# Parallel Noising in Neural Markov Logic Networks

arXiv: https://arxiv.org/abs/2607.19126 · HTML: https://mlsanity.com/paper/2607.19126/

## 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.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 27 of 27)

- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Models](https://mlsanity.com/paper/1811.12823/) (2018)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Scallop: A Language for Neurosymbolic Programming](https://mlsanity.com/paper/2304.04812/) (2023)
- [DeepStochLog: Neural Stochastic Logic Programming](https://mlsanity.com/paper/2106.12574/) (2021)
- [Symbolic Music Generation with Non-Differentiable Rule Guided Diffusion](https://mlsanity.com/paper/2402.14285/) (2024)
- [A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference](https://mlsanity.com/paper/2212.12393/) (2022)
- [NeuPSL: Neural Probabilistic Soft Logic](https://mlsanity.com/paper/2205.14268/) (2022)
- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Data](https://mlsanity.com/paper/2402.04823/) (2024)
- [Neural Markov Logic Networks](https://mlsanity.com/paper/1905.13462/) (2019)
- [Efficient Generation of Structured Objects with Constrained Adversarial Networks](https://mlsanity.com/paper/2007.13197/) (2020)
- [Symmetric Weighted First-Order Model Counting](https://mlsanity.com/paper/1412.1505/) (2014)
- [Relational Neural Machines](https://mlsanity.com/paper/2002.02193/) (2020)
- [Differentiable Sampling of Categorical Distributions Using the CatLog-Derivative Trick](https://mlsanity.com/paper/2311.12569/) (2023)
- [Neurosymbolic Diffusion Models](https://mlsanity.com/paper/2505.13138/) (2025)
- [Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting](https://mlsanity.com/paper/1904.02688/) (2019)
- [Zero-Shot Conditioning of Score-Based Diffusion Models by Neuro-Symbolic Constraints](https://mlsanity.com/paper/2308.16534/) (2023)
- [EXPLAIN, AGREE, LEARN: Scaling Learning for Neural Probabilistic Logic](https://mlsanity.com/paper/2408.08133/) (2024)
- [Relational Neurosymbolic Markov Models](https://mlsanity.com/paper/2412.13023/) (2024)
- [Quantified Markov Logic Networks](https://mlsanity.com/paper/1807.01183/) (2018)

## 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.