Convergence Analysis of Flow Matching in Latent Space with Transformers

TL;DR

This paper provides theoretical convergence guarantees for flow matching in latent space using transformers, demonstrating that generated samples converge to the target distribution under certain conditions.

Contribution

It introduces a convergence analysis for ODE-based generative models with transformers in latent space, including error bounds and approximation capabilities.

Findings

Sample distribution converges in Wasserstein-2 distance

Transformers can approximate smooth Lipschitz functions effectively

The approach is validated under practical assumptions

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.