mlsanityData to 14 Oct 2026

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

arXiv 2604.15171 ↗First posted 16 Apr 2026cs.CV cs.LGcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 9 of its 12 references that are in the map. First posted on arXiv 16 Apr 2026.

Builds on

9 of 12 references.

Closest ancestors · 6

Same direction, newest first

  1. 2024Target Score Matching13 Feb
  2. 2023Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry24 Jul
  3. 2022FP-Diffusion: Improving Score-based Diffusion Models by Enforcing the Underlying Score Fokker-Planck Equation9 Oct
  4. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  6. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 3

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  2. 2020Reliable Fidelity and Diversity Metrics for Generative Modelscited by 434
  3. 2025Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Modelscited by 23

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  1. 2024Fine-tuning of diffusion models via stochastic control: entropy regularization and beyond
  2. 2025Kernel-Smoothed Scores for Denoising Diffusion: A Bias-Variance Study
  3. 2023Reducing Spatial Fitting Error in Distillation of Denoising Diffusion Models
  4. 2023On Error Propagation of Diffusion Models
  5. 2023Denoising Diffusion Samplers
  6. 2025Implicit Regularisation in Diffusion Models: An Algorithm-Dependent Generalisation Analysis
  7. 2024Boosting Diffusion Models with Moving Average Sampling in Frequency Domain
  8. 2024Particle Denoising Diffusion Sampler