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.