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

Anjian Li, Zihan Ding, Adji Bousso Dieng, Ryne Beeson
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:45-58, 2025.

Abstract

Optimal trajectory design is computationally expensive for nonlinear and high-dimensional dynamical systems. The challenge arises from solving a non-convex optimization problem with multiple local optima, where 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 2x to 11x increase in computational efficiency with our proposed method, which generalizes well to trajectory optimization problems of varying challenges.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-li25a, title = {DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization}, author = {Li, Anjian and Ding, Zihan and Dieng, Adji Bousso and Beeson, Ryne}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {45--58}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/li25a/li25a.pdf}, url = {https://proceedings.mlr.press/v283/li25a.html}, abstract = {Optimal trajectory design is computationally expensive for nonlinear and high-dimensional dynamical systems. The challenge arises from solving a non-convex optimization problem with multiple local optima, where 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 2x to 11x increase in computational efficiency with our proposed method, which generalizes well to trajectory optimization problems of varying challenges.} }
Endnote
%0 Conference Paper %T DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization %A Anjian Li %A Zihan Ding %A Adji Bousso Dieng %A Ryne Beeson %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-li25a %I PMLR %P 45--58 %U https://proceedings.mlr.press/v283/li25a.html %V 283 %X Optimal trajectory design is computationally expensive for nonlinear and high-dimensional dynamical systems. The challenge arises from solving a non-convex optimization problem with multiple local optima, where 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 2x to 11x increase in computational efficiency with our proposed method, which generalizes well to trajectory optimization problems of varying challenges.
APA
Li, A., Ding, Z., Dieng, A.B. & Beeson, R.. (2025). DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:45-58 Available from https://proceedings.mlr.press/v283/li25a.html.

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