mlsanityData to 7 Oct 2026

DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization

arXiv 2403.05571 ↗First posted 22 Feb 2024cs.RO cs.LGcited by 19

On the map: Diffusion models → Diffusion and flow policies for robotics

Abstract (arXiv)

Optimal trajectory design is computationally expensive for nonlinear and high-dimensional dynamical systems. The challenge arises from the non-convex nature of the optimization problem with multiple local optima, which usually requires a global search. Traditional numerical solvers struggle to find diverse solutions efficiently without appropriate initial guesses. In this paper, we introduce DiffuSolve, a general diffusion model-based solver for non-convex trajectory optimization. An expressive diffusion model is trained on pre-collected locally optimal solutions and efficiently samples initial guesses, which then warm-starts numerical solvers to fine-tune the feasibility and optimality. We also present DiffuSolve+, a novel constrained diffusion model with an additional loss in training that further reduces the problem constraint violations of diffusion samples. Experimental evaluations on three tasks verify the improved robustness, diversity, and a 2× to 11× increase in computational efficiency with our proposed method, which generalizes well to trajectory optimization problems of varying challenges.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models. Builds on 33 of its 52 references that are in the map. First posted on arXiv 22 Feb 2024.

Builds on

33 of 52 references.

Closest ancestors · 10

Same direction, newest first

  1. 2024Diffusion World Model: Future Modeling Beyond Step-by-Step Rollout for Offline Reinforcement Learning5 Feb
  2. 2023Denoising Heat-inspired Diffusion with Insulators for Collision Free Motion Planning19 Oct
  3. 2023Generative Skill Chaining: Long-Horizon Skill Planning with Diffusion Models13 Oct
  4. 2023NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration11 Oct
  5. 2023Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models3 Aug
  6. 2023Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Models27 Jun
  7. 2023SafeDiffuser: Safe Planning with Diffusion Probabilistic Models31 May
  8. 2023Diffusion Policy: Visuomotor Policy Learning via Action Diffusion7 Mar
  9. 2023AdaptDiffuser: Diffusion Models as Adaptive Self-evolving Planners3 Feb
  10. 2022Is Conditional Generative Modeling all you need for Decision-Making?28 Nov

Other references · 23

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Denoising Diffusion Implicit Modelscited by 9,655
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2022Classifier-Free Diffusion Guidancecited by 5,717
  7. 2022Planning with Diffusion for Flexible Behavior Synthesiscited by 1,023
  8. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  9. 2022The Vendi Score: A Diversity Evaluation Metric for Machine Learningcited by 299
  10. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
  11. 2021DC3: A learning method for optimization with hard constraintscited by 181
  12. 2022Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimizationcited by 96
11 more
  1. 2019Model Inversion Networks for Model-Based Optimizationcited by 83
  2. 2022Tutorial on amortized optimizationcited by 83
  3. 2023Diffusion Models for Black-Box Optimizationcited by 75
  4. 2023Compositional Diffusion-Based Continuous Constraint Solverscited by 39
  5. 2019Large Scale Model Predictive Control with Neural Networks and Primal Active Setscited by 28
  6. 2022End-to-End Learning to Warm-Start for Real-Time Quadratic Optimizationcited by 25
  7. 2017FaSTrack: a Modular Framework for Fast and Guaranteed Safe Motion Planningcited by 21
  8. 2021CoCo: Online Mixed-Integer Control via Supervised Learningcited by 16
  9. 2019Safe and Near-Optimal Policy Learning for Model Predictive Control using Primal-Dual Neural Networkscited by 13
  10. 2023Amortized Global Search for Efficient Preliminary Trajectory Design with Deep Generative Modelscited by 12
  11. 2023Accelerating Diffusion-based Combinatorial Optimization Solvers by Progressive Distillationcited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 9; 2026: 8.

19 papers.

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  1. 2024Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Modelscited by 32
  2. 2024CGD: Constraint-Guided Diffusion Policies for UAV Trajectory Planningcited by 21
  3. 2025Constrained Diffusers for Safe Planning and Controlcited by 9
  4. 2025Global Search for Optimal Low Thrust Spacecraft Trajectories using Diffusion Models and the Indirect Methodcited by 7
  5. 2025Predictive Planner for Autonomous Driving with Consistency Modelscited by 7
  6. 2025Aligning Diffusion Model with Problem Constraints for Trajectory Optimizationcited by 6
  7. 2025Diffusion-Based Approximate MPC: Fast and Consistent Imitation of Multi-Modal Action Distributionscited by 3
  8. 2025Formal Safety Verification and Refinement for Generative Motion Planners via Certified Local Stabilizationcited by 2
  9. 2025Generative Models From and For Sampling-Based MPC: A Bootstrapped Approach For Adaptive Contact-Rich Manipulationcited by 2
  10. 2025Diffusion-based learning framework for Constrained Nonconvex Optimization with Weighted Bootstrapped Refinementcited by 1
  11. 2025Self-supervised diffusion model fine-tuning for costate initialization using Markov chain Monte Carlocited by 1
  12. 2026Adaptive Time Step Flow Matching for Autonomous Driving Motion Planningcited by 1
7 more
  1. 2026Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunitiescited by 1
  2. 2026Transfer Learning of Multiobjective Indirect Low-Thrust Trajectories Using Diffusion Models and Markov Chain Monte Carlocited by 1
  3. 2026GLENS: Global Search via Learning from Solver Iterates with Diffusion Modelscited by 1
  4. 2026Accelerating trajectory optimization with Sobolev-trained diffusion policiescited by 0
  5. 2026Enforcing Constraints in Generative Sampling via Adaptive Correction Schedulingcited by 0
  6. 2026Training-Free Imitation Learning with Closed-Form Diffusion Policiescited by 0
  7. 2026Complexity Bounds and Approaches to Learning Projected Gradient Descent Solver Iteratescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Equality Constrained Diffusion for Direct Trajectory Optimization
  2. 2025PAD-TRO: Projection-Augmented Diffusion for Direct Trajectory Optimization
  3. 2024Constraint-Aware Diffusion Models for Trajectory Optimization
  4. 2026Motion Planning with Model-Based Diffusion via Constraint Optimization and Adaptive Scheduling
  5. 2024Diffusion-ES: Gradient-free Planning with Diffusion for Autonomous Driving and Zero-Shot Instruction Following
  6. 2025Dynamics-aware Diffusion Models for Planning and Control
  7. 2026DiRecT: Safe Diffusion-Based Planning via Receding-Horizon Denoising
  8. 2024Model-Based Diffusion for Trajectory Optimization