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

TL;DR

This paper investigates the effects of regularization on diffusion models for image generation, showing that simpler penalties can reduce computational costs without sacrificing sample quality.

Contribution

It introduces lightweight regularizers that effectively control Fokker-Planck residuals, offering a computationally efficient alternative to traditional FP regularization.

Findings

Lightweight regularizers reduce FP residuals effectively.

Enforcing strict FP adherence does not always improve sample quality.

Simpler penalties achieve similar benefits at lower computational cost.

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.