mlsanityData to 14 Oct 2026

Parallel Noising in Neural Markov Logic Networks

arXiv 2607.19126 ↗First posted 21 Jul 2026cs.LG cs.AIcited by 0

On the map: Diffusion models → Discrete and text diffusion

Abstract (arXiv)

Neural Markov Logic Networks (NMLNs) are a flexible neurosymbolic relational model. Previous work has shown that, although NMLNs achieve strong performance as generative models for small relational structures, they underperform diffusion-based generative graph models on larger structures. In this paper, we strengthen NMLNs along two main dimensions: (i) we increase the expressive capacity of their potential functions using graph neural networks, and (ii) we develop a new training and inference algorithm inspired by parallel-tempering Markov chain Monte Carlo methods, which we name parallel noising. Together, these enhancements enable NMLNs to attain strong performance in graph generation relative to general diffusion-based generative graph models. Furthermore, they allow NMLNs to match the performance of specialized text-based recurrent models when generating small molecular structures.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Discrete and text diffusion, one of 14 directions in Diffusion models. Builds on 27 of its 53 references that are in the map. First posted on arXiv 21 Jul 2026.

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27 of 53 references.

References · 27

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  2. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 520
  3. 2018Assessing Generative Models via Precision and Recallcited by 406
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  11. 2021DeepStochLog: Neural Stochastic Logic Programmingcited by 58
  12. 2024Symbolic Music Generation with Non-Differentiable Rule Guided Diffusioncited by 54
15 more
  1. 2022A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inferencecited by 50
  2. 2022NeuPSL: Neural Probabilistic Soft Logiccited by 34
  3. 2022VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programmingcited by 31
  4. 2024How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Datacited by 29
  5. 2019Neural Markov Logic Networkscited by 27
  6. 2020Efficient Generation of Structured Objects with Constrained Adversarial Networkscited by 27
  7. 2014Symmetric Weighted First-Order Model Countingcited by 19
  8. 2020Relational Neural Machinescited by 19
  9. 2023Differentiable Sampling of Categorical Distributions Using the CatLog-Derivative Trickcited by 14
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  12. 2023Zero-Shot Conditioning of Score-Based Diffusion Models by Neuro-Symbolic Constraintscited by 7
  13. 2024EXPLAIN, AGREE, LEARN: Scaling Learning for Neural Probabilistic Logiccited by 6
  14. 2024Relational Neurosymbolic Markov Modelscited by 6
  15. 2018Quantified Markov Logic Networkscited by 1

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