An Analysis of Regularization and Fokker-Planck Residuals in Diffusion Models for Image Generation
Abstract
Recent work has shown that diffusion models trained with the denoising score matching (DSM) objective often violate the Fokker--Planck (FP) equation that governs the evolution of the true data density. Directly penalizing these deviations in the objective function reduces their magnitude but introduces a significant computational overhead. It is also observed that enforcing strict adherence to the FP equation does not necessarily lead to improvements in the quality of the generated samples, as often the best results are obtained with weaker FP regularization. In this paper, we investigate whether simpler penalty terms can provide similar benefits. We empirically analyze several lightweight regularizers, study their effect on FP residuals and generation quality, and show that the benefits of FP regularization are available at substantially lower computational cost. Our code is available at https://github.com/OnnoNiemann/fp_diffusion_analysis.
Keywords
Cite
@article{arxiv.2604.15171,
title = {An Analysis of Regularization and Fokker-Planck Residuals in Diffusion Models for Image Generation},
author = {Onno Niemann and Gonzalo Martínez Muñoz and Alberto Suárez Gonzalez},
journal= {arXiv preprint arXiv:2604.15171},
year = {2026}
}
Comments
Accepted at IJCNN 2026 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works