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MolmoMotion: Forecasting Point Trajectories in 3D with Language Instruction
Jianing Zhang, Chenhao Zheng, Yajun Yang, Max Argus, Rustin Soraki, Winson Han, Taira Anderson, Chun-Liang Li, Shuo Liu, Jiafei Duan, Zhongzheng Ren, Jieyu Zhang, Ranjay Krishna
TL;DR
Existing motion forecasting representations struggle to transfer across categories, viewpoints, and domains. MolmoMotion introduces language-guided 3D point forecasting with large-scale data and benchmarking, significantly outperforming prior methods while transferring to robot manipulation and video generation.
Problem
Existing motion forecasting methods are limited by category-specific representations, while 2D trajectories entangle object motion with camera and viewpoint changes.
Method
MolmoMotion combines automatically annotated 3D point trajectories from 1.16M videos, a benchmark spanning 111 categories and 61 motion types, and language-guided trajectory prediction.
Results
MolmoMotion significantly outperforms prior motion prediction methods and transfers effectively to robot manipulation and video generation.
Takeaways & Limitations
In MolmoSpaces pick-and-place, MolmoMotion improves training efficiency, closed-loop success, and generalization to unseen objects and scenes, while guiding more realistic generated videos.
Takeaways & Limitations
Sparse eight-point pretraining limits fine-grained geometry and complex deformable-motion understanding, and more downstream evaluations are needed, including closed-loop real-world robot experiments.
Abstract
from arXiv · showhide
Motion forecasting is central to visual intelligence: agents must anticipate how objects will move in order to plan actions, reason about physical interactions, and synthesize realistic futures. We argue that 3D points in world coordinates provide a general representation that is class-agnostic, view-stable, compact, and directly useful for downstream tasks. We formalize the task of goal-conditioned 3D point motion forecasting: given a short visual history, a set of 3D query points on an object of interest, and a language description of the intended goal, the model predicts the future 3D trajectory of each point. We introduce a full stack to study this task at scale: (1) MolmoMotion-1M is a large corpus of action-described, object-grounded 3D point trajectories annotated from 1.16M unconstrained videos; (2) PointMotionBench is a human-verified benchmark spanning 111 object categories and 61 motion types; and (3) MolmoMotion is a general motion forecasting model that supports both autoregressive coordinate prediction and flow-matching-based trajectory generation. MolmoMotion accurately predicts diverse motion patterns with different language instructions, and significantly outperforms existing motion prediction baselines on PointMotionBench. Finally, we show that the learned 3D motion prior transfers well to downstream applications: it improves training efficiency and generalization for robot manipulation, and its predicted trajectories provide effective motion guidance for generative models to synthesize videos with more realistic object motion.
1 Introduction
The paper formulates goal-conditioned 3D point motion prediction as a class-agnostic, view-stable forecasting problem and introduces a complete data, benchmark, and model stack. MolmoMotion predicts language-conditioned future trajectories and transfers its learned motion prior to downstream applications.
- Motivation and representation: Object-attached 3D points in world coordinates represent rigid, articulated, and deformable motion without category-specific templates while remaining stable across cameras and viewpoints.They also express task-relevant quantities such as robot-gripper pose changes and physical-simulation particle trajectories.
- Task formulation: Given visual history, initial 3D query points, and a language goal, the task predicts each point’s future 3D trajectory over time.The instruction disambiguates plausible futures and reduces the search space of future states.
- Datasets and benchmark: 1.16M unconstrained video clips yield MolmoMotion-1M, an automatically annotated corpus of object-grounded 3D point trajectories.The pipeline addresses the lack of large-scale 3D supervision in internet video.
- Datasets and benchmark: PointMotionBench spans 111 object categories and 61 motion types, using ground-truth 3D capture where available and human-verified 3D tracks otherwise.This provides a reliable testbed for evaluating motion prediction.
- Model and applications: MolmoMotion combines autoregressive coordinate prediction with flow matching for continuous trajectory distributions and significantly outperforms existing motion prediction methods on PointMotionBench.The model is pretrained on MolmoMotion-1M and forecasts diverse motion types across scenes and language instructions.
- Model and applications: The learned 3D motion prior improves sample efficiency, closed-loop success, and generalization to unseen objects and scenes in robotics planning.The paper motivates this transfer by noting that object trajectories in 3D world space are largely embodiment-agnostic.
2 MolmoMotion
MolmoMotion forecasts future 3D trajectories for object-attached query points from visual history, initial 3D positions, and an intended action description. It implements autoregressive and flow-matching predictors that share multimodal input encoding but differ in trajectory representation and decoding.
- 2.1 Problem Formulation: The model predicts T-step future 3D positions for N user-specified image points using their lifted initial 3D positions, RGB history, and an intended-action description.Initial positions may be obtained from estimated or measured depth and known camera intrinsics.
- 2.1 Problem Formulation: Future coordinates use a world frame anchored to the camera at t0, making predictions independent of future camera motion.The representation is also relative to the first query point and remains in metric units of meters.
- 2.2 Model Architecture: Both variants encode RGB observations, action text, and 2D query-point features with Molmo2, which provides image tokens, language tokens, and sampled point features.The concatenated tokens are processed by the Molmo2 language-model component.
- 2.2 Model Architecture: The autoregressive variant discretizes anchor-relative coordinates into millimeter bins, serializes trajectories as timestamped text, and decodes future coordinates in temporal order.Each prediction is conditioned on previously generated trajectory coordinates.
- 2.2 Model Architecture: The flow-matching variant predicts trajectories in continuous 3D space with a DiT decoder, training a velocity field from Gaussian-noised trajectories toward clean trajectories.At inference, it starts from Gaussian noise and integrates the learned field with 10 Euler steps.
3 MolmoMotion-1M and PointMotionBench
This section introduces MolmoMotion-1M, an automatically annotated corpus of action-described, object-grounded 3D point trajectories, and PointMotionBench, a human-verified benchmark for object-centric 3D motion forecasting. The corpus spans broad action and object diversity, while the benchmark provides 742 clips across 111 object categories and 61 motion types.
- MolmoMotion-1M: An automatic pipeline extracts object-grounded 3D point trajectories from 1.16M unconstrained public videos, producing MolmoMotion-1M.The pipeline grounds moving objects, samples query points, tracks them in 2D, lifts tracks into metric 3D, filters unreliable trajectories, and clips meaningful motion intervals.
- Annotation pipeline: The annotation pipeline uses semantic object grounding, temporal point correspondence, metric 3D lifting, trajectory-level filtering, and video-level clipping.MolmoPoint localizes the described entity, SAM3 obtains its mask, AllTracker tracks query points, and ViPE estimates metric depth and camera geometry.
- MolmoMotion-1M: The resulting corpus contains approximately 1M motion clips spanning 736 unique action verbs and 5,692 unique manipulated objects.Median clip length is 0.8–1.1 s on manipulation corpora and 1.7 s on Stereo4D; median per-clip 3D displacement ranges from 7–9 cm to 51 cm.
- PointMotionBench: PointMotionBench repurposes ground-truth 3D capture datasets and manually verifies object-grounded trajectories and action descriptions.It combines direct extraction from HOT3D and WorldTrack with pipeline-based annotation for DAVIS.
- PointMotionBench: 742 clips span 111 object categories and 61 action/motion types in PointMotionBench.The benchmark includes indoor manipulation from HOT3D and WorldTrack and outdoor dynamic scenes from DAVIS.
4 Experiments
Experiments evaluate MolmoMotion on 3D point trajectory prediction and transfer its learned motion prior to robotic planning and trajectory-guided video generation. MolmoMotion outperforms prior motion prediction methods and transfers effectively to both downstream settings.
- 3D Point Trajectory Prediction: Evaluation on PointMotionBench predicts motion for up to 2 seconds at 15 fps and uses best-of-5 evaluation for each sample.Methods follow their native input-frame and text-conditioning settings where applicable, and shorter valid horizons use only available frames.
- 3D Point Trajectory Prediction: MolmoMotion substantially outperforms prior methods on nearly all PointMotionBench subsets, with its autoregressive variant achieving the strongest overall performance.The autoregressive model performs better than the flow-matching model under deterministic trajectory metrics.
- Robotic Planning: On held-out DROID videos, MolmoMotion starts with substantially lower 3D trajectory error and reaches its best performance much faster than Molmo2 initialization.Finetuning uses single-camera DROID videos and the same 3D object point trajectory prediction task.
- Trajectory-Guided Video Generation: MolmoMotion-predicted 3D trajectories effectively guide downstream video generation, producing more physically plausible object motion and more faithful adherence to prompted actions.The trajectories guide DaS, a 3D point-trajectory-guided image-to-video model built on CogVideoX-5B.
5 Related work
Prior motion forecasting work varies in its predicted representation, while 3D point tracking enables recovery of motion from ordinary RGB videos but primarily reconstructs observed frames. Human-to-robot transfer methods use retargeted trajectories, cross-embodiment policies, or video-learned motion priors and controls.
- Motion prediction models: Pixel-space methods formulate motion prediction as conditional video generation, whereas latent methods forecast learned feature states.Pixel-space models include latent-action world models and large-scale video generators; latent representations avoid pixels but remain encoder-tied.
- 3D point tracking: 3D point tracking combines 2D tracking, monocular reconstruction, and direct 3D trackers to recover point motion from ordinary RGB videos.Recent methods improve long-range tracking, occlusion reasoning, dense video correspondence, camera-motion estimation, and per-frame depth.
- 3D point tracking: Unlike forecasting methods, existing 3D tracking work primarily tracks points in observed frames rather than predicting future motion.This limitation motivates extending 3D point tracking toward motion forecasting.
- Human-to-robot transfer: Human-to-robot transfer methods retarget human hands, endpoints, or skill trajectories, or train cross-embodiment vision-language-action policies that predict embodiment-specific actions.Some approaches incorporate human video, while others learn motion priors or controls from unlabeled video.
6 Limitations
MolmoMotion has limitations in dense point-track prediction and geometric modeling because training uses only eight query points per example. More downstream evaluations are needed to fully establish the effectiveness of the motion-pretraining task.
- Dense point prediction: MolmoMotion requires multiple forward passes to predict dense point tracks because stage 2 pretraining uses only 8 query points per example.The limitation arises from Molmo2’s context-length constraint during stage 2 training.
- Geometric modeling: The sparse point setting limits dense object-geometry representation, fine-grained structural understanding, and modeling of complex deformable motion.Using only 8 query points is insufficient to densely represent object geometry.
- Evaluation: More downstream evaluations are needed to fully establish the effectiveness of the motion-pretraining task.
7 Conclusions · Appendix
The paper concludes by presenting MolmoMotion as a language-guided predictor of future trajectories for object-attached 3D points, supported by MolmoMotion-1M and PointMotionBench. It reports gains over prior methods and transfer to robot manipulation and video generation, with appendices documenting data, benchmarks, implementation, ablations, robotics, and video-generation experiments.
- 7 Conclusions: MolmoMotion-1M supports pretraining, while PointMotionBench provides evaluation for 3D motion forecasting.These resources form the paper’s principal training and evaluation infrastructure.
- 7 Conclusions: MolmoMotion significantly outperforms prior motion prediction methods and transfers to robot manipulation and video generation.The conclusion identifies both improved motion prediction and downstream transfer as experimental outcomes.
- Appendix: The appendix provides qualitative examples and details the MolmoMotion-1M data-generation pipeline, including source videos, recaptioning, object-name extraction, semantic grounding, and 3D lifting.It also lists trajectory-related data-generation details.
- Appendix: The appendix documents PointMotionBench and its HOT3D, WorldTrack, and DAVIS components.These entries identify the benchmark and its listed constituent datasets.
- Appendix: Model implementation details cover architecture, prompt format, training hyperparameters, and model ablations.The appendix organizes these topics under implementation and ablation sections.
- Appendix: Robotics transfer settings include MolmoSpaces pick-and-place and DROID trajectory finetuning.These are the two listed robotics-transfer subsections.
- Appendix: Video-generation experiment details cover the methods compared and the evaluation protocol.The appendix lists both topics under the video-generation experiments section.
A Qualitative examples
Qualitative examples show that MolmoMotion’s 3D trajectories transfer to real-robot data and provide effective conditioning for downstream video generation. On held-out clips and prompts, it produces accurate robot trajectories and videos with more plausible, identity-preserving, instruction-faithful motion than unconditioned baselines.
- Applications: Together, the examples illustrate transfer to real-world robot data and effective use of predicted 3D trajectories as a control signal for downstream video generation.The qualitative results complement the paper’s quantitative findings and cover real-robot trajectory prediction and trajectory-conditioned video generation.
- Real-robot trajectory prediction on DROID: MolmoMotion plans accurate future 3D point trajectories across diverse held-out DROID manipulation scenes, objects, and tasks after real-robot video finetuning.These qualitative results concern real-robot trajectory prediction on DROID.
- Trajectory-conditioned video generation: MolmoMotion-guided DaS videos show more physically plausible object motion, better manipulated-object identity preservation, and more faithful adherence to prompted actions than unconditioned CogVideoX-5B and Wan-14B.The comparisons use held-out PointMotionBench prompts and MolmoMotion-predicted 3D trajectories as conditioning.
B MolmoMotion-1M Data Generation Details … C.3 DAVIS
The paper constructs MolmoMotion-1M by recaptioning videos, grounding moving objects, lifting tracked points into metric 3D world coordinates, and filtering noisy trajectories. PointMotionBench combines processed HOT3D, WorldTrack, and DAVIS clips with human-verified object-centric motion descriptions and 3D trajectories.
- B MolmoMotion-1M Data Generation Details; B.1 Source video corpora: MolmoMotion-1M aggregates seven corpora spanning egocentric and third-person manipulation, simulated and robot manipulation, and in-the-wild scenes.Stereo4D adds metric stereo depth, outdoor scenes, and deformable subjects; the pipeline recovers object phrases, query points, metric 3D tracks, and filtered trajectories.
- B.2 Recaptioning and object name extraction: For EgoDex and YT-VIS, Molmo2-8B generates concise action-object descriptions from full 15 FPS videos, after which Qwen3-0.6B extracts the manipulated-object noun phrase.The prompt specifies an action verb, a specific object, and any preposition or location, while requiring output without extra words.
- B.3 Semantic grounding and 3D lifting: The grounding pipeline localizes each object with MolmoPoint-8B, segments it with SAM 3, and samples N = 100 K-means query points distributed across the object mask.AllTracker propagates points in 2D, while ViPE estimates metric depth, intrinsics, and camera-to-world poses for back-projecting visible tracks into a world frame.
- B.4 Trajectory filtering and smoothing: Trajectory cleanup selects sixteen reliable anchor tracks, scores inconsistency-based trust, splits spatially separate instances, drops low-trust tracks, and smooths surviving depth rays.The smoothing objective combines trust-weighted pinning with multi-stride acceleration penalties at ∆∈{1, 3, 5}, optimized using first-order gradient descent.
- C PointMotionBench; C.3 DAVIS: PointMotionBench evaluates object-centric 3D motion forecasting across three datasets using identical exclusion lists, leaving 497 HOT3D, 155 WorldTrack, and 90 DAVIS clips.HOT3D and WorldTrack clips are human-verified for object identity and motion descriptions, while DAVIS descriptions are written directly during trajectory review.
- C.1 HOT3D: HOT3D converts 1,415 source clips into 2,534 single-moving-object sub-clips, subsamples 507 clips, and excludes 10 clips without visible query points at frame 0.Objects begin with 2,000 sampled surface points, propagated by per-frame pose transforms; motion windows use a 0.005 m/frame body-speed threshold and discard runs shorter than 0.5 s.
- C.2 WorldTrack: WorldTrack processing identifies dynamic points, clusters them into objects, extracts motion-coherent sub-clips, and captions each clip with Molmo2-8B before human verification.Leiden temporal clustering and conservative SAM 2 merging address object grouping, while active-span gaps determine sub-clip boundaries.
- C.3 DAVIS: DAVIS supplies RGB frames and segmentation masks without 3D ground truth; its 3D trajectories are generated by seeding mask points and applying ViPE depth and camera-pose lifting.The resulting tracks are verified, and per-clip action descriptions are written directly during trajectory review.
C.4 Evaluation Protocol … D.2 Prompt format
The evaluation scores future 3D point predictions only on initially visible points, using displacement and threshold-based metrics with explicit temporal alignment. The model implementation combines an end-to-end Molmo2/Qwen3 backbone with autoregressive and flow-matching trajectory decoders, while prompts encode visual history, actions, and 3D point tracks.
- C.4 Evaluation Protocol: Evaluation observes frames before Tcond and scores only future frames and points visible at frame 0.The evaluation mask is applied before every metric, with Tcond ∈ {1, 3}.
- C.4 Evaluation Protocol: Predictions are temporally aligned to dataset ground truth before scoring, using interpolation, visibility resampling, and overlapping frames.HOT3D and WorldTrack use 30-fps ground truth, DAVIS uses 24-fps ground truth, and Wan2.2 and Cosmos predict at 24 fps.
- C.4 Evaluation Protocol: Metrics are computed in 3D world space using ADE, FDE, and mean PWT over thresholds 0.01, 0.02, 0.05, 0.10, and 0.20 m.ADE and FDE are measured in meters, with lower values preferred; PWT ranges from 0 to 1, with higher values preferred.
- D Model Implementation Details: The implementation section expands the architecture and training recipe for the motion forecasting system.This section introduces the detailed model implementation following the evaluation protocol.
- D.1 Architecture: The vision-language backbone initializes from Molmo2-4B-Pretrain, uses SigLIP2 ViT inputs and a Molmo2 connector, and trains Qwen3-4B end-to-end.The encoder processes 378×378 RGB inputs with 14-pixel patches, producing a 27×27 grid of 1152-D tokens; pooled tokens are projected to hidden dimension 2560.
- D.1 Architecture: The autoregressive decoder retains the Molmo2 LM head with a regex coordinate parser, while flow matching uses a 36-block DiT trajectory expert with LM-layer cross-attention.Each DiT block self-attends over trajectory tokens shaped (N, H+T, 3), then cross-attends to corresponding language-model hidden states.
- D.2 Prompt format: The autoregressive prompt places anchor and history image tokens before text describing the action, 2D history features, and 3D object-history coordinates.The example uses N = 8 points, T = 32 timestamps, and the action “open the drawer”.
- D.2 Prompt format: The supervised answer emits visible-point quadruples containing identifiers and millimetre-quantised anchor-relative coordinate deltas, which greedy decoding parses into predicted trajectories.Occluded points are not imputed, and the parser reassembles ˆP_t0+1:t0+T from recovered quadruples.
D.3 Training hyperparameters · D.4 Flow-matching objective and inference
Training uses Molmo2 supervised-fine-tuning defaults with distributed mixed-precision optimization and masks losses to supervised answer or future trajectory positions. The flow-matching head interpolates noise to future trajectories, predicts the corresponding velocity field, and generates world-frame futures through Euler integration, offering multimodal alternatives to autoregressive decoding.
- D.3 Training hyperparameters: Training uses AdamW with Molmo2 supervised-fine-tuning defaults, including β1 = 0.9, β2 = 0.95, and weight decay 0.1.The supplied passage also states that the learning rate is warmed up over 1K steps before cosine decay.
- D.3 Training hyperparameters: The model uses bf16 activations with fp32 master weights and FSDP2 full-shard across 16 H100 GPUs, with per-device batch 16 and global batch size 256.These settings distribute training across 16 H100 GPUs while maintaining fp32 master weights.
- D.3 Training hyperparameters: The autoregressive cross-entropy masks image, text, point-feature, and history-coordinate prompt tokens, computing loss only on the answer span.The supplied passage contrasts this with flow-matching MSE on future positions.
- D.3 Training hyperparameters: The flow-matching MSE is computed on future positions only, leaving the clean history portion of the trajectory tensor unsupervised.This masking is stated both for the training setup and the flow-matching objective.
- D.4 Flow-matching objective and inference: The flow-matching head predicts future anchor-relative trajectories in continuous metric coordinates, conditioned on multimodal context and clean initial 3D query coordinates.The context includes image, text, point-feature, and history-coordinate tokens.
- D.4 Flow-matching objective and inference: Training samples τ uniformly from 0 to 1 and Gaussian noise, then linearly interpolates from pure noise at τ = 0 to the clean future trajectory at τ = 1.The noise tensor entries are i.i.d. standard Gaussian.
- D.4 Flow-matching objective and inference: The DiT velocity head combines the noised trajectory, sinusoidal timestep embedding, and per-layer Molmo2 hidden states through cross-attention.The trajectory uses clean history concatenated with noisy future and RoPE tags along point and frame axes.
- D.4 Flow-matching objective and inference: At inference, K = 10 Euler steps with ∆τ = 0.1 integrate the learned velocity field, then add the final trajectory to the anchor position to recover world-frame futures.Each step evaluates the velocity head once and roughly costs one LM forward pass because cached LM activations are reused.
E Model Ablations … F.2 DROID trajectory finetuning
The paper evaluates MolmoMotion’s core architectural choices, decoding efficiency, and transfer to robotics. Ablations identify anchor-relative coordinates and language conditioning as important, while downstream experiments show efficient policy integration and faster DROID adaptation.
- E Model Ablations: Removing anchor-relative coordinates causes the largest ablation drop, approximately 50% on ADE/FDE across all PointMotionBench splits.The ablation compares 3D ADE, FDE, and PWT with all other components held identical.
- E Model Ablations: Removing language instruction produces a comparable performance drop, showing that action descriptions provide a directional prior beyond object disambiguation.The language caption is replaced by a fixed “motion” token while image, point-feature, and history-coordinate tokens remain unchanged.
- E Model Ablations: Flow-matching decoding is roughly 150× faster than autoregressive decoding at T=32, while incurring a modest accuracy cost.Autoregressive cost scales linearly with N·T, whereas flow-matching cost is independent of T.
- F Robotics Transfer Settings: The robotics-transfer appendix specifies closed-loop MolmoSpaces pick-and-place and 3D-trajectory finetuning on DROID as the two downstream experiments.These experiments use MolmoMotion components in downstream policy or trajectory-prediction settings.
- F.1 MolmoSpaces pick-and-place: The MolmoSpaces policy combines a Molmo2-4B backbone with a 36-block flow-matching ActionExpert that predicts 8-dimensional, 16-step action chunks.Inference integrates the ActionExpert velocity field for 10 Euler steps from Gaussian noise.
- F.1 MolmoSpaces pick-and-place: MolmoSpaces training uses 20K pick-and-place episodes restricted to post-grasp phases, with only the ActionExpert flow-matching MSE contributing gradients.Execution re-queries after 8 simulated steps and clamps per-joint deltas to ±0.2 rad/step.
- F.2 DROID trajectory finetuning: After approximately 2K DROID finetuning steps, MolmoMotion initialization reaches the matched control’s 12K-step held-out test error.Evaluation uses 3D test L2 on a fixed 10 percent DROID test split, computed analogously to ADE.
G Video generation experiment details · G.1 Methods compared · G.2 Evaluation protocol
The video-generation experiment tests whether MolmoMotion’s predicted 3D tracks improve image-to-video synthesis from a first frame and action description. Three generators are compared under a standardized evaluation protocol using five video-quality metrics aggregated over PointMotionBench.
- G Video generation experiment details: The experiment starts from each clip’s first frame and action description, then asks three image-to-video generators to synthesize the remaining frames.Outputs are compared using standard video-quality metrics.
- G.1 Methods compared: DaS is a 3D-track-conditioned image-to-video model built on CogVideoX-5B and the only method consuming MolmoMotion’s predicted 3D trajectories.This directly evaluates video generation with MolmoMotion track conditioning.
- G.1 Methods compared: CogVideoX-5B-I2V uses the same backbone without the tracking branch, isolating the contribution of track conditioning when compared with DaS+MolmoMotion.The shared backbone controls for the underlying generator.
- G.1 Methods compared: Wan2.2-I2V-A14B is an unconditioned image-to-video baseline with roughly 2.8× the parameter count of CogVideoX-5B-I2V.It compares a much larger generator without explicit motion conditioning against a smaller track-conditioned alternative.
- G.2 Evaluation protocol: All generators receive the same first-frame image and caption, while DaS additionally receives the MolmoMotion prediction track.Each generated clip is transformed to the ground-truth frame count, frame rate, and resolution before scoring.
- G.2 Evaluation protocol: Five higher-is-better metrics score each generated clip: subject consistency, motion smoothness, dynamic degree, background consistency, and CLIP-based temporal consistency.The first four are standard VBench dimensions, while the CLIP-based score provides a complementary frame-to-frame coherence check.
- G.2 Evaluation protocol: Scores are aggregated over PointMotionBench for held-out prompts including “stack red bowl on black one” and “move object to container.”The evaluation figures also include held-out prompt comparisons.