Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flows
- URL: http://arxiv.org/abs/2405.14392v1
- Date: Thu, 23 May 2024 10:08:19 GMT
- Title: Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flows
- Authors: Alberto Cabezas, Louis Sharrock, Christopher Nemeth,
- Abstract summary: Continuous normalizing flows (CNFs) learn the probability path between a reference and a target density by modeling the vector field generating said path using neural networks.
Recently, Lipman et al. (2022) introduced a simple and inexpensive method for training CNFs in generative modeling, termed flow matching (FM)
We re-purpose this method for probabilistic inference by incorporating Markovian sampling methods in evaluating the FM objective and using the learned probability path to improve Monte Carlo sampling.
- Score: 2.2530496464901106
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Continuous normalizing flows (CNFs) learn the probability path between a reference and a target density by modeling the vector field generating said path using neural networks. Recently, Lipman et al. (2022) introduced a simple and inexpensive method for training CNFs in generative modeling, termed flow matching (FM). In this paper, we re-purpose this method for probabilistic inference by incorporating Markovian sampling methods in evaluating the FM objective and using the learned probability path to improve Monte Carlo sampling. We propose a sequential method, which uses samples from a Markov chain to fix the probability path defining the FM objective. We augment this scheme with an adaptive tempering mechanism that allows the discovery of multiple modes in the target. Under mild assumptions, we establish convergence to a local optimum of the FM objective, discuss improvements in the convergence rate, and illustrate our methods on synthetic and real-world examples.
Related papers
- Dynamical Measure Transport and Neural PDE Solvers for Sampling [77.38204731939273]
We tackle the task of sampling from a probability density as transporting a tractable density function to the target.
We employ physics-informed neural networks (PINNs) to approximate the respective partial differential equations (PDEs) solutions.
PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently.
arXiv Detail & Related papers (2024-07-10T17:39:50Z) - Ai-Sampler: Adversarial Learning of Markov kernels with involutive maps [28.229819253644862]
We propose a method to parameterize and train transition kernels of Markov chains to achieve efficient sampling and good mixing.
This training procedure minimizes the total variation distance between the stationary distribution of the chain and the empirical distribution of the data.
arXiv Detail & Related papers (2024-06-04T17:00:14Z) - Flow matching achieves minimax optimal convergence [50.38891696297888]
Flow matching (FM) has gained significant attention as a simulation-free generative model.
This paper discusses the convergence properties of FM in terms of the $p$-Wasserstein distance, a measure of distributional discrepancy.
We establish that FM can achieve the minmax optimal convergence rate for $1 leq p leq 2$, presenting the first theoretical evidence that FM can reach convergence rates comparable to those of diffusion models.
arXiv Detail & Related papers (2024-05-31T14:54:51Z) - Diffusion Generative Flow Samplers: Improving learning signals through
partial trajectory optimization [87.21285093582446]
Diffusion Generative Flow Samplers (DGFS) is a sampling-based framework where the learning process can be tractably broken down into short partial trajectory segments.
Our method takes inspiration from the theory developed for generative flow networks (GFlowNets)
arXiv Detail & Related papers (2023-10-04T09:39:05Z) - 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) - Improving and generalizing flow-based generative models with minibatch
optimal transport [90.01613198337833]
We introduce the generalized conditional flow matching (CFM) technique for continuous normalizing flows (CNFs)
CFM features a stable regression objective like that used to train the flow in diffusion models but enjoys the efficient inference of deterministic flow models.
A variant of our objective is optimal transport CFM (OT-CFM), which creates simpler flows that are more stable to train and lead to faster inference.
arXiv Detail & Related papers (2023-02-01T14:47:17Z) - Flow Matching for Generative Modeling [44.66897082688762]
Flow Matching is a simulation-free approach for training Continuous Normalizing Flows (CNFs)
We find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models.
Training CNFs using Flow Matching on ImageNet leads to state-of-the-art performance in terms of both likelihood and sample quality.
arXiv Detail & Related papers (2022-10-06T08:32:20Z) - Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC [83.48593305367523]
Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions.
We introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions.
We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.
arXiv Detail & Related papers (2021-02-04T02:21:08Z)
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.