Coloring the Noise: Adversarial Sobolev Alignment for Faithful Image Super Resolution

2026-05-22

AI Summary

Existing generative image super-resolution methods often produce artifacts or hallucinated details due to a mismatch between their objective functions and the spectral characteristics of natural images. This work proposes a novel framework that integrates Sobolev-induced Riemannian geometry with adversarial learning: it explicitly models the spectral decay of natural images using a spectrally colored noise kernel and constructs a parameterized adversarial mechanism grounded in the Riesz representation theorem, steering optimization along tangent directions where true structural information is lost. Additionally, it introduces a negative sample synthesis strategy equivalent to worst-case Sobolev gradients. This approach represents the first successful integration of Sobolev geometry into generative modeling, achieving superior performance in spectral alignment and structural fidelity compared to existing methods, effectively suppressing distortions and enhancing reconstruction realism.

Abstract

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.

Problem

• Image Super-Resolution
• spectral misalignment
• generative priors
• hallucinations
• structural fidelity

Innovation

• Sobolev alignment
• colored noise
• generative super-resolution
• Riemannian geometry
• adversarial optimization