# Generative Unordered Flow for Set-Structured Data Generation

arXiv: https://arxiv.org/abs/2501.17770 · HTML: https://mlsanity.com/paper/2501.17770/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 68 references that are in the map.
- First posted on arXiv 29 Jan 2025.

## Builds on (most cited first, 30 of 40)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [A Conditional Point Diffusion-Refinement Paradigm for 3D Point Cloud Completion](https://mlsanity.com/paper/2112.03530/) (2021)
- [Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimization](https://mlsanity.com/paper/1707.06618/) (2017)
- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Score-based Diffusion Models in Function Space](https://mlsanity.com/paper/2302.07400/) (2023)
- [Functional Flow Matching](https://mlsanity.com/paper/2305.17209/) (2023)
- [Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Trees](https://mlsanity.com/paper/2309.09968/) (2023)
- [Generative PointNet: Deep Energy-Based Learning on Unordered Point Sets for 3D Generation, Reconstruction and Classification](https://mlsanity.com/paper/2004.01301/) (2020)
- [Spatio-temporal Diffusion Point Processes](https://mlsanity.com/paper/2305.12403/) (2023)
- [Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion](https://mlsanity.com/paper/2211.02590/) (2022)

## Built on by (most cited first, 2 of 2)

- [Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Once](https://mlsanity.com/paper/2605.08424/) (2026)
- [SetPlanner: A Lightweight Plug-in Point-Set Planner for Frozen SAM](https://mlsanity.com/paper/2609.18037/) (2026)

## Abstract (arXiv)

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.