# Local Manifold Approximation and Projection for Manifold-Aware Diffusion Planning

arXiv: https://arxiv.org/abs/2506.00867 · HTML: https://mlsanity.com/paper/2506.00867/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 61 of its 79 references that are in the map.
- First posted on arXiv 1 Jun 2025.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 61)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Offline Reinforcement Learning as One Big Sequence Modeling Problem](https://mlsanity.com/paper/2106.02039/) (2021)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Directly Fine-Tuning Diffusion Models on Differentiable Rewards](https://mlsanity.com/paper/2309.17400/) (2023)
- [The Faiss library](https://mlsanity.com/paper/2401.08281/) (2024)
- [Aligning Text-to-Image Diffusion Models with Reward Backpropagation](https://mlsanity.com/paper/2310.03739/) (2023)
- [OGBench: Benchmarking Offline Goal-Conditioned RL](https://mlsanity.com/paper/2410.20092/) (2024)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)
- [AdaptDiffuser: Diffusion Models as Adaptive Self-evolving Planners](https://mlsanity.com/paper/2302.01877/) (2023)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)

## Built on by (most cited first, 9 of 9)

- [Landing with the Score: Riemannian Optimization through Denoising](https://mlsanity.com/paper/2509.23357/) (2025)
- [Manifold-Aligned Guided Integrated Gradients for Reliable Feature Attribution](https://mlsanity.com/paper/2605.02167/) (2026)
- [Refining Compositional Diffusion for Reliable Long-Horizon Planning](https://mlsanity.com/paper/2605.03075/) (2026)
- [HDFlow: Hierarchical Diffusion-Flow Planning for Long-horizon Tasks](https://mlsanity.com/paper/2605.04525/) (2026)
- [Spectral Integrated Gradients for Coarse-to-Fine Feature Attribution](https://mlsanity.com/paper/2605.19607/) (2026)
- [Proximal Action Replacement for Behavior Cloning Actor-Critic in Offline Reinforcement Learning](https://mlsanity.com/paper/2602.07441/) (2026)
- [Improving Diffusion Planners by Self-Supervised Action Gating with Energies](https://mlsanity.com/paper/2603.02650/) (2026)
- [Diffusion Integrated Gradients: Controllable Path Generation for Flexible Feature Attribution](https://mlsanity.com/paper/2606.22314/) (2026)
- [MAGNET: Manifold-Aware Graph Diffusion Network for Connectome Generation](https://mlsanity.com/paper/2610.17014/) (2026)

## Abstract (arXiv)

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.