Generative Unordered Flow for Set-Structured Data Generation

2025-01-29

AI Summary

Conventional normalizing flow models for unordered point sets (e.g., 3D point clouds) rely on artificial ordering or symmetric aggregation, failing to intrinsically respect permutation invariance. Method: We propose *unordered flow*, a novel paradigm that models point sets as permutation-invariant functional representations and establishes a flow matching framework directly in the function-value space. To enable differentiable, invertible reconstruction from function values to raw points, we design a Langevin-based warm-up initialization and a gradient-driven particle refinement scheme. Contribution/Results: The method inherently satisfies set permutation invariance—no sorting, pooling, or explicit symmetrization is required. Evaluated on multiple real-world point-set benchmarks, it achieves superior generation quality (lower FID and MMD) and diversity compared to state-of-the-art flow-based and set-generation baselines, demonstrating both effectiveness and generality for modeling intrinsic unordered structures.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Flow-based Models
• Unordered Data Generation
• Point Clouds

Innovation

• Unordered Streams Model
• Probability Distribution Learning
• Gradient Adjustment