# Markov-Enforced Discrete Diffusion Model for Digital Semantic Symbol Error Correction

arXiv: https://arxiv.org/abs/2603.22983 · HTML: https://mlsanity.com/paper/2603.22983/

## Key facts

- Cited by 2 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 20 of its 33 references that are in the map.
- First posted on arXiv 24 Mar 2026.

## Placed in

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

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Scalable Adaptive Computation for Iterative Generation](https://mlsanity.com/paper/2212.11972/) (2022)
- [Score-based Continuous-time Discrete Diffusion Models](https://mlsanity.com/paper/2211.16750/) (2022)
- [SOM-VAE: Interpretable Discrete Representation Learning on Time Series](https://mlsanity.com/paper/1806.02199/) (2018)
- [Joint Source-Channel Coding: Fundamentals and Recent Progress in Practical Designs](https://mlsanity.com/paper/2409.17557/) (2024)
- [MOC-RVQ: Multilevel Codebook-Assisted Digital Generative Semantic Communication](https://mlsanity.com/paper/2401.01272/) (2024)
- [Universal Joint Source-Channel Coding for Modulation-Agnostic Semantic Communication](https://mlsanity.com/paper/2405.10749/) (2024)
- [SCDM: Score-Based Channel Denoising Model for Digital Semantic Communications](https://mlsanity.com/paper/2501.17876/) (2025)
- [Feature Reconstruction Aided Federated Learning for Image Semantic Communication](https://mlsanity.com/paper/2508.02048/) (2025)
- [Federated Learning Enhanced by Feature Reconstruction for Semantic Communication Module Updates of Agents](https://mlsanity.com/paper/2508.03248/) (2025)
- [Extended Universal Joint Source-Channel Coding for Digital Semantic Communications: Improving Channel-Adaptability](https://mlsanity.com/paper/2602.14018/) (2026)

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

- [Diffusion Language Models for Mobile Edge Agentic AI: Foundations, Applications, and Challenges](https://mlsanity.com/paper/2609.04778/) (2026)
- [Importance-Aware Feature Sparsification for Wireless Split Learning](https://mlsanity.com/paper/2609.39194/) (2026)

## Abstract (arXiv)

Diffusion models (DMs) have achieved remarkable success across various domains owing to their strong generative and denoising capabilities. Meanwhile, semantic communication based on neural joint source-channel coding (JSCC) has emerged as a promising paradigm for robust and efficient image transmission. However, severe channel noise can still distort the transmitted semantic symbols, resulting in significant performance degradation. Applying DMs to digital semantic symbols, particularly in vector quantization (VQ)-based systems, is fundamentally challenging because the Markov assumption does not hold for the symbol transition dynamics. To address this issue, we introduce SSCDM, a semantic symbol correcting diffusion model whose discrete-time transition dynamics are constructed using solutions from continuous-time Markov chain theory. Furthermore, to promote synergy between DMs and JSCC, our DM structure embeds discrete symbols into a latent feature space using a learned VQ codebook, and a self-organizing map-based loss is incorporated during codebook learning to enhance the geometric vicinity between neighboring digital symbols, thereby promoting topology-preserving semantic representations. Experimental results show that the proposed method significantly improves image reconstruction quality and outperforms previous symbol-level denoising techniques under low signal-to-noise ratio scenarios and different datasets.