# Marrying Optimal Transport and ODEs for Unified Continuous-Time 4D Reconstruction and Tracking

arXiv: https://arxiv.org/abs/2608.09613 · HTML: https://mlsanity.com/paper/2608.09613/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 19 of its 68 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 19 of 19)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
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- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Zero123++: a Single Image to Consistent Multi-view Diffusion Base Model](https://mlsanity.com/paper/2310.15110/) (2023)
- [MonST3R: A Simple Approach for Estimating Geometry in the Presence of Motion](https://mlsanity.com/paper/2410.03825/) (2024)
- [Hunyuan3D 2.0: Scaling Diffusion Models for High Resolution Textured 3D Assets Generation](https://mlsanity.com/paper/2501.12202/) (2025)
- [π3: Permutation-Equivariant Visual Geometry Learning](https://mlsanity.com/paper/2507.13347/) (2025)
- [Animate124: Animating One Image to 4D Dynamic Scene](https://mlsanity.com/paper/2311.14603/) (2023)
- [Efficiently Reconstructing Dynamic Scenes One D4RT at a Time](https://mlsanity.com/paper/2512.08924/) (2025)
- [V-DPM: 4D Video Reconstruction with Dynamic Point Maps](https://mlsanity.com/paper/2601.09499/) (2026)
- [Trace Anything: Representing Any Video in 4D via Trajectory Fields](https://mlsanity.com/paper/2510.13802/) (2025)
- [Hunyuan3D-Omni: A Unified Framework for Controllable Generation of 3D Assets](https://mlsanity.com/paper/2509.21245/) (2025)
- [SeeU: Seeing the Unseen World via 4D Dynamics-aware Generation](https://mlsanity.com/paper/2512.03350/) (2025)
- [Choreographing a World of Dynamic Objects](https://mlsanity.com/paper/2601.04194/) (2026)
- [Spatial-Temporal State Propagation Autoregressive Model for 4D Object Generation](https://mlsanity.com/paper/2602.18830/) (2026)

## Abstract (arXiv)

Existing unified 4D reconstruction and point tracking approaches typically rely on heuristic interpolations or just predict at integer timestamps, lacking kinematic coherence and failing to model dynamics at any arbitrary timestamp. In this paper, we propose Uni4R, a framework that unifies these tasks by learning continuous velocity fields through the synergy of Optimal Transport (OT) and Ordinary Differential Equation (ODE). Importantly, this continuous velocity field acts as a kinematic prior that mutually benefits both 4D reconstruction and point tracking. Specifically, we propose the Flow Matching Guided Decoder (FMGD). A global velocity branch first extracts anchor features that capture the global dynamic state of the sequence. Then, FMGD leverages Flow Matching (FM) theory to formulate a probability path defined by OT on the anchor feature manifold, instantiating it as FM-guided velocity features for velocity prediction. This establishes a robust kinematic inductive bias. Meanwhile, a point reconstruction branch provides geometric features. The local velocity prediction module then joint above features and time embeddings, to decode velocities at arbitrary timestamps. To overcome the absence of high-quality ground-truth velocities in fractional frames, we propose an integral-consistency training strategy. This strategy uses an ODE solver to integrate velocities to recover target pointmaps, enabling the model to be supervised end-to-end directly from integer timestamps. Experimental results demonstrate that Uni4R achieves SOTA performance in both 4D reconstruction and point tracking, and achieves SOTA in our new kinematics-aware benchmark at continuous time.