ItDPDM: Information-Theoretic Discrete Poisson Diffusion Model

Existing methods for generative modeling of discrete data, such as symbolic music tokens, face two primary challenges: (1) they either embed discrete inputs into continuous state-spaces or (2) rely on variational losses that only approximate the true negative log-likelihood. Previous efforts have individually targeted these limitations. While information-theoretic Gaussian diffusion models alleviate the suboptimality of variational losses, they still perform modeling in continuous domains. In this work, we introduce the Information-Theoretic Discrete Poisson Diffusion Model (ItDPDM), which simultaneously addresses both limitations by directly operating in a discrete state-space via a Poisson diffusion process inspired by photon arrival processes in camera sensors. We introduce a novel Poisson Reconstruction Loss (PRL) and derive an exact relationship between PRL and the true negative log-likelihood, thereby eliminating the need for approximate evidence lower bounds. Experiments conducted on the Lakh MIDI symbolic music dataset and the CIFAR-10 image benchmark demonstrate that ItDPDM delivers significant improvements, reducing test NLL by up to 80% compared to prior baselines, while also achieving faster convergence.

@article{bhattacharya2025_2505.05082,
  title={ ItDPDM: Information-Theoretic Discrete Poisson Diffusion Model },
  author={ Sagnik Bhattacharya and Abhiram Gorle and Ahmed Mohsin and Ahsan Bilal and Connor Ding and Amit Kumar Singh Yadav and Tsachy Weissman },
  journal={arXiv preprint arXiv:2505.05082},
  year={ 2025 }
}