# Probabilistic Constellation Shaping With Denoising Diffusion Probabilistic Models: A Novel Approach

arXiv: https://arxiv.org/abs/2309.08688 · HTML: https://mlsanity.com/paper/2309.08688/

## Key facts

- Cited by 4 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 13 of its 18 references that are in the map.
- First posted on arXiv 15 Sep 2023.

## Placed in

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

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Toward a 6G AI-Native Air Interface](https://mlsanity.com/paper/2012.08285/) (2020)
- [MIMO Channel Estimation using Score-Based Generative Models](https://mlsanity.com/paper/2204.07122/) (2022)
- [Massive Access for 5G and Beyond](https://mlsanity.com/paper/2002.03491/) (2020)
- [Deep Generative Model and Its Applications in Efficient Wireless Network Management: A Tutorial and Case Study](https://mlsanity.com/paper/2303.17114/) (2023)
- [CDDM: Channel Denoising Diffusion Models for Wireless Communications](https://mlsanity.com/paper/2305.09161/) (2023)
- [Twelve Scientific Challenges for 6G: Rethinking the Foundations of Communications Theory](https://mlsanity.com/paper/2207.01843/) (2022)
- [MRI Reconstruction with Side Information using Diffusion Models](https://mlsanity.com/paper/2303.14795/) (2023)
- [Joint Learning of Geometric and Probabilistic Constellation Shaping](https://mlsanity.com/paper/1906.07748/) (2019)
- [Waveform Learning for Next-Generation Wireless Communication Systems](https://mlsanity.com/paper/2109.00998/) (2021)
- [Waveform Learning for Reduced Out-of-Band Emissions Under a Nonlinear Power Amplifier](https://mlsanity.com/paper/2201.05524/) (2022)

## Built on by (most cited first, 4 of 4)

- [Diffusion-Driven Semantic Communication for Generative Models with Bandwidth Constraints](https://mlsanity.com/paper/2407.18468/) (2024)
- [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)
- [Generative AI-Based Probabilistic Constellation Shaping With Diffusion Models](https://mlsanity.com/paper/2311.09349/) (2023)

## Abstract (arXiv)

With the incredible results achieved from generative pre-trained transformers (GPT) and diffusion models, generative AI (GenAI) is envisioned to yield remarkable breakthroughs in various industrial and academic domains. In this paper, we utilize denoising diffusion probabilistic models (DDPM), as one of the state-of-the-art generative models, for probabilistic constellation shaping in wireless communications. While the geometry of constellations is predetermined by the networking standards, probabilistic constellation shaping can help enhance the information rate and communication performance by designing the probability of occurrence (generation) of constellation symbols. Unlike conventional methods that deal with an optimization problem over the discrete distribution of constellations, we take a radically different approach. Exploiting the ``denoise-and-generate'' characteristic of DDPMs, the key idea is to learn how to generate constellation symbols out of noise, ``mimicking'' the way the receiver performs symbol reconstruction. By doing so, we make the constellation symbols sent by the transmitter, and what is inferred (reconstructed) at the receiver become as similar as possible. Our simulations show that the proposed scheme outperforms deep neural network (DNN)-based benchmark and uniform shaping, while providing network resilience as well as robust out-of-distribution performance under low-SNR regimes and non-Gaussian noise. Notably, a threefold improvement in terms of mutual information is achieved compared to DNN-based approach for 64-QAM geometry.