Generative Unordered Flow for Set-Structured Data Generation

Flow-based generative models have demonstrated promising performance across a broad spectrum of data modalities (e.g., image and text). However, there are few works exploring their extension to unordered data (e.g., spatial point set), which is not trivial because previous models are mostly designed for vector data that are naturally ordered. In this paper, we present unordered flow, a type of flow-based generative model for set-structured data generation. Specifically, 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 propose a method similar to particle filtering, with Langevin dynamics to first warm-up the initial particles and gradient-based search to update them until convergence. We have conducted extensive experiments on multiple real-world datasets, showing that our unordered flow model is very effective in generating set-structured data and significantly outperforms previous baselines.