title: Neurosymbolic Diffusion Models
summary: 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.
paper_authors._id: 682da62a975206d1caa8c9d9
paper_authors.name: Emile van Krieken
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-05-21T10:14:44.208Z
paper_authors._id: 62cd4ae83e5ba89c40f15156
paper_authors.avatarUrl: /avatars/f70aca85f8836edaedcee324a18140b5.svg
paper_authors.fullname: Emile van Krieken
paper_authors.type: user
paper_authors.user: HEmile
paper_authors._id: 682da62a975206d1caa8c9da
paper_authors.name: Pasquale Minervini
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-05-21T10:16:57.876Z
paper_authors._id: 61001311e043e15c13412d30
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/61001311e043e15c13412d30/6yAbTweYR16XtxMBEyOWl.png
paper_authors.fullname: Pasquale Minervini
paper_authors.type: user
paper_authors.user: pminervini
paper_authors._id: 682da62a975206d1caa8c9db
paper_authors.name: Edoardo Ponti
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-05-21T10:30:14.820Z
paper_authors._id: 60809ad44ad99100d63ce36a
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/1619040921084-noauth.jpeg
paper_authors.fullname: Edoardo Maria Ponti
paper_authors.type: user
paper_authors.user: ducdauge
paper_authors._id: 682da62a975206d1caa8c9dc
paper_authors.name: Antonio Vergari
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-05-22T07:17:41.289Z
paper_authors._id: 64f6eeb113e91ef83ba82ce8
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/64f6eeb113e91ef83ba82ce8/sJkSu363cEmqHThSBtCOp.jpeg
paper_authors.fullname: Antonio Vergari
paper_authors.type: user
paper_authors.user: softmarx
paper_title: Neurosymbolic Diffusion Models
paper_summary: 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.
paper_ai_summary: Neurosymbolic diffusion models address limitations of standard neurosymbolic predictors by modeling dependencies between symbols using discrete diffusion, leading to improved accuracy and calibration.
paper_ai_keywords: neurosymbolic predictors symbolic reasoning conditional independence discrete diffusion symbol dependencies uncertainty quantification synthetic benchmarks real-world benchmarks high-dimensional visual path planning rule-based autonomous driving state-of-the-art accuracy strong calibration