mlsanityData to 7 Oct 2026

Constrained Synthesis with Projected Diffusion Models

arXiv 2402.03559 ↗First posted 5 Feb 2024cs.LG cs.AIcited by 83

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative diffusion models as a constrained optimization problem, steering the generated data distribution to remain within a specified region to ensure adherence to the given constraints. These capabilities are validated on applications featuring both convex and challenging, non-convex, constraints as well as ordinary differential equations, in domains spanning from synthesizing new materials with precise morphometric properties, generating physics-informed motion, optimizing paths in planning scenarios, and human motion synthesis.

Key facts. Cited by 83 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 25 of its 35 references that are in the map. First posted on arXiv 5 Feb 2024.

Builds on

25 of 35 references.

Closest ancestors · 7

Same direction, newest first

  1. 2023Mirror Diffusion Models for Constrained and Watermarked Generation2 Oct
  2. 2023Metropolis Sampling for Constrained Diffusion Models11 Jul
  3. 2023Diffusion Models for Constrained Domains11 Apr
  4. 2023Reflected Diffusion Models10 Apr
  5. 2022Classifier-Free Diffusion Guidance26 Jul
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  7. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 18

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2022Planning with Diffusion for Flexible Behavior Synthesiscited by 1,023
  5. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  6. 2022PhysDiff: Physics-Guided Human Motion Diffusion Modelcited by 365
  7. 2021Score-based diffusion models for accelerated MRIcited by 308
  8. 2022MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolationcited by 307
  9. 2022Guided Conditional Diffusion for Controllable Traffic Simulationcited by 189
  10. 2023Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Modelscited by 155
  11. 2022Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Modelscited by 97
  12. 2017Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimizationcited by 96
6 more
  1. 2022Diffusion Models Beat GANs on Topology Optimizationcited by 79
  2. 2023Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generationcited by 51
  3. 2022High-Frequency Space Diffusion Models for Accelerated MRIcited by 41
  4. 2023DiffuseBot: Breeding Soft Robots With Physics-Augmented Generative Diffusion Modelscited by 30
  5. 2020Deep learning for synthetic microstructure generation in a materials-by-design framework for heterogeneous energetic materialscited by 18
  6. 2022Artificial intelligence approaches for materials-by-design of energetic materials: state-of-the-art, challenges, and future directionscited by 6

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 8; 2025: 37; 2026: 38.

83 papers.

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By area:

  1. 2024Physics-Informed Diffusion Modelscited by 88
  2. 2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraintscited by 46
  3. 2025Simultaneous Multi-Robot Motion Planning with Projected Diffusion Modelscited by 37
  4. 2024Diffusion Predictive Control with Constraintscited by 32
  5. 2024Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Modelscited by 32
  6. 2024CGD: Constraint-Guided Diffusion Policies for UAV Trajectory Planningcited by 21
  7. 2025GuideFlow: Constraint-Guided Flow Matching for Planning in End-to-End Autonomous Drivingcited by 21
  8. 2025Training-Free Constrained Generation With Stable Diffusion Modelscited by 20
  9. 2024Generative Modelling of Structurally Constrained Graphscited by 17
  10. 2025Constrained Discrete Diffusioncited by 16
  11. 2025DDAT: Diffusion Policies Enforcing Dynamically Admissible Robot Trajectoriescited by 14
  12. 2025Discrete-Guided Diffusion for Scalable and Safe Multi-Robot Motion Planningcited by 10
38 more
  1. 2025HardFlow: Hard-Constrained Sampling for Flow-Matching Models via Trajectory Optimizationcited by 10
  2. 2025Constraint-Aware Diffusion Guidance for Robotics: Real-Time Obstacle Avoidance for Autonomous Racingcited by 9
  3. 2025Neuro-Symbolic Generative Diffusion Models for Physically Grounded, Robust, and Safe Generationcited by 9
  4. 2025Constrained Diffusers for Safe Planning and Controlcited by 9
  5. 2025Constrained Generative Modeling with Manually Bridged Diffusion Modelscited by 8
  6. 2025Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problemscited by 8
  7. 2025Composition and Alignment of Diffusion Models using Constrained Learningcited by 8
  8. 2025Mirror Flow Matching with Heavy-Tailed Priors for Generative Modeling on Convex Domainscited by 8
  9. 2025Chance-constrained Flow Matching for High-Fidelity Constraint-aware Generationcited by 7
  10. 2024Constrained Posterior Sampling: Time Series Generation with Hard Constraintscited by 6
  11. 2025Zero-Shot Trajectory Planning for Signal Temporal Logic Taskscited by 6
  12. 2025Aligning Diffusion Model with Problem Constraints for Trajectory Optimizationcited by 6
  13. 2025Strictly Constrained Generative Modeling via Split Augmented Langevin Samplingcited by 6
  14. 2025Projected Coupled Diffusion for Test-Time Constrained Joint Generationcited by 6
  15. 2025Constrained Diffusion for Protein Design with Hard Structural Constraintscited by 4
  16. 2026FlowRefiner: Flow Matching-Based Iterative Refinement for 3D Turbulent Flow Simulationcited by 4
  17. 2025Pick-and-place Manipulation Across Grippers Without Retraining: A Learning-optimization Diffusion Policy Approachcited by 3
  18. 2025Risk-Guided Diffusion: Toward Deploying Robot Foundation Models in Space, Where Failure Is Not An Optioncited by 3
  19. 2026Constraint-Aware Flow Matching: Decision Aligned End-to-End Training for Constrained Samplingcited by 3
  20. 2026Simulation-Informed Diffusion for Decentralized Multi-robot Motion Planningcited by 3
  21. 2025Diffusion-based Planning with Learned Viability Filterscited by 2
  22. 2025Constrained Diffusion Models for Synthesizing Representative Power Flow Datasetscited by 2
  23. 2025Inference-stage Adaptation-projection Strategy Adapts Diffusion Policy to Cross-manipulators Scenarioscited by 2
  24. 2025Score-based constrained generative modeling via Langevin diffusions with boundary conditionscited by 2
  25. 2026Manifold-Aware Perturbations for Constrained Generative Modelingcited by 2
  26. 2026Learning Flow Distributions via Projection-Constrained Diffusion on Manifoldscited by 2
  27. 2026Inverse Design of Multi-Layer Sub-Pixel-Resolution RF Passives Through Grayscale Diffusion with Flexible S-Parameter Conditioningcited by 2
  28. 2026Unlearning in Diffusion Models: A Unified Framework with KL Divergence and Likelihood Constraintscited by 2
  29. 2026Constrained Diffusion Models with Primal-Dual Inferencecited by 2
  30. 2024Linearly Constrained Diffusion Implicit Modelscited by 1
  31. 2025Diffusion-based learning framework for Constrained Nonconvex Optimization with Weighted Bootstrapped Refinementcited by 1
  32. 2025Interleaved Gibbs Diffusion: Generating Discrete-Continuous Data with Implicit Constraintscited by 1
  33. 2025Constraint-Aware Flow Matching via Randomized Explorationcited by 1
  34. 2025Scaling Multi-Agent Environment Co-Design with Diffusion Modelscited by 1
  35. 2026Predict-Project-Renoise: Sampling Diffusion Models under Hard Constraintscited by 1
  36. 2026Constrained Diffusion for Accelerated Structure Relaxation of Inorganic Solids with Point Defectscited by 1
  37. 2026PolyFlow: Safe and Efficient Polytope-Constrained Flow Matching with Constraint Embedding and Projection-free Updatecited by 1
  38. 2026DiRecT: Safe Diffusion-Based Planning via Receding-Horizon Denoisingcited by 1

50 most cited of 83 All 83 (JSON)

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  1. 2024Constrained Diffusion with Trust Sampling
  2. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Models
  3. 2023Generative Modeling with Phase Stochastic Bridges
  4. 2026Formalizing the Sampling Design Space of Diffusion-Based Generative Models via Adaptive Solvers and Wasserstein-Bounded Timesteps
  5. 2023Interpretable ODE-style Generative Diffusion Model via Force Field Construction
  6. 2023State of the Art on Diffusion Models for Visual Computing
  7. 2022Unite and Conquer: Plug & Play Multi-Modal Synthesis using Diffusion Models
  8. 2026Model-Based Geometry-Aware Generative Optimization for Constrained Locomotion Planning ↗