An Analysis of Regularization and Fokker-Planck Residuals in Diffusion Models for Image Generation
Onno Niemann, Gonzalo Martínez Muñoz, Alberto Suárez Gonzalez
TLDR
This paper explores lightweight regularization methods for diffusion models, showing they can reduce Fokker-Planck violations and improve image generation efficiency.
Key contributions
- Identifies that diffusion models often violate the Fokker-Planck equation, with costly direct penalization.
- Proposes and empirically analyzes lightweight regularizers as efficient alternatives to FP penalties.
- Demonstrates these simpler regularizers reduce FP residuals and maintain generation quality.
- Concludes that FP regularization benefits are achievable at substantially lower computational cost.
Why it matters
Current diffusion models struggle with Fokker-Planck equation violations, leading to computational overhead for correction. This paper offers a practical solution by introducing lightweight regularizers. It shows how to maintain high-quality image generation while significantly reducing computational costs, making diffusion models more efficient and accessible.
Original 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.
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