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Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution

NeurIPS 2026 · Image generation › Super-resolution · approach: Perceptual and real-world SR · 0 citations (OpenAlex)

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Proposes SKILD, a scale-invariant DCT-space diffusion whose forward process attenuates fine-to-coarse modes and injects dataset-spectrum-matched noise, so one unconditional checkpoint handles both generation and continuous super-resolution by varying the starting timestep.

Problem

Generation and super-resolution are usually handled by separate conditional or task-specific diffusion models; the paper asks whether a single unconditional scale-ordered diffusion process can do both, exploiting approximate scale invariance of natural images and critical physical systems.

Approach

Replace isotropic noising with a frequency-space forward process that damps high-frequency DCT modes first and injects noise with the dataset's variance spectrum (S0), so intermediate states are coarse-grained noisy versions of the data; super-resolution is then a partial reverse diffusion started from an intermediate timestep chosen by an SNR threshold.

Key results

• Reaches FID 2.65 and IS 9.63 on unconditional CIFAR-10, best among frequency/scale-informed models listed but behind EDM (FID 1.97) among all models.
• At 4x super-resolution on ImageNet-256, SKILD achieves best LPIPS (0.186), CLIPIQA (0.612) and MUSIQ (59.226), while PSNR (24.10) trails I2SB (26.76) and RESHIFT-type baselines.
• On critical Ising 32->128 super-resolution, the reconstructed connected four-point correlator closely tracks ground truth whereas SR3 deviates significantly (qualitative figure).

Surprising findings

• FID reaches its best value before the final checkpoint and then worsens while IS keeps improving on CIFAR-10, indicating mode-collapse-like behavior.
• PSNR of the unconditional model is below several conditional baselines, so perceptual gains do not translate to pixel accuracy.

Limitations

• Requires 1000 ancestral sampling steps; no faster sampler provided.
• Low-frequency/global structure generation remains a bottleneck for unconditional generation.
• Super-resolution uses exact forward marginals of HR images as LR inputs rather than real-world degradations.

Experimental setup

Datasets: CIFAR-10 ImageNet Critical 2D Ising model samples (Wolff algorithm)

Benchmarks: CIFAR-10 ImageNet-Test Critical Ising four-point correlator

Metrics: FID Inception Score PSNR SSIM LPIPS MUSIQ CLIPIQA connected four-point correlator

Baselines: DDPM DDPM++ NCSN++ EDM Cold diffusion EqualSNR WaveDiff IHDM DCTdiff BSRGAN SwinIR RealESRGAN

Builds on: DDPM NCSN++ Score-based SDE Cold diffusion

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