# Diffusion Models for Radio Map Estimation: Theoretical Performance Analysis and Sampling Rate Guideline

arXiv: https://arxiv.org/abs/2606.25310 · HTML: https://mlsanity.com/paper/2606.25310/

## 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 16 of its 51 references that are in the map.
- First posted on arXiv 24 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, 16 of 16)

- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022)
- [RadioUNet: Fast Radio Map Estimation with Convolutional Neural Networks](https://mlsanity.com/paper/1911.09002/) (2019)
- [RadioDiff: An Effective Generative Diffusion Model for Sampling-Free Dynamic Radio Map Construction](https://mlsanity.com/paper/2408.08593/) (2024)
- [RME-GAN: A Learning Framework for Radio Map Estimation based on Conditional Generative Adversarial Network](https://mlsanity.com/paper/2212.12817/) (2022)
- [Low-Rank Matrix Completion: A Contemporary Survey](https://mlsanity.com/paper/1907.11705/) (2019)
- [Radio Map Estimation: A Data-Driven Approach to Spectrum Cartography](https://mlsanity.com/paper/2202.03269/) (2022)
- [RadioGAT: A Joint Model-based and Data-driven Framework for Multi-band Radiomap Reconstruction via Graph Attention Networks](https://mlsanity.com/paper/2403.16397/) (2024)
- [Denoising Diffusion Probabilistic Model for Radio Map Estimation in Generative Wireless Networks](https://mlsanity.com/paper/2501.06604/) (2025)
- [Radiomap Inpainting for Restricted Areas based on Propagation Priority and Depth Map](https://mlsanity.com/paper/2305.15526/) (2023)
- [On the Asymptotic Mean Square Error Optimality of Diffusion Models](https://mlsanity.com/paper/2403.02957/) (2024)
- [RadioMamba: Breaking the Accuracy-Efficiency Trade-off in Radio Map Construction via a Hybrid Mamba-UNet](https://mlsanity.com/paper/2508.09140/) (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)
- [A Fine-Grained 3D Radio Map Construction Paradigm with Ultra-Low Sampling Rates by Large Generative Models](https://mlsanity.com/paper/2509.11571/) (2025)

## Abstract (arXiv)

Radio maps, which characterize the spatial distribution of radio frequency metrics, such as the received signal strength, are essential for a wide range of wireless applications. The problem of radio map estimation involves constructing a radio map from a limited set of radio samples measured by sparsely distributed sensors.Recently, diffusion models have been increasingly adopted for this problem, yet their theoretical performance remains largely unexamined. Consequently, it is difficult to evaluate their performance when ground-truth radio maps are unavailable, as is often the case in practice. To bridge this gap, we first formulate radio map estimation as a non-linear matrix completion problem. We then derive a theoretical expression for the estimation error of a diffusion model, capturing the effects of the mismatch between the training and deployment environments, the model design, and the sampling strategy on the quality of the estimated radio map. Moreover, considering that the derived error expression depends on certain information that is difficult to obtain in practice, we propose an empirical approximation that is readily computable from observable data. Finally, extensive simulations demonstrate that the empirical formula closely approximates the theoretical error expression, validating its effectiveness for practical deployment. Our results provide guidelines not only for evaluating the performance of a diffusion model when ground truth is unavailable, but also for determining how many sensors are required to spatially sample the region to achieve a given estimation accuracy. They further reveal a critical sensor count beyond which the estimation performance of diffusion models converges.