Gaussian Mixture Solvers for Diffusion Models

• URL: http://arxiv.org/abs/2311.00941v1
• Date: Thu, 2 Nov 2023 02:05:38 GMT
• Title: Gaussian Mixture Solvers for Diffusion Models
• Authors: Hanzhong Guo, Cheng Lu, Fan Bao, Tianyu Pang, Shuicheng Yan, Chao Du, Chongxuan Li
• Abstract summary: We introduce a novel class of SDE-based solvers called GMS for diffusion models. Our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis.
• Score: 84.83349474361204
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently, diffusion models have achieved great success in generative tasks. Sampling from diffusion models is equivalent to solving the reverse diffusion stochastic differential equations (SDEs) or the corresponding probability flow ordinary differential equations (ODEs). In comparison, SDE-based solvers can generate samples of higher quality and are suited for image translation tasks like stroke-based synthesis. During inference, however, existing SDE-based solvers are severely constrained by the efficiency-effectiveness dilemma. Our investigation suggests that this is because the Gaussian assumption in the reverse transition kernel is frequently violated (even in the case of simple mixture data) given a limited number of discretization steps. To overcome this limitation, we introduce a novel class of SDE-based solvers called \emph{Gaussian Mixture Solvers (GMS)} for diffusion models. Our solver estimates the first three-order moments and optimizes the parameters of a Gaussian mixture transition kernel using generalized methods of moments in each step during sampling. Empirically, our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis in various diffusion models, which validates the motivation and effectiveness of GMS. Our code is available at https://github.com/Guohanzhong/GMS.

Related papers

• AdjointDEIS: Efficient Gradients for Diffusion Models [2.0795007613453445]
  We show that continuous adjoint equations for diffusion SDEs actually simplify to a simple ODE. We also demonstrate the effectiveness of AdjointDEIS for guided generation with an adversarial attack in the form of the face morphing problem.
  arXiv  Detail & Related papers  (2024-05-23T19:51:33Z)
• Diffusion models for Gaussian distributions: Exact solutions and Wasserstein errors [0.0]
  Diffusion or score-based models recently showed high performance in image generation. We study theoretically the behavior of diffusion models and their numerical implementation when the data distribution is Gaussian.
  arXiv  Detail & Related papers  (2024-05-23T07:28:56Z)
• On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
  Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
  arXiv  Detail & Related papers  (2024-05-18T15:59:41Z)
• SA-Solver: Stochastic Adams Solver for Fast Sampling of Diffusion Models [66.67616086310662]
  Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed. We propose SA-of-r, which is an improved efficient Adams method for solving diffusion SDE to generate data with high quality.
  arXiv  Detail & Related papers  (2023-09-10T12:44:54Z)
• Exploring the Optimal Choice for Generative Processes in Diffusion Models: Ordinary vs Stochastic Differential Equations [6.2284442126065525]
  We study the problem mathematically for two limiting scenarios: the zero diffusion (ODE) case and the large diffusion case. Our findings indicate that when the perturbation occurs at the end of the generative process, the ODE model outperforms the SDE model with a large diffusion coefficient.
  arXiv  Detail & Related papers  (2023-06-03T09:27:15Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• SEEDS: Exponential SDE Solvers for Fast High-Quality Sampling from Diffusion Models [0.49478969093606673]
  A potent class of generative models known as Diffusion Probabilistic Models (DPMs) has become prominent. Despite being quick, such solvers do not usually reach the optimal quality achieved by available slow SDE solvers. Our goal is to propose SDE solvers that reach optimal quality without requiring several hundreds or thousands of NFEs to achieve that goal.
  arXiv  Detail & Related papers  (2023-05-23T17:19:54Z)
• Reflected Diffusion Models [93.26107023470979]
  We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data. Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
  arXiv  Detail & Related papers  (2023-04-10T17:54:38Z)
• Score-Based Generative Modeling through Stochastic Differential Equations [114.39209003111723]
  We present a differential equation that transforms a complex data distribution to a known prior distribution by injecting noise. A corresponding reverse-time SDE transforms the prior distribution back into the data distribution by slowly removing the noise. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks. We demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.
  arXiv  Detail & Related papers  (2020-11-26T19:39:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.