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Simplified Diffusion Schrödinger Bridge

Zhicong Tang, Tiankai Hang, Shuyang Gu, Dong Chen, Baining Guo

TL;DR

A novel theoretical simplification of the Diffusion Schr\"odinger Bridge is introduced that facilitates its unification with Score-based Generative Models (SGMs), addressing the limitations of DSB in complex data generation and enabling faster convergence and enhanced performance.

Abstract

This paper introduces a novel theoretical simplification of the Diffusion Schrödinger Bridge (DSB) that facilitates its unification with Score-based Generative Models (SGMs), addressing the limitations of DSB in complex data generation and enabling faster convergence and enhanced performance. By employing SGMs as an initial solution for DSB, our approach capitalizes on the strengths of both frameworks, ensuring a more efficient training process and improving the performance of SGM. We also propose a reparameterization technique that, despite theoretical approximations, practically improves the network's fitting capabilities. Our extensive experimental evaluations confirm the effectiveness of the simplified DSB, demonstrating its significant improvements. We believe the contributions of this work pave the way for advanced generative modeling.

Simplified Diffusion Schrödinger Bridge

TL;DR

A novel theoretical simplification of the Diffusion Schr\"odinger Bridge is introduced that facilitates its unification with Score-based Generative Models (SGMs), addressing the limitations of DSB in complex data generation and enabling faster convergence and enhanced performance.

Abstract

This paper introduces a novel theoretical simplification of the Diffusion Schrödinger Bridge (DSB) that facilitates its unification with Score-based Generative Models (SGMs), addressing the limitations of DSB in complex data generation and enabling faster convergence and enhanced performance. By employing SGMs as an initial solution for DSB, our approach capitalizes on the strengths of both frameworks, ensuring a more efficient training process and improving the performance of SGM. We also propose a reparameterization technique that, despite theoretical approximations, practically improves the network's fitting capabilities. Our extensive experimental evaluations confirm the effectiveness of the simplified DSB, demonstrating its significant improvements. We believe the contributions of this work pave the way for advanced generative modeling.
Paper Structure (25 sections, 7 theorems, 45 equations, 13 figures, 1 table, 2 algorithms)

This paper contains 25 sections, 7 theorems, 45 equations, 13 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Score-based Generative Models
  4. Schrödinger Bridge and Diffusion Schrödinger Bridge
  5. A General Perspective of Dynamic Generative Models
  6. Simplified Diffusion Schrödinger Bridge
  7. Simplified training target
  8. The convergence analysis
  9. SGM as the first backward epoch
  10. Initialization of the first forward epoch
  11. Reparameterized Diffusion Schrödinger Bridge
  12. Experiment
  13. Simplified training objectives
  14. Convergence of DSB
  15. Improving SGM
  16. ...and 10 more sections

Key Result

proposition thmcounterproposition

Assume $p_N>0$, $p_\textup{prior}>0$, $\left|\textup{H}(p_\textup{prior})\right|<+\infty$, $\int_{\mathbb{R}^d}\left|\log p_{N|0}(x_N|x_0)\right|p_\textup{data}(x_0)p_\textup{prior}(x_N)\mathrm{d}x_0\mathrm{d}x_N<+\infty$. Then $(\pi^n)_{n\in\mathbb{N}}$ is well-defined and for any $n>1$ we have In addition, $\left(\left\|\pi^{n+1}-\pi^n\right\|_\textup{TV}\right)_{n\in\mathbb{N}}$ and $\left(\te

Figures (13)

  • Figure 1: Illustration of the pipeline of Diffusion Schrödinger Bridge.
  • Figure 2: Comparison between DSB, S-DSB with different initialization, and R-DSB on checkerboard$\leftrightarrow$pinwheel.
  • Figure 3: Evolution of performance with the increase of training iterations per epoch.
  • Figure 4: Evolution of performance with the increase of total training iterations.
  • Figure 5: Improving pretrained SGM with S-DSB. First row illustrates the results of converged SGMs. KL divergences $\textup{KL}(q_N|p_\textup{data})$ measure the average generation performance of each rows.
  • ...and 8 more figures

Theorems & Definitions (11)

  • proposition thmcounterproposition
  • proposition thmcounterproposition
  • proposition thmcounterproposition
  • proof
  • proposition thmcounterproposition
  • lemma thmcounterlemma
  • proof
  • lemma thmcounterlemma
  • proof
  • lemma thmcounterlemma
  • ...and 1 more