# Lagrangian Motion Fields for Long-term Motion Generation

arXiv: https://arxiv.org/abs/2409.01522 · HTML: https://mlsanity.com/paper/2409.01522/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 53 references that are in the map.
- First posted on arXiv 3 Sep 2024.

## Builds on (most cited first, 30 of 39)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [T2M-GPT: Generating Human Motion from Textual Descriptions with Discrete Representations](https://mlsanity.com/paper/2301.06052/) (2023)
- [GroupViT: Semantic Segmentation Emerges from Text Supervision](https://mlsanity.com/paper/2202.11094/) (2022)
- [AI Choreographer: Music Conditioned 3D Dance Generation with AIST++](https://mlsanity.com/paper/2101.08779/) (2021)
- [Action2Motion: Conditioned Generation of 3D Human Motions](https://mlsanity.com/paper/2007.15240/) (2020)
- [TM2T: Stochastic and Tokenized Modeling for the Reciprocal Generation of 3D Human Motions and Texts](https://mlsanity.com/paper/2207.01696/) (2022)
- [Human Motion Diffusion as a Generative Prior](https://mlsanity.com/paper/2303.01418/) (2023)
- [EDGE: Editable Dance Generation From Music](https://mlsanity.com/paper/2211.10658/) (2022)
- [Language2Pose: Natural Language Grounded Pose Forecasting](https://mlsanity.com/paper/1907.01108/) (2019)
- [Guided Motion Diffusion for Controllable Human Motion Synthesis](https://mlsanity.com/paper/2305.12577/) (2023)
- [MoFusion: A Framework for Denoising-Diffusion-based Motion Synthesis](https://mlsanity.com/paper/2212.04495/) (2022)
- [FLAME: Free-form Language-based Motion Synthesis & Editing](https://mlsanity.com/paper/2209.00349/) (2022)
- [Bailando: 3D Dance Generation by Actor-Critic GPT with Choreographic Memory](https://mlsanity.com/paper/2203.13055/) (2022)
- [Listen, Denoise, Action! Audio-Driven Motion Synthesis with Diffusion Models](https://mlsanity.com/paper/2211.09707/) (2022)
- [Generating Holistic 3D Human Motion from Speech](https://mlsanity.com/paper/2212.04420/) (2022)
- [TEACH: Temporal Action Composition for 3D Humans](https://mlsanity.com/paper/2209.04066/) (2022)
- [Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models](https://mlsanity.com/paper/2208.06677/) (2022)
- [GestureDiffuCLIP: Gesture Diffusion Model with CLIP Latents](https://mlsanity.com/paper/2303.14613/) (2023)
- [Text2Gestures: A Transformer-Based Network for Generating Emotive Body Gestures for Virtual Agents](https://mlsanity.com/paper/2101.11101/) (2021)
- [HumanTOMATO: Text-aligned Whole-body Motion Generation](https://mlsanity.com/paper/2310.12978/) (2023)
- [DiffCollage: Parallel Generation of Large Content with Diffusion Models](https://mlsanity.com/paper/2303.17076/) (2023)
- [CLIP-FO3D: Learning Free Open-world 3D Scene Representations from 2D Dense CLIP](https://mlsanity.com/paper/2303.04748/) (2023)
- [FineDance: A Fine-grained Choreography Dataset for 3D Full Body Dance Generation](https://mlsanity.com/paper/2212.03741/) (2022)
- [Superpixel Sampling Networks](https://mlsanity.com/paper/1807.10174/) (2018)
- [UDE: A Unified Driving Engine for Human Motion Generation](https://mlsanity.com/paper/2211.16016/) (2022)

## Built on by (most cited first, 5 of 5)

- [StableGuard: Towards Unified Copyright Protection and Tamper Localization in Latent Diffusion Models](https://mlsanity.com/paper/2509.17993/) (2025)
- [ReactMotion: Generating Reactive Listener Motions from Speaker Utterance](https://mlsanity.com/paper/2603.15083/) (2026)
- [Spatial Temporal Synergy: Balancing Change and Invariance in Text Driven 3D Human Motion Editing](https://mlsanity.com/paper/2608.16008/) (2026)
- [MotionMERGE: A Multi-granular Framework for Human Motion Editing, Reasoning, Generation, and Explanation](https://mlsanity.com/paper/2605.18956/) (2026)
- [From Where to How: Continuous 4D Interaction Forecasting from Egocentric Video](https://mlsanity.com/paper/2609.08636/) (2026)

## Abstract (arXiv)

Long-term motion generation is a challenging task that requires producing coherent and realistic sequences over extended durations. Current methods primarily rely on framewise motion representations, which capture only static spatial details and overlook temporal dynamics. This approach leads to significant redundancy across the temporal dimension, complicating the generation of effective long-term motion. To overcome these limitations, we introduce the novel concept of Lagrangian Motion Fields, specifically designed for long-term motion generation. By treating each joint as a Lagrangian particle with uniform velocity over short intervals, our approach condenses motion representations into a series of "supermotions" (analogous to superpixels). This method seamlessly integrates static spatial information with interpretable temporal dynamics, transcending the limitations of existing network architectures and motion sequence content types. Our solution is versatile and lightweight, eliminating the need for neural network preprocessing. Our approach excels in tasks such as long-term music-to-dance generation and text-to-motion generation, offering enhanced efficiency, superior generation quality, and greater diversity compared to existing methods. Additionally, the adaptability of Lagrangian Motion Fields extends to applications like infinite motion looping and fine-grained controlled motion generation, highlighting its broad utility. Video demonstrations are available at https://plyfager.github.io/LaMoG.