An Analysis of Regularization and Fokker-Planck Residuals in Diffusion Models for Image Generation

2026-04-16

AI Summary

This work addresses the discrepancy in diffusion models between the denoising score matching objective and the Fokker-Planck (FP) equation that governs the true data evolution. While existing strong FP regularization methods are computationally expensive and do not consistently improve generation quality, this study systematically evaluates lightweight regularization terms targeting FP residuals. The authors propose a low-overhead weak FP regularization strategy that substantially reduces computational burden while preserving high-fidelity image generation. Empirical results demonstrate that such lightweight regularization effectively balances efficiency and performance, confirming its feasibility and advantages in practical diffusion model training.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• diffusion models
• Fokker-Planck equation
• regularization
• denoising score matching
• image generation

Innovation

• diffusion models
• Fokker-Planck equation
• regularization
• denoising score matching
• lightweight regularizers