Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Debiasing Kernel-Based Generative Models

Tian Qin, Wei-Min Huang

TL;DR

Debiasing Kernel-Based Generative Models (DKGM) tackles the challenge of high-quality image generation without explicit density estimation by coupling kernel density estimation (KDE) with a novel debiasing procedure. The method first generates KDE-based initial samples and then applies an iterative debiasing process, inspired by stochastic approximation and expressed as a stochastic differential equation, to recover sharp, high-fidelity images. The two-stage design leverages a KDE-driven stage and a time-step embedded U‑Net for refinement, yielding competitive results on CIFAR‑10 and strong performance on CelebA and LSUN when compared to diffusion and GAN baselines. DKGM also explores the roles of KDE bandwidth and the debiasing noise level, discusses connections to score-based models, and highlights potential for data augmentation, albeit with computational trade-offs in stage-2 training.

Abstract

We propose a novel two-stage framework of generative models named Debiasing Kernel-Based Generative Models (DKGM) with the insights from kernel density estimation (KDE) and stochastic approximation. In the first stage of DKGM, we employ KDE to bypass the obstacles in estimating the density of data without losing too much image quality. One characteristic of KDE is oversmoothing, which makes the generated image blurry. Therefore, in the second stage, we formulate the process of reducing the blurriness of images as a statistical debiasing problem and develop a novel iterative algorithm to improve image quality, which is inspired by the stochastic approximation. Extensive experiments illustrate that the image quality of DKGM on CIFAR10 is comparable to state-of-the-art models such as diffusion models and GAN models. The performance of DKGM on CelebA 128x128 and LSUN (Church) 128x128 is also competitive. We conduct extra experiments to exploit how the bandwidth in KDE affects the sample diversity and debiasing effect of DKGM. The connections between DKGM and score-based models are also discussed.

Debiasing Kernel-Based Generative Models

TL;DR

Debiasing Kernel-Based Generative Models (DKGM) tackles the challenge of high-quality image generation without explicit density estimation by coupling kernel density estimation (KDE) with a novel debiasing procedure. The method first generates KDE-based initial samples and then applies an iterative debiasing process, inspired by stochastic approximation and expressed as a stochastic differential equation, to recover sharp, high-fidelity images. The two-stage design leverages a KDE-driven stage and a time-step embedded U‑Net for refinement, yielding competitive results on CIFAR‑10 and strong performance on CelebA and LSUN when compared to diffusion and GAN baselines. DKGM also explores the roles of KDE bandwidth and the debiasing noise level, discusses connections to score-based models, and highlights potential for data augmentation, albeit with computational trade-offs in stage-2 training.

Abstract

We propose a novel two-stage framework of generative models named Debiasing Kernel-Based Generative Models (DKGM) with the insights from kernel density estimation (KDE) and stochastic approximation. In the first stage of DKGM, we employ KDE to bypass the obstacles in estimating the density of data without losing too much image quality. One characteristic of KDE is oversmoothing, which makes the generated image blurry. Therefore, in the second stage, we formulate the process of reducing the blurriness of images as a statistical debiasing problem and develop a novel iterative algorithm to improve image quality, which is inspired by the stochastic approximation. Extensive experiments illustrate that the image quality of DKGM on CIFAR10 is comparable to state-of-the-art models such as diffusion models and GAN models. The performance of DKGM on CelebA 128x128 and LSUN (Church) 128x128 is also competitive. We conduct extra experiments to exploit how the bandwidth in KDE affects the sample diversity and debiasing effect of DKGM. The connections between DKGM and score-based models are also discussed.

Paper Structure

This paper contains 34 sections, 2 theorems, 37 equations, 14 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Kernel density estimation (KDE)
  4. Bias of data restoration
  5. Stochastic approximation
  6. SDE version of iteration process \ref{['SA iteration']} and a choice of weight coefficients $a_{k}$
  7. Choice of network to approximate restored data $\Tilde{\mathbf{x}}$ given input $\hat{\mathbf{x}}_{k}$
  8. Debiasing Kernel Based Generative Models
  9. First stage: Initial generation model
  10. Second stage: Iterative debiasing
  11. Experiments
  12. Toy example: 1-d Swiss Roll
  13. Real datasets
  14. Enhancement from Stage 2 of DKGM
  15. Noise level $\alpha$ in DKGM
  16. ...and 19 more sections

Key Result

Theorem 2.1

Under assumptions $\textbf{A1}-\textbf{A5}$, the sequence of vector $\{\hat{\mathbf{x}}_{k}\}$ generated by iteration ID iteration converges to $\mathbf{x}^{*}$ in probability, which is the solution of the inverse problem $\hat{\mathbf{x}}_{0}=H(\mathbf{x}^{*})$.

Figures (14)

  • Figure 1: The Stage 2 DKGM trained on 1-d swiss roll data. The leftmost subplot (a) is the transformed data, which is the input of stage 2 model. Subplot (f) represents the ground truth.The rest subplots (b)-(d) are reconstructed data corresponding to different values of $k>0$.
  • Figure 2: The flow chart of second stage DKGM
  • Figure 3: LSUN Church samples from DKGM ($\alpha=0.5, b\sim Unif[0.5,1.0]$), FID=4.99
  • Figure 4: Randomly generated samples on unconditional CIFAR10 through two stages in DKGM (a) Generated samples from the model trained in Stage 1 with noise level $\alpha=1.0$ (b) Enhanced samples after stage 2 of DKGM with $b\sim Unif(0.8,1.2)$
  • Figure 5: Randomly generated samples on CelebA 128$\times$128 with same input under different noise levels of DKGM. (a) Generated samples from DKGM trained with noise level $\alpha=0.5$ (b) Generated samples from DKGM trained with noise level $\alpha=1.0$
  • ...and 9 more figures

Theorems & Definitions (2)

  • Theorem 2.1
  • Proposition 2.2: SDEDEVAE