Flow Matching on Unordered Sets

Yangming Li, Chaoyu Liu, Carola-Bibiane Schönlieb

Keywords: Unordered Set, Flow Matching, Generative Models

TL;DR: A permutation-invariant flow-based generative model for unordered set generation.

Abstract: Flow matching has achieved promising performance across a broad spectrum of data modalities (e.g., image and text). However, there are few works exploring their extension to unordered point sets. Indeed, previous generative models are mostly designed for vector data, with a natural ordering along dimensions. In this paper, we present unordered flow, a type of flow-based generative model for generating point sets. Specifically, we propose a lifting approach where we convert unordered data into an appropriate function representation, and learn the probability measure of such representations through function-valued flow matching. For the inverse map from a function representation to unordered data, we introduce a particle filtering method that first warms up the initial particles with Langevin dynamics and then updates them until convergence through gradient-based search. We have conducted extensive experiments on multiple real-world datasets, showing that our unordered flow model is highly effective in generating set-structured data and significantly outperforms previous baselines.

Primary Area: generative models

Submission Number: 5823