Table of Contents
Fetching ...

Don't Play Favorites: Minority Guidance for Diffusion Models

Soobin Um, Suhyeon Lee, Jong Chul Ye

TL;DR

This work presents a novel framework that can make the generation process of the diffusion models focus on the minority samples, and develops minority guidance, a sampling technique that can guide the generation process toward regions with desired likelihood levels.

Abstract

We explore the problem of generating minority samples using diffusion models. The minority samples are instances that lie on low-density regions of a data manifold. Generating a sufficient number of such minority instances is important, since they often contain some unique attributes of the data. However, the conventional generation process of the diffusion models mostly yields majority samples (that lie on high-density regions of the manifold) due to their high likelihoods, making themselves ineffective and time-consuming for the minority generating task. In this work, we present a novel framework that can make the generation process of the diffusion models focus on the minority samples. We first highlight that Tweedie's denoising formula yields favorable results for majority samples. The observation motivates us to introduce a metric that describes the uniqueness of a given sample. To address the inherent preference of the diffusion models w.r.t. the majority samples, we further develop minority guidance, a sampling technique that can guide the generation process toward regions with desired likelihood levels. Experiments on benchmark real datasets demonstrate that our minority guidance can greatly improve the capability of generating high-quality minority samples over existing generative samplers. We showcase that the performance benefit of our framework persists even in demanding real-world scenarios such as medical imaging, further underscoring the practical significance of our work. Code is available at https://github.com/soobin-um/minority-guidance.

Don't Play Favorites: Minority Guidance for Diffusion Models

TL;DR

This work presents a novel framework that can make the generation process of the diffusion models focus on the minority samples, and develops minority guidance, a sampling technique that can guide the generation process toward regions with desired likelihood levels.

Abstract

We explore the problem of generating minority samples using diffusion models. The minority samples are instances that lie on low-density regions of a data manifold. Generating a sufficient number of such minority instances is important, since they often contain some unique attributes of the data. However, the conventional generation process of the diffusion models mostly yields majority samples (that lie on high-density regions of the manifold) due to their high likelihoods, making themselves ineffective and time-consuming for the minority generating task. In this work, we present a novel framework that can make the generation process of the diffusion models focus on the minority samples. We first highlight that Tweedie's denoising formula yields favorable results for majority samples. The observation motivates us to introduce a metric that describes the uniqueness of a given sample. To address the inherent preference of the diffusion models w.r.t. the majority samples, we further develop minority guidance, a sampling technique that can guide the generation process toward regions with desired likelihood levels. Experiments on benchmark real datasets demonstrate that our minority guidance can greatly improve the capability of generating high-quality minority samples over existing generative samplers. We showcase that the performance benefit of our framework persists even in demanding real-world scenarios such as medical imaging, further underscoring the practical significance of our work. Code is available at https://github.com/soobin-um/minority-guidance.
Paper Structure (34 sections, 6 theorems, 32 equations, 29 figures, 8 tables)

This paper contains 34 sections, 6 theorems, 32 equations, 29 figures, 8 tables.

Key Result

Proposition 1

Consider the DSM optimization in Eq. (eq:DSM). Assume that a given noise-conditioned score network ${\boldsymbol s}_{\boldsymbol{\theta}}({\boldsymbol x}_t, t)$ have enough capacity. Then for each timestep $t$, the optimality of the score network is achievable at:

Figures (29)

  • Figure 1: Inherent bias of Tweedie-based denoiser toward majority features. (a) (Left column) Clean images ${\boldsymbol x}_0$ from CelebA; (Middle column) Noised samples ${\boldsymbol x}_t$ made by the DDPM perturbation (i.e., Eq. (\ref{['eq:DDPM_perturb']})) with $t = 0.9T$ on the clean versions in the left column; (Right column) Denoised samples $\hat{{\boldsymbol x}}_0$ using Tweedie's formula (i.e., Eq. (\ref{['eq:tweedie_with_score']})) on the perturbed ones. The top (bottom) row represents the perturbation-denoising sequence performed on majority (minority) featured samples. (b) Geometric interpretation of the bias based on optimal score expression ${\boldsymbol s}_{\boldsymbol\theta}^* ({\boldsymbol x}_t, t) = \mathbb{E}_{q_{\alpha_t}({\boldsymbol x}_0 | {\boldsymbol x}_t)} \left[ \nabla_{{\boldsymbol x}_t} \log{ q_{\alpha_t} ( {\boldsymbol x}_t | {\boldsymbol x}_0 ) } \right]$.
  • Figure 2: Real samples with the smallest (left column), moderate (middle column), and the highest (right column) minority score, our proposed metric for identifying minorities.
  • Figure 3: Impacts of minority class $\tilde{l}$ (left) and classifier scale $w$ (right) on the density of Local Outlier Factor (LOF). The other parameters are fixed: $w=2.0$ (left) and $\tilde{l}=0$ (right).
  • Figure 4: Sample comparison on LSUN-Bedrooms. Generated samples by StyleGAN karras2019style (left), ADM dhariwal2021diffusion with ancestral sampling (middle), and minority guidance (right) are exhibited. We use the same random seed for the diffusion-based samplers.
  • Figure 5: Sample comparison on the brain MRI data. Generated samples by StyleGAN2-ADA Karras2020ada (left), ADM dhariwal2021diffusion with ancestral sampling (middle), and minority guidance (right) are exhibited. We use the same seed for the diffusion-based samplers.
  • ...and 24 more figures

Theorems & Definitions (10)

  • Proposition 1
  • Corollary 1
  • Proposition \ref{prop}
  • proof
  • Corollary \ref{corollary}
  • proof
  • Proposition 2
  • proof
  • Lemma 1
  • proof