Conservation Laws for Diffusion Models

2026-07-14 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

A new paper, "Conservation Laws for Diffusion Models" (arXiv:2607.10067), introduces conservation laws based on generalized extrinsic information transfer (GEXIT) functions for memoryless noise processes. This research precisely characterizes the data-model cross-entropy (CE) as an integral of local information-theoretic derivatives along the noise path, offering a unified likelihood characterization for both discrete and continuous diffusion models. The Gaussian case specifically reduces to the known mutual information-minimum mean-square error (I-MMSE) relationship. A key implication is a locality property, enabling computation of these derivatives using only marginal posteriors. Consequently, training simplifies to learning marginal posteriors by minimizing the negative log-likelihood. While entropy is shown to be noise-path independent, finite-capacity denoisers exhibit varying accuracy across noise types, impacting performance. The findings are validated on synthetic Markov sources and benchmarks like text8 and CIFAR-10.

Key takeaway

For AI Scientists developing diffusion models and seeking to optimize likelihood estimation or understand model limitations, this work provides a unified theoretical framework for characterizing data-model cross-entropy. It simplifies likelihood computation to learning marginal posteriors. You should consider integrating GEXIT-based analysis to refine training objectives and diagnose performance variations across different noise types in your models.

Key insights

Conservation laws based on GEXIT functions characterize diffusion model likelihood via local information-theoretic derivatives.

Principles

• Data-model cross-entropy is an integral of local information-theoretic derivatives.
• Information-theoretic derivatives can be computed using marginal posteriors.
• Entropy in diffusion models is independent of the noise path.

Method

Training diffusion models reduces to learning marginal posteriors by minimizing the negative log-likelihood, leveraging the locality property of information-theoretic derivatives along the noise path.

In practice

• Apply GEXIT functions to analyze memoryless noise processes.
• Evaluate diffusion model performance on text8 and CIFAR-10.

Topics

• Diffusion Models
• Conservation Laws
• Information Theory
• Cross-Entropy
• Machine Learning
• Denoising Objectives

Best for: Research Scientist, AI Scientist, AI Student

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.