# Neurosymbolic Diffusion Models

arXiv: https://arxiv.org/abs/2505.13138 · HTML: https://mlsanity.com/paper/2505.13138/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 62 of its 90 references that are in the map.
- First posted on arXiv 19 May 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)
- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 62)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Masked Diffusion Models are Secretly Time-Agnostic Masked Models and Exploit Inaccurate Categorical Sampling](https://mlsanity.com/paper/2409.02908/) (2024)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Beyond Autoregression: Discrete Diffusion for Complex Reasoning and Planning](https://mlsanity.com/paper/2410.14157/) (2024)
- [Gradient Estimation Using Stochastic Computation Graphs](https://mlsanity.com/paper/1506.05254/) (2015)
- [Analyzing Differentiable Fuzzy Logic Operators](https://mlsanity.com/paper/2002.06100/) (2020)
- [Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions](https://mlsanity.com/paper/2106.01798/) (2021)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [Explainable Object-induced Action Decision for Autonomous Vehicles](https://mlsanity.com/paper/2003.09405/) (2020)
- [Sequential Monte Carlo Steering of Large Language Models using Probabilistic Programs](https://mlsanity.com/paper/2306.03081/) (2023)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Tractable Control for Autoregressive Language Generation](https://mlsanity.com/paper/2304.07438/) (2023)
- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
- [Scallop: A Language for Neurosymbolic Programming](https://mlsanity.com/paper/2304.04812/) (2023)
- [Discrete Copula Diffusion](https://mlsanity.com/paper/2410.01949/) (2024)
- [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)

## Built on by (most cited first, 14 of 14)

- [Discrete Diffusion in Large Language and Multimodal Models: A Survey](https://mlsanity.com/paper/2506.13759/) (2025)
- [Learning to Disentangle Latent Reasoning Rules with Language VAEs: A Systematic Study](https://mlsanity.com/paper/2506.19418/) (2025)
- [Neurosymbolic Reasoning Shortcuts under the Independence Assumption](https://mlsanity.com/paper/2507.11357/) (2025)
- [Propositional Logic for Probing Generalization in Neural Networks](https://mlsanity.com/paper/2506.08978/) (2025)
- [Entropy-Aligned Decoding of LMs for Better Writing and Reasoning](https://mlsanity.com/paper/2601.01714/) (2026)
- [Formal Semantic Control over Language Models](https://mlsanity.com/paper/2602.00638/) (2026)
- [The Theory and Practice of MAP Inference over Non-Convex Constraints](https://mlsanity.com/paper/2602.08681/) (2026)
- [Can I Have Your Order? Monte-Carlo Tree Search for Slot Filling Ordering in Diffusion Language Models](https://mlsanity.com/paper/2602.12586/) (2026)
- [Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models](https://mlsanity.com/paper/2605.18202/) (2026)
- [Autoregressive Models for Knowledge Graph Generation](https://mlsanity.com/paper/2602.06707/) (2026)
- [Can VLMs Reason Robustly? A Neuro-Symbolic Investigation](https://mlsanity.com/paper/2603.23867/) (2026)
- [Parallel Noising in Neural Markov Logic Networks](https://mlsanity.com/paper/2607.19126/) (2026)
- [Neuro-symbolic learning over OWL 2 DL via consequence-based compilation to differentiable circuits](https://mlsanity.com/paper/2608.17741/) (2026)
- [Calibration in One Go: Jointly Learning Accurate and Calibrated Neural Networks](https://mlsanity.com/paper/2610.13693/) (2026)

## Abstract (arXiv)

Neurosymbolic (NeSy) predictors combine neural perception with symbolic reasoning to solve tasks like visual reasoning. However, standard NeSy predictors assume conditional independence between the symbols they extract, thus limiting their ability to model interactions and uncertainty - often leading to overconfident predictions and poor out-of-distribution generalisation. To overcome the limitations of the independence assumption, we introduce neurosymbolic diffusion models (NeSyDMs), a new class of NeSy predictors that use discrete diffusion to model dependencies between symbols. Our approach reuses the independence assumption from NeSy predictors at each step of the diffusion process, enabling scalable learning while capturing symbol dependencies and uncertainty quantification. Across both synthetic and real-world benchmarks - including high-dimensional visual path planning and rule-based autonomous driving - NeSyDMs achieve state-of-the-art accuracy among NeSy predictors and demonstrate strong calibration.