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One-step Diffusion Models with Bregman Density Ratio Matching

Yuanzhi Zhu, Eleftherios Tsonis, Lucas Degeorge, Vicky Kalogeiton

TL;DR

The paper tackles slow sampling in diffusion models by proposing a one-step distillation approach. It introduces Di-Bregman, a unified framework that formulates diffusion distillation as Bregman divergence-based density-ratio matching, pushing the density ratio $r(x)=\frac{q(x)}{p(x)}$ toward 1 using a convex function $h$, and deriving a closed-form gradient. The method shows that common objectives (e.g., KL, LS) arise as special cases, and density ratios can be estimated with a classifier via $r_t(x)=e^{-l_t(x)}$, enabling practical training without repeated teacher simulations. Empirical results on CIFAR-10 and text-to-image benchmarks demonstrate improved one-step FID over reverse-KL distillation while maintaining high fidelity to multi-step teacher models, highlighting a principled and effective route to efficient one-step diffusion.

Abstract

Diffusion and flow models achieve high generative quality but remain computationally expensive due to slow multi-step sampling. Distillation methods accelerate them by training fast student generators, yet most existing objectives lack a unified theoretical foundation. In this work, we propose Di-Bregman, a compact framework that formulates diffusion distillation as Bregman divergence-based density-ratio matching. This convex-analytic view connects several existing objectives through a common lens. Experiments on CIFAR-10 and text-to-image generation demonstrate that Di-Bregman achieves improved one-step FID over reverse-KL distillation and maintains high visual fidelity compared to the teacher model. Our results highlight Bregman density-ratio matching as a practical and theoretically-grounded route toward efficient one-step diffusion generation.

One-step Diffusion Models with Bregman Density Ratio Matching

TL;DR

The paper tackles slow sampling in diffusion models by proposing a one-step distillation approach. It introduces Di-Bregman, a unified framework that formulates diffusion distillation as Bregman divergence-based density-ratio matching, pushing the density ratio toward 1 using a convex function , and deriving a closed-form gradient. The method shows that common objectives (e.g., KL, LS) arise as special cases, and density ratios can be estimated with a classifier via , enabling practical training without repeated teacher simulations. Empirical results on CIFAR-10 and text-to-image benchmarks demonstrate improved one-step FID over reverse-KL distillation while maintaining high fidelity to multi-step teacher models, highlighting a principled and effective route to efficient one-step diffusion.

Abstract

Diffusion and flow models achieve high generative quality but remain computationally expensive due to slow multi-step sampling. Distillation methods accelerate them by training fast student generators, yet most existing objectives lack a unified theoretical foundation. In this work, we propose Di-Bregman, a compact framework that formulates diffusion distillation as Bregman divergence-based density-ratio matching. This convex-analytic view connects several existing objectives through a common lens. Experiments on CIFAR-10 and text-to-image generation demonstrate that Di-Bregman achieves improved one-step FID over reverse-KL distillation and maintains high visual fidelity compared to the teacher model. Our results highlight Bregman density-ratio matching as a practical and theoretically-grounded route toward efficient one-step diffusion generation.
Paper Structure (13 sections, 1 theorem, 10 equations, 6 figures, 1 table)

This paper contains 13 sections, 1 theorem, 10 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Variational Score Distillation
  4. Bregman Divergence for Density Ratio Matching
  5. Method
  6. Experiments
  7. Conclusion
  8. Limitations and Future Works.
  9. Related Works: Diffusion Distillation
  10. Experimental Setup
  11. Instances in Bregman divergence
  12. Additional qualitative results
  13. Additional quantitative results

Key Result

Theorem 1

Let $p_t$ be a reference (teacher) marginal density at time $t$ and let $q_t=q_{\theta,t}$ be the marginal induced by the generator $G_\theta$ at time $t$. These intermediate densities are obtained via the forward diffusion process. Define the intermediate density ratio $r_t(x)\coloneqq \frac{q_{\th

Figures (6)

  • Figure 1: Images generated with only one-step by model trained with Di-Bregman. More images are shown in Appendix \ref{['sec:app_quali']}
  • Figure 2: Evolution of one-step FID against number of iterated images: Di-Bregman achieves a lower one-step FID.
  • Figure 3: Qualitative comparison at $512\times512$: Teacher 50 NFEs (first, third columns) vs Student 1 NFE (second, last columns) for six prompts (left and right blocks per row). The teacher is the Stable Diffusion v1.5 rombach2022high model.
  • Figure 4: Evolution of one-step FID against number of iterated images. For $\lambda=3.0, \lambda=5.0$ or $\lambda=10.0$ Di-Bregman achieves a lower one-step FID.
  • Figure 5: Evolution of one-step IS against number of iterated images. For $\lambda=3.0, \lambda=5.0$ or $\lambda=10.0$ Di-Bregman achieves a higher one-step IS.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Theorem 1: Gradient of Bregman divergence
  • proof