# A Perception vs. Distortion Perspective on Score-Based Generative Channel Estimation

arXiv: https://arxiv.org/abs/2606.16815 · HTML: https://mlsanity.com/paper/2606.16815/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion for compression and wireless, one of 14 directions in Diffusion models.
- Builds on 28 of its 45 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Placed in

- Diffusion models / [Diffusion for compression and wireless](https://mlsanity.com/diffusion/diffusion-for-compression-and-wireless/)

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Sionna: An Open-Source Library for Next-Generation Physical Layer Research](https://mlsanity.com/paper/2203.11854/) (2022)
- [MIMO Channel Estimation using Score-Based Generative Models](https://mlsanity.com/paper/2204.07122/) (2022)
- [Generative Diffusion Models for High Dimensional Channel Estimation](https://mlsanity.com/paper/2408.10501/) (2024)
- [Generative AI for Physical Layer Communications: A Survey](https://mlsanity.com/paper/2312.05594/) (2023)
- [DiracDiffusion: Denoising and Incremental Reconstruction with Assured Data-Consistency](https://mlsanity.com/paper/2303.14353/) (2023)
- [Denoising Diffusion Probabilistic Model for Radio Map Estimation in Generative Wireless Networks](https://mlsanity.com/paper/2501.06604/) (2025)
- [Generative Diffusion Models for Wireless Networks: Fundamental, Architecture, and State-of-the-Art](https://mlsanity.com/paper/2507.16733/) (2025)
- [Joint channel estimation and data detection in massive MIMO systems based on diffusion models](https://mlsanity.com/paper/2311.10311/) (2023)
- [Diffusion Models as Network Optimizers: Explorations and Analysis](https://mlsanity.com/paper/2411.00453/) (2024)
- [On the Asymptotic Mean Square Error Optimality of Diffusion Models](https://mlsanity.com/paper/2403.02957/) (2024)
- [Diffusion Models for Wireless Communications](https://mlsanity.com/paper/2310.07312/) (2023)
- [Diffusion Models for Future Networks and Communications: A Comprehensive Survey](https://mlsanity.com/paper/2508.01586/) (2025)
- [Traversing Distortion-Perception Tradeoff using a Single Score-Based Generative Model](https://mlsanity.com/paper/2503.20297/) (2025)
- [Successive Interference Cancellation-aided Diffusion Models for Joint Channel Estimation and Data Detection in Low Rank Channel Scenarios](https://mlsanity.com/paper/2501.11229/) (2025)
- [Improve the Training Efficiency of DRL for Wireless Communication Resource Allocation: The Role of Generative Diffusion Models](https://mlsanity.com/paper/2502.07211/) (2025)
- [WiFi-Diffusion: Achieving Fine-Grained WiFi Radio Map Estimation With Ultra-Low Sampling Rate by Diffusion Models](https://mlsanity.com/paper/2503.12004/) (2025)
- [Enhancements in Score-based Channel Estimation for Real-Time Wireless Systems](https://mlsanity.com/paper/2509.07839/) (2025)
- [Bayesian Radio Map Estimation: Fundamentals and Implementation via Diffusion Models](https://mlsanity.com/paper/2508.06037/) (2025)

## Abstract (arXiv)

Driven by their remarkable success in computer vision and inverse problem solving, score-based models are increasingly applied to wireless communications, where they show promise across a range of physical-layer tasks. However, despite this growing interest, the current literature often lacks a rigorous analysis of when score-matching offers a tangible advantage over traditional discriminative learning. This paper aims to address this gap through the use-case of channel estimation, a fundamental inverse problem in wireless systems. We present a theoretically grounded interpretation of score-based channel estimation through the lens of the perception-distortion tradeoff, identifying the conditions where score matching excels as well as its key limitations. In particular, by modeling downstream wireless tasks (e.g., capacity maximization) as functionals of the channel estimation process, we quantify the excess risk incurred by standard distortion-minimization approaches. Extensive numerical results show that under high predictive uncertainty, the large excess risk gap can be offset by score-based estimation, enabling near Bayesian-optimal precoding via the learned posterior, whereas in the low predictive uncertainty regime, discriminative distortion-minimization approaches are preferable due to lower complexity and more efficient use of model capacity.