# Generative Diffusion Models for High Dimensional Channel Estimation

arXiv: https://arxiv.org/abs/2408.10501 · HTML: https://mlsanity.com/paper/2408.10501/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion for compression and wireless, one of 14 directions in Diffusion models.
- Builds on 30 of its 60 references that are in the map.
- First posted on arXiv 20 Aug 2024.

## Placed in

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

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (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)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Deep Learning-Based Channel Estimation](https://mlsanity.com/paper/1810.05893/) (2018)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [MIMO Channel Estimation using Score-Based Generative Models](https://mlsanity.com/paper/2204.07122/) (2022)
- [Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data](https://mlsanity.com/paper/2305.01166/) (2023)
- [High Dimensional Channel Estimation Using Deep Generative Networks](https://mlsanity.com/paper/2006.13494/) (2020)
- [A Tutorial on Extremely Large-Scale MIMO for 6G: Fundamentals, Signal Processing, and Applications](https://mlsanity.com/paper/2307.07340/) (2023)
- [Diffusion-based Generative Prior for Low-Complexity MIMO Channel Estimation](https://mlsanity.com/paper/2403.03545/) (2024)
- [Wideband Channel Estimation with A Generative Adversarial Network](https://mlsanity.com/paper/2012.12063/) (2020)
- [Quantized Compressed Sensing with Score-based Generative Models](https://mlsanity.com/paper/2211.13006/) (2022)
- [An Asymptotically MSE-Optimal Estimator based on Gaussian Mixture Models](https://mlsanity.com/paper/2112.12499/) (2021)
- [On the Asymptotic Mean Square Error Optimality of Diffusion Models](https://mlsanity.com/paper/2403.02957/) (2024)
- [An Overview of Signal Processing Techniques for Terahertz Communications](https://mlsanity.com/paper/2005.13176/) (2020)
- [Semantic Communications using Foundation Models: Design Approaches and Open Issues](https://mlsanity.com/paper/2309.13315/) (2023)
- [Leveraging Variational Autoencoders for Parameterized MMSE Estimation](https://mlsanity.com/paper/2307.05352/) (2023)
- [Deep Learning based Channel Extrapolation for Large-Scale Antenna Systems: Opportunities, Challenges and Solutions](https://mlsanity.com/paper/2102.12859/) (2021)
- [Over-the-Air Design of GAN Training for mmWave MIMO Channel Estimation](https://mlsanity.com/paper/2205.12445/) (2022)
- [Channel Estimation for Quantized Systems based on Conditionally Gaussian Latent Models](https://mlsanity.com/paper/2309.04014/) (2023)

## Built on by (most cited first, 26 of 26)

- [Generative Diffusion Models for Wireless Networks: Fundamental, Architecture, and State-of-the-Art](https://mlsanity.com/paper/2507.16733/) (2025)
- [Diffusion Models for Future Networks and Communications: A Comprehensive Survey](https://mlsanity.com/paper/2508.01586/) (2025)
- [ICDM: Interference Cancellation Diffusion Models for Wireless Semantic Communications](https://mlsanity.com/paper/2505.19983/) (2025)
- [Environment-Aware Channel Inference via Cross-Modal Flow: From Multimodal Sensing to Wireless Channels](https://mlsanity.com/paper/2512.04966/) (2025)
- [Channel Estimation for RIS-Assisted mmWave Systems via Diffusion Models](https://mlsanity.com/paper/2506.07770/) (2025)
- [Enhancements in Score-based Channel Estimation for Real-Time Wireless Systems](https://mlsanity.com/paper/2509.07839/) (2025)
- [Telecom World Models: Unifying Digital Twins, Foundation Models, and Predictive Planning for 6G](https://mlsanity.com/paper/2604.06882/) (2026)
- [Non-Identical Diffusion Models in MIMO-OFDM Channel Generation](https://mlsanity.com/paper/2509.01641/) (2025)
- [Generative AI Meets Wireless Sensing: Towards Wireless Foundation Model](https://mlsanity.com/paper/2509.15258/) (2025)
- [Robust MIMO Channel Estimation Using Energy-Based Generative Diffusion Models](https://mlsanity.com/paper/2510.22230/) (2025)
- [Diffusion Models for Wireless Transceivers: From Pilot-Efficient Channel Estimation to AI-Native 6G Receivers](https://mlsanity.com/paper/2510.24495/) (2025)
- [Channel Estimation in MIMO Systems Using Flow Matching Models](https://mlsanity.com/paper/2601.13827/) (2026)
- [EVT-Based Generative AI for Tail-Aware Channel Estimation](https://mlsanity.com/paper/2604.25008/) (2026)
- [Generator-Guided Inverse Sampling for L'evy-Driven Generative Models](https://mlsanity.com/paper/2608.10384/) (2026)
- [Generative Diffusion Model Driven Massive Random Access in Massive MIMO Systems](https://mlsanity.com/paper/2505.12382/) (2025)
- [A look at adversarial attacks on radio waveforms from discrete latent space](https://mlsanity.com/paper/2506.09896/) (2025)
- [Conditional Diffusion Model-Enabled Scenario-Specific Neural Receivers for Superimposed Pilot Schemes](https://mlsanity.com/paper/2511.01173/) (2025)
- [RSS map-assisted MIMO channel estimation in the upper mid-band under pilot constraints](https://mlsanity.com/paper/2603.00112/) (2026)
- [Improving Channel Estimation via Multimodal Diffusion Models with Flow Matching](https://mlsanity.com/paper/2603.13440/) (2026)
- [Cross-Modal Generation: From Commodity WiFi to High-Fidelity mmWave and RFID Sensing](https://mlsanity.com/paper/2604.16558/) (2026)
- [Null-Space Flow Matching for MIMO Channel Estimation in Latency-Constrained Systems](https://mlsanity.com/paper/2604.22005/) (2026)
- [Mixture-of-Experts Diffusion Models for Adaptive Massive MIMO Channel Estimation via Variational Bayesian Inference](https://mlsanity.com/paper/2605.18325/) (2026)
- [A Perception vs. Distortion Perspective on Score-Based Generative Channel Estimation](https://mlsanity.com/paper/2606.16815/) (2026)
- [Condition-Wise Sinkhorn Drifting for One-Shot Learned Channel Simulation](https://mlsanity.com/paper/2606.17893/) (2026)
- [Restoration Flow Matching-Based Channel Refinement and Equalization Correction for MIMO Semantic Communications](https://mlsanity.com/paper/2607.23615/) (2026)
- [Geometry-Aided Channel Deduction with Partial Channel Estimates and Uncalibrated Digital Twin](https://mlsanity.com/paper/2609.37277/) (2026)

## Abstract (arXiv)

Along with the prosperity of generative artificial intelligence (AI), its potential for solving conventional challenges in wireless communications has also surfaced. Inspired by this trend, we investigate the application of the advanced diffusion models (DMs), a representative class of generative AI models, to high dimensional wireless channel estimation. By capturing the structure of multiple-input multiple-output (MIMO) wireless channels via a deep generative prior encoded by DMs, we develop a novel posterior inference method for channel reconstruction. We further adapt the proposed method to recover channel information from low-resolution quantized measurements. Additionally, to enhance the over-the-air viability, we integrate the DM with the unsupervised Stein's unbiased risk estimator to enable learning from noisy observations and circumvent the requirements for ground truth channel data that is hardly available in practice. Results reveal that the proposed estimator achieves high-fidelity channel recovery while reducing estimation latency by a factor of 10 compared to state-of-the-art schemes, facilitating real-time implementation. Moreover, our method outperforms existing estimators while reducing the pilot overhead by half, showcasing its scalability to ultra-massive antenna arrays.