Conservation Laws for Diffusion Models Unify Likelihood Characterization

Jul 14, 2026

Researchers have developed conservation laws for diffusion models using generalized extrinsic information transfer (GEXIT) functions. Their work shows that the data–model cross-entropy can be exactly characterized as an integral of local information-theoretic derivatives along the noise path, providing a unified framework for both discrete and continuous diffusion models. This approach implies that training diffusion models reduces to learning marginal posteriors, and the theory is validated on synthetic data and benchmarks such as text8 and CIFAR-10.

Why it matters: This framework offers a unified theoretical understanding of diffusion model training, which could inform the development of more principled and efficient denoising objectives.

Full story at: arXiv Machine Learning ↗