Coloring the Noise: Adversarial Sobolev Alignment for Faithful Image Super Resolution
Abstract
ASASR addresses spectral misalignment in image super-resolution by leveraging Riemannian geometry and adversarial training to improve structural fidelity and reduce artifacts.
Generative priors in Image Super-Resolution (SR) often compromise faithful restoration, we attribute this limitation to a fundamental spectral misalignment between isotropic objectives and the intrinsic natural image manifold. While Direct Preference Optimization offers a path to alignment, its reliance on spectrally flat Gaussian noise fails to distinguish authentic high-frequency details from hallucinations. To bridge this geometric gap, we propose ASASR, a theoretically grounded framework that recasts the generative flow into a Sobolev-induced Riemannian geometry by explicitly coloring the noise transition kernel to mirror natural spectral decay. Driving this geometric alignment, we integrate a parametric adversary grounded in the Riesz Representation Theorem, which synthesizes targeted negative samples equivalent to worst-case Sobolev gradients to direct optimization along the tangent space of plausible structural failures. Extensive evaluations demonstrate that ASASR outperforms leading generative baselines, particularly in preserving spectral consistency and structural fidelity, offering a robust solution that effectively mitigates artifacts.
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Excited to share our ICML 2026 paper, ASASR: Coloring the Noise for Faithful Image Super-Resolution.
We believe faithful image super-resolution requires more than realistic textures: it requires spectral and structural alignment with natural images. ASASR explores this idea by coloring the noise and using adversarial Sobolev guidance to reduce hallucinations and preserve fine details.
the part that really sticks is how they recenter sr optimization around a Sobolev geometry by coloring the noise with a structured covariance. the adversarial module, grounded in the Riesz representation, produces worst-case Sobolev gradients to steer updates along the tangent space of plausible structures, which feels like a nontrivial shift from standard flow matching. i wonder how sensitive the gains are to the choice of the Sobolev exponent and the exact noise coloring, since natural image spectra can swing across datasets. the arxivlens breakdown helped me parse the method details and sanity-check the equations, worth a skim alongside the paper (https://arxivlens.com/PaperView/Details/coloring-the-noise-adversarial-sobolev-alignment-for-faithful-image-super-resolution-4691-db59c1cc).
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