# Motion Manifold Flow Primitives for Task-Conditioned Trajectory Generation under Complex Task-Motion Dependencies

arXiv: https://arxiv.org/abs/2407.19681 · HTML: https://mlsanity.com/paper/2407.19681/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 29 Jul 2024.

## Builds on (most cited first, 18 of 18)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [3D Diffusion Policy: Generalizable Visuomotor Policy Learning via Simple 3D Representations](https://mlsanity.com/paper/2403.03954/) (2024)
- [Riemannian Flow Matching Policy for Robot Motion Learning](https://mlsanity.com/paper/2403.10672/) (2024)
- [Dynamic Movement Primitives in Robotics: A Tutorial Survey](https://mlsanity.com/paper/2102.03861/) (2021)
- [Learning Riemannian Manifolds for Geodesic Motion Skills](https://mlsanity.com/paper/2106.04315/) (2021)
- [On Explicit Curvature Regularization in Deep Generative Models](https://mlsanity.com/paper/2309.10237/) (2023)
- [A Geometric Perspective on Autoencoders](https://mlsanity.com/paper/2309.08247/) (2023)
- [MMP++: Motion Manifold Primitives with Parametric Curve Models](https://mlsanity.com/paper/2310.17072/) (2023)
- [Incremental Learning of Full-Pose Via-Point Movement Primitives on Riemannian Manifolds](https://mlsanity.com/paper/2312.08030/) (2023)

## Built on by (most cited first, 2 of 2)

- [CF-VLA: Efficient Coarse-to-Fine Action Generation for Vision-Language-Action Policies](https://mlsanity.com/paper/2604.24622/) (2026)
- [Differentiable Motion Manifold Primitives for Reactive Motion Generation under Kinodynamic Constraints](https://mlsanity.com/paper/2410.12193/) (2024)

## Abstract (arXiv)

Effective movement primitives should be capable of encoding and generating a rich repertoire of trajectories -- typically collected from human demonstrations -- conditioned on task-defining parameters such as vision or language inputs. While recent methods based on the motion manifold hypothesis, which assumes that a set of trajectories lies on a lower-dimensional nonlinear subspace, address challenges such as limited dataset size and the high dimensionality of trajectory data, they often struggle to capture complex task-motion dependencies, i.e., when motion distributions shift drastically with task variations. To address this, we introduce Motion Manifold Flow Primitives (MMFP), a framework that decouples the training of the motion manifold from task-conditioned distributions. Specifically, we employ flow matching models, state-of-the-art conditional deep generative models, to learn task-conditioned distributions in the latent coordinate space of the learned motion manifold. Experiments are conducted on language-guided trajectory generation tasks, where many-to-many text-motion correspondences introduce complex task-motion dependencies, highlighting MMFP's superiority over existing methods.