the cutoff. This is necessarily an approximation, especially for non-isotropic noise. The CIFAR-10 and SIDD experiments provide empirical support that the mapping yields artifact-reduced outputs. In the revision we will add an explicit supplementary figure overlaying the RAPSD-derived cutoff against the theoretical cumulative variance schedule for both datasets to make the equivalence more transparent. revision: yes

  2. Referee: [§4.1–4.2] §4.1–4.2 (Quantitative experiments): The reported gains over baselines rest on the mapping's accuracy, yet no ablation compares the RAPSD-derived timestep against an oracle or grid-searched timestep; if the improvement is comparable under a simple fixed-timestep SDEdit, the specific contribution of the RAPSD mapping is not isolated and the central claim is weakened.

    Authors: We agree that an ablation isolating the RAPSD mapping is necessary. The current results use the derived timestep, but we will add a controlled ablation in the revised Section 4 comparing (i) the RAPSD-derived t, (ii) a grid-searched oracle t, and (iii) several fixed-timestep SDEdit baselines. This will quantify how close the automatic mapping comes to the oracle and demonstrate that it outperforms naive fixed-t choices, thereby strengthening the claim that the spectral derivation is the key enabler. revision: yes

  3. Referee: [§4.2] §4.2 (SIDD results): Real-world noise spectra are not guaranteed to be radially symmetric or to match the assumed power-law decay used for the cutoff; the paper should quantify failure cases where the mapping injects structured noise that the model has memorized from the noisy training distribution, as this directly tests the skeptic's concern about unverified equivalence.

    Authors: We recognize that SIDD noise is not guaranteed to be radially symmetric. The RAPSD provides a rotationally averaged estimate that has worked well in our reported results, but we will expand the SIDD analysis with a dedicated limitations paragraph and additional qualitative examples highlighting images with strong directional noise patterns. In these cases we will report both visual artifacts and quantitative metrics (e.g., FID on the subset) to illustrate where the mapping may still inject memorized structured noise, thereby addressing the concern directly. revision: partial

Circularity Check

0 steps flagged

RAPSD-to-timestep mapping is a first-principles derivation independent of target clean distribution

full rationale

The paper's core step derives a cutoff-frequency to SDEdit-timestep mapping from RAPSD of the noisy training images and the known diffusion noise schedule. This calculation uses only the observed power spectrum of the noisy data and the forward-process variance schedule; it does not fit any parameter to clean-image statistics or to the regeneration outcome itself. No self-citation supplies a uniqueness theorem or ansatz that the present work merely renames. The spectral-bias assumption is stated as an empirical property of diffusion models and is tested by downstream experiments on held-out synthetic and real noisy sets, rather than being presupposed by the mapping. Consequently the claimed regeneration of high-frequency content does not reduce to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the domain assumption of spectral bias in diffusion models and the validity of the RAPSD-derived frequency-to-timestep mapping; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption Diffusion models exhibit spectral bias, inferring high-frequency details from low-frequency cues.
    This bias is leveraged to justify regenerating high-frequency components after cutoff.

pith-pipeline@v0.9.0 · 5468 in / 1312 out tokens · 33722 ms · 2026-05-10T18:09:51.547552+00:00 · methodology

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Reference graph

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