Accelerating Convergence of Score-Based Diffusion Models, Provably

• URL: http://arxiv.org/abs/2403.03852v1
• Date: Wed, 6 Mar 2024 17:02:39 GMT
• Title: Accelerating Convergence of Score-Based Diffusion Models, Provably
• Authors: Gen Li, Yu Huang, Timofey Efimov, Yuting Wei, Yuejie Chi, Yuxin Chen
• Abstract summary: Score-based diffusion models often suffer from low sampling speed due to extensive function evaluations needed during the sampling phase. We design novel training-free algorithms to accelerate popular deterministic (i.e., DDIM) and (i.e., DDPM) samplers. Our theory accommodates $ell$-accurate score estimates, and does not require log-concavity or smoothness on the target distribution.
• Score: 44.11766377798812
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards speeding up diffusion generative modeling in practice, theoretical underpinnings for acceleration techniques remain severely limited. In this paper, we design novel training-free algorithms to accelerate popular deterministic (i.e., DDIM) and stochastic (i.e., DDPM) samplers. Our accelerated deterministic sampler converges at a rate $O(1/{T}^2)$ with $T$ the number of steps, improving upon the $O(1/T)$ rate for the DDIM sampler; and our accelerated stochastic sampler converges at a rate $O(1/T)$, outperforming the rate $O(1/\sqrt{T})$ for the DDPM sampler. The design of our algorithms leverages insights from higher-order approximation, and shares similar intuitions as popular high-order ODE solvers like the DPM-Solver-2. Our theory accommodates $\ell_2$-accurate score estimates, and does not require log-concavity or smoothness on the target distribution.

Related papers

• Provable Acceleration for Diffusion Models under Minimal Assumptions [8.15094483029656]
  We propose a novel training-free acceleration scheme for score-based samplers. Under minimal assumptions, our scheme achieves $varepsilon$-accuracy in total variation within $widetildeO(d5/4/sqrtvarepsilon)$ iterations.
  arXiv  Detail & Related papers  (2024-10-30T17:59:06Z)
• Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Models [21.961189407928853]
  We propose and analyze a training-free acceleration algorithm for SDE-style diffusion samplers, based on the KL Runge-Kutta method. The proposed sampler provably attains $varepsilon2$ error -- measured in divergence -- using $widetilde O(d3/2 / varepsilon)$ score function evaluations.
  arXiv  Detail & Related papers  (2024-10-07T05:34:51Z)
• Broadening Target Distributions for Accelerated Diffusion Models via a Novel Analysis Approach [49.97755400231656]
  We show that a novel accelerated DDPM sampler achieves accelerated performance for three broad distribution classes not considered before. Our results show an improved dependency on the data dimension $d$ among accelerated DDPM type samplers.
  arXiv  Detail & Related papers  (2024-02-21T16:11:47Z)
• Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models [49.81937966106691]
  We develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach.
  arXiv  Detail & Related papers  (2023-06-15T16:30:08Z)
• Fast Diffusion Model [122.36693015093041]
  Diffusion models (DMs) have been adopted across diverse fields with their abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a DM optimization perspective.
  arXiv  Detail & Related papers  (2023-06-12T09:38:04Z)
• Fast Diffusion Probabilistic Model Sampling through the lens of Backward Error Analysis [26.907301901503835]
  Denoising diffusion probabilistic models (DDPMs) are a class of powerful generative models. DDPMs generally need hundreds or thousands of sequential function evaluations (steps) of neural networks to generate a sample. This paper aims to develop a fast sampling method for DDPMs requiring much fewer steps while retaining high sample quality.
  arXiv  Detail & Related papers  (2023-04-22T16:58:47Z)
• Accelerating Diffusion Models via Early Stop of the Diffusion Process [114.48426684994179]
  Denoising Diffusion Probabilistic Models (DDPMs) have achieved impressive performance on various generation tasks. In practice DDPMs often need hundreds even thousands of denoising steps to obtain a high-quality sample. We propose a principled acceleration strategy, referred to as Early-Stopped DDPM (ES-DDPM), for DDPMs.
  arXiv  Detail & Related papers  (2022-05-25T06:40:09Z)
• Denoising Diffusion Implicit Models [117.03720513930335]
  We present denoising diffusion implicit models (DDIMs) for iterative implicit probabilistic models with the same training procedure as DDPMs. DDIMs can produce high quality samples $10 times$ to $50 times$ faster in terms of wall-clock time compared to DDPMs.
  arXiv  Detail & Related papers  (2020-10-06T06:15:51Z)

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.