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

arXiv: https://arxiv.org/abs/2605.23264 · HTML: https://mlsanity.com/paper/2605.23264/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 50 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 30 of 41)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [MUSIQ: Multi-scale Image Quality Transformer](https://mlsanity.com/paper/2108.05997/) (2021)
- [Exploring CLIP for Assessing the Look and Feel of Images](https://mlsanity.com/paper/2207.12396/) (2022)
- [Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data](https://mlsanity.com/paper/2107.10833/) (2021)
- [Image Quality Assessment: Unifying Structure and Texture Similarity](https://mlsanity.com/paper/2004.07728/) (2020)
- [Designing a Practical Degradation Model for Deep Blind Image Super-Resolution](https://mlsanity.com/paper/2103.14006/) (2021)
- [MANIQA: Multi-dimension Attention Network for No-Reference Image Quality Assessment](https://mlsanity.com/paper/2204.08958/) (2022)
- [Exploiting Diffusion Prior for Real-World Image Super-Resolution](https://mlsanity.com/paper/2305.07015/) (2023)
- [Toward Real-World Single Image Super-Resolution: A New Benchmark and A New Model](https://mlsanity.com/paper/1904.00523/) (2019)
- [SeeSR: Towards Semantics-Aware Real-World Image Super-Resolution](https://mlsanity.com/paper/2311.16518/) (2023)
- [Scaling Up to Excellence: Practicing Model Scaling for Photo-Realistic Image Restoration In the Wild](https://mlsanity.com/paper/2401.13627/) (2024)
- [DiffBIR: Towards Blind Image Restoration with Generative Diffusion Prior](https://mlsanity.com/paper/2308.15070/) (2023)
- [Component Divide-and-Conquer for Real-World Image Super-Resolution](https://mlsanity.com/paper/2008.01928/) (2020)
- [PP-OCRv3: More Attempts for the Improvement of Ultra Lightweight OCR System](https://mlsanity.com/paper/2206.03001/) (2022)
- [DreamClear: High-Capacity Real-World Image Restoration with Privacy-Safe Dataset Curation](https://mlsanity.com/paper/2410.18666/) (2024)
- [DiT4SR: Taming Diffusion Transformer for Real-World Image Super-Resolution](https://mlsanity.com/paper/2503.23580/) (2025)
- [One Diffusion Step to Real-World Super-Resolution via Flow Trajectory Distillation](https://mlsanity.com/paper/2502.01993/) (2025)
- [Visual Autoregressive Modeling for Image Super-Resolution](https://mlsanity.com/paper/2501.18993/) (2025)
- [4KAgent: Agentic Any Image to 4K Super-Resolution](https://mlsanity.com/paper/2507.07105/) (2025)

## Built on by (most cited first, 1 of 1)

- [LPM: Industrial-Scale Generative Video Restoration](https://mlsanity.com/paper/2607.13460/) (2026)

## Abstract (arXiv)

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.