# Score-Based Generative Models for Robust Channel Estimation

arXiv: https://arxiv.org/abs/2111.08177 · HTML: https://mlsanity.com/paper/2111.08177/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 16 Nov 2021.

## Builds on (most cited first, 8 of 8)

- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [RefineNet: Multi-Path Refinement Networks for High-Resolution Semantic Segmentation](https://mlsanity.com/paper/1611.06612/) (2016)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Deep Learning-Based Channel Estimation](https://mlsanity.com/paper/1810.05893/) (2018)
- [Instance-Optimal Compressed Sensing via Posterior Sampling](https://mlsanity.com/paper/2106.11438/) (2021)
- [High Dimensional Channel Estimation Using Deep Generative Networks](https://mlsanity.com/paper/2006.13494/) (2020)

## Built on by (most cited first, 8 of 8)

- [Conditional Denoising Diffusion Probabilistic Models for Data Reconstruction Enhancement in Wireless Communications](https://mlsanity.com/paper/2310.19460/) (2023)
- [Over-the-Air Design of GAN Training for mmWave MIMO Channel Estimation](https://mlsanity.com/paper/2205.12445/) (2022)
- [Generative AI-Based Probabilistic Constellation Shaping With Diffusion Models](https://mlsanity.com/paper/2311.09349/) (2023)
- [Generative AI Meets 6G and Beyond: Diffusion Models for Semantic Communications](https://mlsanity.com/paper/2511.08416/) (2025)
- [A Comparative Study of Deep Learning and Iterative Algorithms for Joint Channel Estimation and Signal Detection in OFDM Systems](https://mlsanity.com/paper/2303.03678/) (2023)
- [Denoising Diffusion Probabilistic Models for Hardware-Impaired Communications](https://mlsanity.com/paper/2309.08568/) (2023)
- [A look at adversarial attacks on radio waveforms from discrete latent space](https://mlsanity.com/paper/2506.09896/) (2025)
- [Generative Models for Modeling and Synthesizing MIMO Channels in Adverse Weather Conditions](https://mlsanity.com/paper/2608.00156/) (2026)

## Abstract (arXiv)

Channel estimation is a critical task in digital communications that greatly impacts end-to-end system performance. In this work, we introduce a novel approach for multiple-input multiple-output (MIMO) channel estimation using score-based generative models. Our method uses a deep neural network that is trained to estimate the gradient of the log-prior of wireless channels at any point in high-dimensional space, and leverages this model to solve channel estimation via posterior sampling. We train a score-based model on channel realizations from the CDL-D model for two antenna spacings and show that the approach leads to competitive in- and out-of-distribution performance when compared to generative adversarial network (GAN) and compressed sensing (CS) methods. When tested on CDL-D channels, the approach leads to a gain of at least 5 dB in channel estimation error compared to GAN methods in-distribution at λ/2 antenna spacing. When tested on CDL-C channels which are never seen during training or fine-tuned on, the approach leads to end-to-end coded performance gains of up to 3 dB compared to CS methods and losses of only 0.5 dB compared to ideal channel knowledge.