mlsanityData to 14 Oct 2026

Neurosymbolic Diffusion Models

arXiv 2505.13138 ↗First posted 19 May 2025cs.LGcited by 13

On the map: LLM reasoning → Reasoning benchmarks and evaluation

also in 1 more
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.

Key facts. Cited by 13 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.

Builds on

62 of 90 references.

Closest ancestors · 6

Same direction, newest first

  1. 2025Neural Probabilistic Circuits: Enabling Compositional and Interpretable Predictions through Logical Reasoning13 Jan
  2. 2024Mapping the Neuro-Symbolic AI Landscape by Architectures: A Handbook on Augmenting Deep Learning Through Symbolic Reasoning29 Oct
  3. 2024On the Hardness of Probabilistic Neurosymbolic Learning6 Jun
  4. 2023Scallop: A Language for Neurosymbolic Programming10 Apr
  5. 2022A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference23 Dec
  6. 2022VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming7 Feb

Other references · 56

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  2. 2015Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networkscited by 9,639
  3. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  4. 2021Variational Diffusion Modelscited by 1,153
  5. 2025Large Language Diffusion Modelscited by 912
  6. 2024Simple and Effective Masked Diffusion Language Modelscited by 848
  7. 2019On the Variance of the Adaptive Learning Rate and Beyondcited by 772
  8. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 626
  9. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 451
  10. 2019Neural Probabilistic Logic Programming in DeepProbLogcited by 394
  11. 2022Understanding Diffusion Models: A Unified Perspectivecited by 340
  12. 2019Monte Carlo Gradient Estimation in Machine Learningcited by 283
38 more
  1. 2017A Semantic Loss Function for Deep Learning with Symbolic Knowledgecited by 270
  2. 2019Differentiation of Blackbox Combinatorial Solverscited by 226
  3. 2024Masked Diffusion Models are Secretly Time-Agnostic Masked Models and Exploit Inaccurate Categorical Samplingcited by 208
  4. 2020Logic Tensor Networkscited by 199
  5. 2024Beyond Autoregression: Discrete Diffusion for Complex Reasoning and Planningcited by 135
  6. 2015Gradient Estimation Using Stochastic Computation Graphscited by 121
  7. 2020Analyzing Differentiable Fuzzy Logic Operatorscited by 101
  8. 2021Implicit MLE: Backpropagating Through Discrete Exponential Family Distributionscited by 98
  9. 2024Probabilistic Inference in Language Models via Twisted Sequential Monte Carlocited by 90
  10. 2020Explainable Object-induced Action Decision for Autonomous Vehiclescited by 88
  11. 2023Sequential Monte Carlo Steering of Large Language Models using Probabilistic Programscited by 80
  12. 2021From Statistical Relational to Neurosymbolic Artificial Intelligence: a Surveycited by 72
  13. 2023Tractable Control for Autoregressive Language Generationcited by 65
  14. 2023Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcutscited by 63
  15. 2024Symbolic Music Generation with Non-Differentiable Rule Guided Diffusioncited by 54
  16. 2024Discrete Copula Diffusioncited by 54
  17. 2025Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlocited by 46
  18. 2024BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcutscited by 37
  19. 2022ROAD-R: The Autonomous Driving Dataset with Logical Requirementscited by 34
  20. 2023Neuro-Symbolic Continual Learning: Knowledge, Reasoning Shortcuts and Concept Rehearsalcited by 33
  21. 2022Mitigating Modality Collapse in Multimodal VAEs via Impartial Optimizationcited by 32
  22. 2024Adaptable Logical Control for Large Language Modelscited by 30
  23. 2024Logically Consistent Language Models via Neuro-Symbolic Integrationcited by 30
  24. 2024How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Datacited by 29
  25. 2020Efficient Generation of Structured Objects with Constrained Adversarial Networkscited by 27
  26. 2023Neural Probabilistic Logic Programming in Discrete-Continuous Domainscited by 25
  27. 2023A Pseudo-Semantic Loss for Autoregressive Models with Logical Constraintscited by 22
  28. 2019A Boxology of Design Patterns for Hybrid Learning and Reasoning Systemscited by 20
  29. 2024A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcutscited by 19
  30. 2024On the Independence Assumption in Neurosymbolic Learningcited by 18
  31. 2025Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraintscited by 18
  32. 2024KLay: Accelerating Arithmetic Circuits for Neurosymbolic AIcited by 16
  33. 2023Differentiable Sampling of Categorical Distributions Using the CatLog-Derivative Trickcited by 14
  34. 2023Semantic Strengthening of Neuro-Symbolic Learningcited by 12
  35. 2021Storchastic: A Framework for General Stochastic Automatic Differentiationcited by 11
  36. 2022Refining neural network predictions using background knowledgecited by 11
  37. 2024Plug-and-Play Controllable Generation for Discrete Masked Modelscited by 11
  38. 2024Controllable Generation via Locally Constrained Resamplingcited by 11

50 most cited of 56 All 56 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 9.

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  1. 2025Discrete Diffusion in Large Language and Multimodal Models: A Surveycited by 61
  2. 2025Learning to Disentangle Latent Reasoning Rules with Language VAEs: A Systematic Studycited by 2
  3. 2025Neurosymbolic Reasoning Shortcuts under the Independence Assumptioncited by 2
  4. 2025Propositional Logic for Probing Generalization in Neural Networkscited by 1
  5. 2026Entropy-Aligned Decoding of LMs for Better Writing and Reasoningcited by 1
  6. 2026The Theory and Practice of MAP Inference over Non-Convex Constraintscited by 1
  7. 2026Can I Have Your Order? Monte-Carlo Tree Search for Slot Filling Ordering in Diffusion Language Modelscited by 1
  8. 2026Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Modelscited by 1
  9. 2026Autoregressive Models for Knowledge Graph Generationcited by 0
  10. 2026Can VLMs Reason Robustly? A Neuro-Symbolic Investigationcited by 0
  11. 2026Parallel Noising in Neural Markov Logic Networkscited by 0
  12. 2026Neuro-symbolic learning over OWL 2 DL via consequence-based compilation to differentiable circuitscited by 0
1 more
  1. 2026Calibration in One Go: Jointly Learning Accurate and Calibrated Neural Networkscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Parameter Choice and Neuro-Symbolic Approaches for Deep Domain-Invariant Learning
  2. 2026Neuro-Symbolic Artificial Intelligence: A Task-Directed Survey in the Black-Box Models Era
  3. 2026EM-NeSy: Expectation Maximization for Neurosymbolic Learning
  4. 2024Relational Neurosymbolic Markov Models
  5. 2024NeSyA: Neurosymbolic Automata
  6. 2024Simple and Effective Transfer Learning for Neuro-Symbolic Integration
  7. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling
  8. 2025NeSyPr: Neurosymbolic Proceduralization For Efficient Embodied Reasoning