Convergence Analysis of Flow Matching in Latent Space with Transformers

• URL: http://arxiv.org/abs/2404.02538v2
• Date: Sun, 28 Apr 2024 10:10:33 GMT
• Title: Convergence Analysis of Flow Matching in Latent Space with Transformers
• Authors: Yuling Jiao, Yanming Lai, Yang Wang, Bokai Yan,
• Abstract summary: We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a transformer network is trained to predict the velocity field of the transformation from a standard normal distribution to the target latent distribution.
• Score: 7.069772598731282
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a transformer network is trained to predict the velocity field of the transformation from a standard normal distribution to the target latent distribution. Our error analysis demonstrates the effectiveness of this approach, showing that the distribution of samples generated via estimated ODE flow converges to the target distribution in the Wasserstein-2 distance under mild and practical assumptions. Furthermore, we show that arbitrary smooth functions can be effectively approximated by transformer networks with Lipschitz continuity, which may be of independent interest.

Related papers

• Straightness of Rectified Flow: A Theoretical Insight into Wasserstein Convergence [54.580605276017096]
  Diffusion models have emerged as a powerful tool for image generation and denoising. Recently, Liu et al. designed a novel alternative generative model Rectified Flow (RF) RF aims to learn straight flow trajectories from noise to data using a sequence of convex optimization problems.
  arXiv  Detail & Related papers  (2024-10-19T02:36:11Z)
• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional general score-mismatched diffusion samplers. We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions. This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• 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)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Arbitrary Distributions Mapping via SyMOT-Flow: A Flow-based Approach Integrating Maximum Mean Discrepancy and Optimal Transport [2.7309692684728617]
  We introduce a novel model called SyMOT-Flow that trains an invertible transformation by minimizing the symmetric maximum mean discrepancy between samples from two unknown distributions. The resulting transformation leads to more stable and accurate sample generation.
  arXiv  Detail & Related papers  (2023-08-26T08:39:16Z)
• SE(3) Equivariant Augmented Coupling Flows [16.65770540017618]
  Coupling normalizing flows allow for fast sampling and density evaluation. Standard coupling architecture precludes endowing flows that operate on the Cartesian coordinates of atoms.
  arXiv  Detail & Related papers  (2023-08-20T20:49:15Z)
• Adversarial Likelihood Estimation With One-Way Flows [44.684952377918904]
  Generative Adversarial Networks (GANs) can produce high-quality samples, but do not provide an estimate of the probability density around the samples. We show that our method converges faster, produces comparable sample quality to GANs with similar architecture, successfully avoids over-fitting to commonly used datasets and produces smooth low-dimensional latent representations of the training data.
  arXiv  Detail & Related papers  (2023-07-19T10:26:29Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Resampling Base Distributions of Normalizing Flows [0.0]
  We introduce a base distribution for normalizing flows based on learned rejection sampling. We develop suitable learning algorithms using both maximizing the log-likelihood and the optimization of the reverse Kullback-Leibler divergence.
  arXiv  Detail & Related papers  (2021-10-29T14:44:44Z)

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.