mlsanityData to 7 Oct 2026

Existence-Field Diffusion Model for Spatial Point Processes with Variable Cardinality

arXiv 2607.26428 ↗First posted 29 Jul 2026cs.LG stat.MLcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We study generative modeling of spatial point processes (SPP), where both the number of points and their spatial configuration are governed by a joint distribution. While diffusion models have achieved strong performance in modeling complex distributions, extending them to variable-cardinality SPP remains challenging. Existing approaches either sample cardinality before generating locations conditionally, or introduce specialized discrete operations to change the number of points during generation. We propose the existence-field diffusion model (EFDM), which associates each potential point with a continuous variable representing its degree of presence. EFDM uses Gaussian diffusion to jointly model point locations and cardinality through a simple continuous representation. Existence probabilities can increase or decrease in both forward and reverse diffusion, without explicit point-addition or point-deletion steps. The same construction naturally accommodates categorical attributes, allowing locations, existence, and attributes to be modeled together. Experiments demonstrate improved molecular stability and validity over the compared baselines on the molecular dataset, alongside competitive performance on real-world spatial and synthetic datasets.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 17 of its 32 references that are in the map. First posted on arXiv 29 Jul 2026.

Builds on

17 of 32 references.

Closest ancestors · 3

Same direction, newest first

  1. 2023Trans-Dimensional Generative Modeling via Jump Diffusion Models25 May
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  3. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 14

  1. 2017Attention Is All You Needcited by 59,932
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2021E(n) Equivariant Graph Neural Networkscited by 951
  4. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 734
  5. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  6. 2016Deep Transfer Learning with Joint Adaptation Networkscited by 609
  7. 2019PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flowscited by 487
  8. 2020Learning Gradient Fields for Shape Generationcited by 245
  9. 2018PointGrow: Autoregressively Learned Point Cloud Generation with Self-Attentioncited by 105
  10. 2020Neural Spatio-Temporal Point Processescited by 92
  11. 2021Neural Point Process for Learning Spatiotemporal Event Dynamicscited by 42
  12. 2024Unlocking Point Processes through Point Set Diffusioncited by 12
2 more
  1. 2021Deep Neyman-Scott Processescited by 6
  2. 2022Distance and Kernel-Based Measures for Global and Local Two-Sample Conditional Distribution Testingcited by 5

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  4. 2026GLIDE: Graph-guided Leap Inference for Diffusion Estimation of Spatio-Temporal Point Processes
  5. 2025Generative diffusion models from a PDE perspective
  6. 2025Foundations of Diffusion Models in General State Spaces: A Self-Contained Introduction
  7. 2023Continuous-Time Functional Diffusion Processes
  8. 2026A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models