The Poisson Midpoint Method for Langevin Dynamics: Provably Efficient Discretization for Diffusion Models

• URL: http://arxiv.org/abs/2405.17068v2
• Date: Tue, 29 Oct 2024 05:34:23 GMT
• Title: The Poisson Midpoint Method for Langevin Dynamics: Provably Efficient Discretization for Diffusion Models
• Authors: Saravanan Kandasamy, Dheeraj Nagaraj,
• Abstract summary: Langevin Monte Carlo (LMC) is the simplest and most studied algorithm. We propose the Poisson Midpoint Method, which approximates a small step-size LMC with large step-sizes. We show that it maintains the quality of DDPM with 1000 neural network calls with just 50-80 neural network calls and outperforms ODE based methods with similar compute.
• Score: 9.392691963008385
• License:
• Abstract: Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest and most studied algorithm. LMC can suffer from slow convergence - requiring a large number of steps of small step-size to obtain good quality samples. This becomes stark in the case of diffusion models where a large number of steps gives the best samples, but the quality degrades rapidly with smaller number of steps. Randomized Midpoint Method has been recently proposed as a better discretization of Langevin dynamics for sampling from strongly log-concave distributions. However, important applications such as diffusion models involve non-log concave densities and contain time varying drift. We propose its variant, the Poisson Midpoint Method, which approximates a small step-size LMC with large step-sizes. We prove that this can obtain a quadratic speed up of LMC under very weak assumptions. We apply our method to diffusion models for image generation and show that it maintains the quality of DDPM with 1000 neural network calls with just 50-80 neural network calls and outperforms ODE based methods with similar compute.

Related papers

• 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)
• Gaussian Mixture Solvers for Diffusion Models [84.83349474361204]
  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.
  arXiv  Detail & Related papers  (2023-11-02T02:05:38Z)
• Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference [60.32804641276217]
  We propose Latent Consistency Models (LCMs), enabling swift inference with minimal steps on any pre-trained LDMs. A high-quality 768 x 768 24-step LCM takes only 32 A100 GPU hours for training. We also introduce Latent Consistency Fine-tuning (LCF), a novel method that is tailored for fine-tuning LCMs on customized image datasets.
  arXiv  Detail & Related papers  (2023-10-06T17:11:58Z)
• Accelerating Markov Chain Monte Carlo sampling with diffusion models [0.0]
  We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the posterior.
  arXiv  Detail & Related papers  (2023-09-04T09:03:41Z)
• Fast Inference in Denoising Diffusion Models via MMD Finetuning [23.779985842891705]
  We present MMD-DDM, a novel method for fast sampling of diffusion models. Our approach is based on the idea of using the Maximum Mean Discrepancy (MMD) to finetune the learned distribution with a given budget of timesteps. Our findings show that the proposed method is able to produce high-quality samples in a fraction of the time required by widely-used diffusion models.
  arXiv  Detail & Related papers  (2023-01-19T09:48:07Z)
• Fast Sampling of Diffusion Models via Operator Learning [74.37531458470086]
  We use neural operators, an efficient method to solve the probability flow differential equations, to accelerate the sampling process of diffusion models. Compared to other fast sampling methods that have a sequential nature, we are the first to propose a parallel decoding method. We show our method achieves state-of-the-art FID of 3.78 for CIFAR-10 and 7.83 for ImageNet-64 in the one-model-evaluation setting.
  arXiv  Detail & Related papers  (2022-11-24T07:30:27Z)
• Pseudo Numerical Methods for Diffusion Models on Manifolds [77.40343577960712]
  Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality samples such as image and audio samples. DDPMs require hundreds to thousands of iterations to produce final samples. We propose pseudo numerical methods for diffusion models (PNDMs) PNDMs can generate higher quality synthetic images with only 50 steps compared with 1000-step DDIMs (20x speedup)
  arXiv  Detail & Related papers  (2022-02-20T10:37:52Z)
• 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.