# Erasing Noise in Signal Detection with Diffusion Model: From Theory to Application

arXiv: https://arxiv.org/abs/2501.07030 · HTML: https://mlsanity.com/paper/2501.07030/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 2 of its 22 references that are in the map.
- First posted on arXiv 13 Jan 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 2 of 2)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [DiffBIR: Towards Blind Image Restoration with Generative Diffusion Prior](https://mlsanity.com/paper/2308.15070/) (2023)

## Built on by (most cited first, 2 of 2)

- [Diffusion Models for Future Networks and Communications: A Comprehensive Survey](https://mlsanity.com/paper/2508.01586/) (2025)
- [Non-Identical Diffusion Models in MIMO-OFDM Channel Generation](https://mlsanity.com/paper/2509.01641/) (2025)

## Abstract (arXiv)

In this paper, a signal detection method based on the denoise diffusion model (DM) is proposed, which outperforms the maximum likelihood (ML) estimation method that has long been regarded as the optimal signal detection technique. Theoretically, a novel mathematical theory for intelligent signal detection based on stochastic differential equations (SDEs) is established in this paper, demonstrating the effectiveness of DM in reducing the additive white Gaussian noise in received signals. Moreover, a mathematical relationship between the signal-to-noise ratio (SNR) and the timestep in DM is established, revealing that for any given SNR, a corresponding optimal timestep can be identified. Furthermore, to address potential issues with out-of-distribution inputs in the DM, we employ a mathematical scaling technique that allows the trained DM to handle signal detection across a wide range of SNRs without any fine-tuning. Building on the above theoretical foundation, we propose a DM-based signal detection method, with the diffusion transformer (DiT) serving as the backbone neural network, whose computational complexity of this method is O(n2). Simulation results demonstrate that, for BPSK and QAM modulation schemes, the DM-based method achieves a significantly lower symbol error rate (SER) compared to ML estimation, while maintaining a much lower computational complexity.