Local Manifold Approximation and Projection for Manifold-Aware Diffusion Planning

Kyowoon Lee, Jaesik Choi
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:32987-33004, 2025.

Abstract

Recent advances in diffusion-based generative modeling have demonstrated significant promise in tackling long-horizon, sparse-reward tasks by leveraging offline datasets. While these approaches have achieved promising results, their reliability remains inconsistent due to the inherent stochastic risk of producing infeasible trajectories, limiting their applicability in safety-critical applications. We identify that the primary cause of these failures is inaccurate guidance during the sampling procedure, and demonstrate the existence of manifold deviation by deriving a lower bound on the guidance gap. To address this challenge, we propose Local Manifold Approximation and Projection (LoMAP), a training-free method that projects the guided sample onto a low-rank subspace approximated from offline datasets, preventing infeasible trajectory generation. We validate our approach on standard offline reinforcement learning benchmarks that involve challenging long-horizon planning. Furthermore, we show that, as a standalone module, LoMAP can be incorporated into the hierarchical diffusion planner, providing further performance enhancements.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-lee25f, title = {Local Manifold Approximation and Projection for Manifold-Aware Diffusion Planning}, author = {Lee, Kyowoon and Choi, Jaesik}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {32987--33004}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/lee25f/lee25f.pdf}, url = {https://proceedings.mlr.press/v267/lee25f.html}, abstract = {Recent advances in diffusion-based generative modeling have demonstrated significant promise in tackling long-horizon, sparse-reward tasks by leveraging offline datasets. While these approaches have achieved promising results, their reliability remains inconsistent due to the inherent stochastic risk of producing infeasible trajectories, limiting their applicability in safety-critical applications. We identify that the primary cause of these failures is inaccurate guidance during the sampling procedure, and demonstrate the existence of manifold deviation by deriving a lower bound on the guidance gap. To address this challenge, we propose Local Manifold Approximation and Projection (LoMAP), a training-free method that projects the guided sample onto a low-rank subspace approximated from offline datasets, preventing infeasible trajectory generation. We validate our approach on standard offline reinforcement learning benchmarks that involve challenging long-horizon planning. Furthermore, we show that, as a standalone module, LoMAP can be incorporated into the hierarchical diffusion planner, providing further performance enhancements.} }
Endnote
%0 Conference Paper %T Local Manifold Approximation and Projection for Manifold-Aware Diffusion Planning %A Kyowoon Lee %A Jaesik Choi %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-lee25f %I PMLR %P 32987--33004 %U https://proceedings.mlr.press/v267/lee25f.html %V 267 %X Recent advances in diffusion-based generative modeling have demonstrated significant promise in tackling long-horizon, sparse-reward tasks by leveraging offline datasets. While these approaches have achieved promising results, their reliability remains inconsistent due to the inherent stochastic risk of producing infeasible trajectories, limiting their applicability in safety-critical applications. We identify that the primary cause of these failures is inaccurate guidance during the sampling procedure, and demonstrate the existence of manifold deviation by deriving a lower bound on the guidance gap. To address this challenge, we propose Local Manifold Approximation and Projection (LoMAP), a training-free method that projects the guided sample onto a low-rank subspace approximated from offline datasets, preventing infeasible trajectory generation. We validate our approach on standard offline reinforcement learning benchmarks that involve challenging long-horizon planning. Furthermore, we show that, as a standalone module, LoMAP can be incorporated into the hierarchical diffusion planner, providing further performance enhancements.
APA
Lee, K. & Choi, J.. (2025). Local Manifold Approximation and Projection for Manifold-Aware Diffusion Planning. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:32987-33004 Available from https://proceedings.mlr.press/v267/lee25f.html.

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