Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Neurosymbolic Diffusion Models
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Introduces neurosymbolic diffusion models, which apply masked discrete diffusion over NeSy concepts with a NELBO that uses per-step independent unmasking models, to capture concept dependencies and be reasoning-shortcut aware.
Problem
Standard neurosymbolic predictors assume conditional independence between extracted concepts, which causes overconfidence, reasoning shortcuts, and poor OOD generalisation, while expressive alternatives do not scale to high-dimensional reasoning.
Approach
Use masked diffusion models over concepts and outputs, keeping the conditional independence assumption locally at each denoising step while capturing global dependencies; derive a NELBO that extends MDM losses to non-factorised output distributions and optimise the output WMC term with a RLOO-based sampling estimator.
Key results
- On 30x30 visual path planning, the method reaches 97.40% accuracy versus 93.7% for I-MLE and 80.85% for EXAL.
- On RSBench MNIST Half, conditional-entropy variant reduces ID concept ECE to 4.18 versus 36.81 for BEARS.
- On 4-digit MNIST Addition, the method is competitive (92.49%) with A-NeSI (92.56%).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use neurosymbolic diffusion instead of independent approximate NeSy prediction | Visual path planning · Visual path planning 30×30 | accuracy: 93.7 ± 0.6 -> 97.40 ± 1.23 | Helped |
| use neurosymbolic diffusion instead of A-NeSI+RL | Visual path planning · Visual path planning 12×12 | accuracy: 98.96 -> 99.41 | No clear effect |
| use neurosymbolic diffusion instead of the best listed exact method | MNIST Addition · MNIST Addition N=4 | accuracy: 93.5 ± 0.6 -> 92.49 | No clear effect |
| use neurosymbolic diffusion instead of PLIA | MNIST Addition · MNIST Addition N=15 | accuracy: 79.00 -> 77.29 | Hurt |
| use conditional rather than unconditional entropy | MNIST Diffusion · MNIST Half | Acc_y OOD: 10.9 -> 28.44 | Helped |
| use conditional rather than unconditional entropy | MNIST Diffusion · MNIST Half | ECE_c ID: 39.52 -> 4.18 | Helped |
| use conditional rather than unconditional entropy | MNIST Diffusion · MNIST E-O | Acc_c: 0.36 -> 20.33 | Helped |
| use conditional rather than unconditional entropy | MNIST Diffusion · MNIST E-O | ECE_c OOD: 19.13 -> 5.77 | Helped |
| use neurosymbolic diffusion rather than BEARS PNP | MNIST Half · MNIST Half | Acc_c: 43.26 -> 79.41 | Helped |
| use neurosymbolic diffusion rather than BEARS PNP | MNIST Half · MNIST Half | ECE_c ID: 36.81 -> 4.18 | Helped |
| use neurosymbolic diffusion rather than BEARS PNP | MNIST E-O · MNIST E-O | Acc_c: 0.48 -> 20.33 | Helped |
| use neurosymbolic diffusion rather than PNP | BDD-OIA · BDD-OIA | mF1_y: 63.71 -> 62.63 | Hurt |
Surprising findings
- On MNIST E-O, the method's OOD output accuracy is near zero (0.02), so OOD calibration gains do not translate to OOD label accuracy.
Limitations
- Scalability limited to tasks with efficient circuit representations or decomposable output spaces.
- Variational entropy term approximated with biased 1-step estimates; the conditional entropy is intractable in general.
- Gradient through sampling of the variational distribution is sidestepped.
Experimental setup
Datasets: MNIST Addition RSBench MNIST Half RSBench MNIST Even-Odd RSBench BDD-OIA visual path planning
Benchmarks: MNIST Addition visual path planning RSBench MNIST Half RSBench MNIST E-O RSBench BDD-OIA
Metrics: accuracy concept accuracy OOD accuracy ECE mF1
Baselines: DeepSoftLog PLIA Scallop EXAL A-NeSI I-MLE A-NeSI+RL BEARS Semantic Loss PNP
Builds on: masked diffusion models A-NeSI BEARS semantic loss RSBench
Closest papers by meaning
- EM-NeSy: Expectation Maximization for Neurosymbolic Learning (NeurIPS 2026 · similarity 0.86)
- Relational Neurosymbolic Markov Models (AAAI 2025 · similarity 0.86)
- NeSyPr: Neurosymbolic Proceduralization For Efficient Embodied Reasoning (NeurIPS 2025 · similarity 0.85)
- On the Independence Assumption in Neurosymbolic Learning (ICML 2024 · similarity 0.85)
- Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling (NeurIPS 2024 · similarity 0.85)
- LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulation (NeurIPS 2024 · similarity 0.84)
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