LPA-CWM: A Learned Physical Adjudicator for Motion Reasoning with Counterfactual World Models
Authors: Kunwei Wu, Xiang Liu, Guocai Yao, Junming Chen, Zhikang Chen, Min Zhang, Pengwei Wang, Sen Cui
Organizations: National University of Singapore · Tsinghua University · Beijing Academy of Artificial Intelligence · The Hong Kong University of Science and Technology · University of Oxford · East China Normal University
Counterfactual world models (CWM) extract motion from pretrained video predictors by comparing factual and intervened predictions, but uniform aggregation weights responses equally without explicitly incorporating physical priors. Our key insight is to incorporate physical priors into candidate reliability learning, motivating LPA-CWM with a lightweight Learned Physical Adjudicator (LPA). Trained on dense MOVi-F trajectories, the 3.0M-parameter LPA compares visual context and response structure across an unordered candidate set to predict relative weights; windowed localization and one paired re-evaluation recover motion with the CWM frozen. Existing video-level benchmarks do not directly assess motion correspondence, where low localization error can conceal missing trajectory segments. We introduce Completeness-aware Motion Correspondence (CMC), a ground-truth-anchored protocol jointly measuring localization, completeness, visibility, and continuity, counting missing predictions as failures on visible dynamic points. Across DAVIS, Kinetics, and RoboTAP, LPA-CWM improves all main CMC measures over Uniform CWM, with relative gains of 18.1%--60.0% in average Dynamic Correspondence Accuracy (DCAavg), and improves TAP-Vid First tracking accuracy (overview: https://LPA-CWM.github.io).
Figures & tables
Figure 1: Overview of our work. Uniform CWM can suffer from three characteristic failures in motion reasoning: drifting from moving objects, being distracted by competing motion, and losing track under appearance changes. Our Learned Physical Adjudicator (LPA) identifies reliable counterfactual motion evidence, enabling LPA-CWM to recover more coherent trajectories. We further introduce the CMC protocol to evaluate motion correspondence across localization, completeness, visibility, and continuity. Compared with external methods, Uniform CWM, and APA-CWM, LPA-CWM performs strongly across all four dimensions.
Figure 2: Overview of APA-CWM and LPA-CWM. Given a source–target RGB frame pair (It,It+1) and a query point pt , a frozen CWM generates motion candidates {Δm} . APA-CWM derives candidate weights from the NSG-derived map P around candidate peaks pt+1(m) . LPA-CWM instead encodes local crops, full responses, the frame pair, and response statistics; the resulting tokens zm are processed by a trainable Set Transformer to predict weights. The weighted response undergoes windowed localization and one CWM re-evaluation to obtain refined motion. During LPA training, endpoint errors from MOVi-F trajectories are converted into soft targets q .
Figure 3: Windowed localization progressively suppresses distant modes. Top: flattened maps from π(0) to π(2) . Bottom: the corresponding 3D views.
Figure 4: Qualitative motion correspondence. Five methods are compared on identical frames and visible queries across manipulation, human-action, and animal-motion scenes. Badges report mean EPE in pixels. LPA-CWM yields accurate, coherent correspondences across the displayed cases.
Table 1: Cross-dataset evaluation on DAVIS, Kinetics, and RoboTAP. LPA is trained exclusively on MOVi-F and directly evaluated on all three datasets without adaptation. CMC metrics are percentages. For TAP-Vid First, AJ, <δavgx , and OA are percentages, while AD and MD are pixels. Bold marks the best result among the three CWM variants. Stronger external results are shaded separately.
Table 2: Ablations on DAVIS under CMC and TAP-Vid First. All configurations use M=10 and R=1 . Architecture and objective variants use windowed localization; “Std.” and “Win.” denote standard and windowed localization. Metric conventions follow Table 1 ; best values within each block are bold, enabling direct comparison across design choices.
Figure 6: Candidate weighting on MOVi-F validation videos. (a) Candidate-space weighted-coordinate EPE with video-macro means. (b) Weight versus ground-truth candidate rank; the inset reports top-1 hit rates. Error bars and shading show 95% video-cluster bootstrap intervals.
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
Dim.
Statistic
Definition
Support
1
Normalized vertical displacement
Candidate y displacement normalized by image height
Global
2
Normalized horizontal displacement
Candidate x displacement normalized by image width
Global
3
Endpoint response
Response magnitude at the candidate endpoint
Single pixel
4
Global response mean
Mean response magnitude
Full response
5
Global response standard deviation
Population standard deviation of response magnitude
Full response
6
Global response median
Median response magnitude
Full response
Appendix
Table A.1: Candidate scalar descriptor used by LPA. The support column indicates the spatial region used to compute each statistic.
Figure A.1: Evidence chain for the NSG-derived analytic precursor on a real frame pair. The reference frame and observed change define the temporal evidence; score magnitude and score–change alignment produce the analytic reliability map P . APA-CWM averages this map within a local neighborhood around CWM candidate peaks p^t+1(m) . LPA-CWM does not use the diffusion score map; it learns candidate reliability from the features described in Section 3.3 . Heatmaps are independently normalized for visualization.
Table C.1: Full threshold-wise CMC accuracy results on DAVIS, Kinetics, and RoboTAP. All entries use the same 0–100 scale as Table 1 . Cov. and [email protected] denote Coverage and [email protected]; CTS4 and CTS8 denote CTS@(4,0.8) and CTS@(8,0.8), respectively. Results follow the presentation convention of Table 1 .
Method
DAVIS
Kinetics
RoboTAP
VisBA ↑
OF1 ↑
LCC ↑
Frag. ↓
VisBA ↑
OF1 ↑
LCC ↑
Frag. ↓
VisBA ↑
OF1 ↑
LCC ↑
Frag. ↓
SMURF
56.64
14.92
83.29
21.54
62.69
35.11
82.40
9.66
57.17
28.66
78.28
16.35
GMRW
63.24
45.22
35.46
8.46
65.99
46.34
51.43
7.16
61.48
35.21
28.76
7.59
DODUO
58.94
45.83
28.44
12.88
78.37
58.39
59.83
16.82
73.28
53.09
47.15
17.33
CoTracker3
76.43
58.97
81.01
1.25
78.00
58.56
80.41
8.41
73.11
59.35
75.21
5.05
RAFT
70.16
41.66
62.02
7.62
74.93
60.72
71.71
9.38
70.60
44.27
69.46
22.24
Appendix
Table C.2: Visibility and continuity diagnostics for CMC on DAVIS, Kinetics, and RoboTAP. OF1 denotes occlusion F1. VisBA, OF1, and LCC are percentages; Frag. is the mean fragmentation count ×100 . Results follow the presentation convention of Table 1 .
Figure C.1: CMC threshold sensitivity on DAVIS. (a) DCA avg as the dynamic-track motion threshold varies over {2,4,8} pixels. (b) CTS@(4, c ) as the coverage threshold varies over {0.6,0.7,0.8,0.9} with Lmotion=4 pixels. Dashed vertical lines indicate the default settings.
Method
Visibility source
Threshold
Sampling
RAFT
Direct query-to-target forward–backward consistency
6 px
Forward at integer query; backward bilinear
SEA-RAFT
Direct query-to-target forward–backward consistency
6 px
Forward at integer query; backward bilinear
DODUO
Direct query-to-target forward–backward consistency
6 px
Forward at integer query; backward bilinear
CoTracker3
Native visibility from official offline predictor
0.9
Native sparse-query trajectory; no additional FB test
SMURF
Native occlusion map
0.5
Query-location lookup
GMRW
Official tracking utility with adjacent-frame forward–backward consistency
3 px
Bilinear at propagated positions
Appendix
Table D.1: Visibility adaptation for external estimators. Thresholds are defined on the corresponding evaluator grid.
Figure E.1: Joint sensitivity to mask count and paired re-evaluation depth. Full LPA-CWM results on 40 fixed MOVi-F query groups. (a) Final deployed endpoint EPE. (b) End-to-end inference time per query. R=0 omits paired re-evaluation; M=10,R=1 is the deployed setting.
Figure F.1: Additional qualitative results on fourteen cases distinct from Figure 4 . Columns show SEA-RAFT, CoTracker3, Uniform CWM, APA-CWM, and LPA-CWM in this order. Every method receives the same frame pair and the same five query identities. A method uses one color throughout; continuous lines connect source queries to target predictions, and badges report mean EPE over the displayed queries.
Point tracking follows selected or dense image points through video, enabling motion analysis, 3D reconstruction, and precise spatiotemporal understanding.
Embodied world models learn to predict future physical dynamics from visual observations and control signals, where physical knowledge is implicitly entangled within latent representations. We introduce CausalWM, a 16B embodied world model that performs explicit causal chain-of-thought reasoning before future video prediction. CausalWM organizes useful variables into a reasoning trajectory, allowing the model to progressively capture causal dependencies underlying physical evolution. To train CausalWM, we collect 31K hours embodied data and develop a three-stage paradigm consisting of large-scale video pre-training, causal CoT mid-training, and multi-objective RL post-training. Despite using only a limited set of supervised CoT variables, CausalWM exhibits emergent in-context learning capabilities, enabling contextual visual feature guidance and efficient few-step generation. CausalWM achieves state-of-the-art performance across language-conditioned, action-conditioned, single-view and multi-view benchmarks, including Top-1 performance on TriWorldBench leaderboard.
Ziming Xu, Shuang Liang, Ruobing Han +10
Aether AI · University of California, San Diego · Vanderbilt University
Learning predictive world models from unlabelled video is a foundational challenge in artificial intelligence. While Joint Embedding Predictive Architectures (JEPA) have set new benchmarks in semantic classification, they often remain physics-blind, failing to capture the causal dynamics necessary for downstream reasoning. We hypothesize that this stems from standard patch-based masking strategies, which prioritize visual texture over rare but informative kinematic events. We propose Interaction-Aware JEPA (IA-JEPA), which utilizes a self-supervised motion-centric masking strategy to prioritize physical interactions. By specifically targeting entities engaged in collisions or momentum transfers, we force the architecture to reconstruct latent trajectories rather than static background features. Evaluated on the CLEVRER benchmark, IA-JEPA achieves 14.26% accuracy on causal reasoning tasks, a significant lead over the 3.22% achieved by standard patch-masked baselines. Crucially, we demonstrate that IA-JEPA breaks the "static bias" of standard self-supervision by inducing a higher-entropy, more discriminative latent space (+10% entropy gain) that linearizes physical energy (R2=0.43). We show that this interaction bias generalizes to real-world human actions (Something-Something V2) and zero-shot physical puzzles (PHYRE-Lite). Our results provide a scalable, fully self-supervised path toward building foundational world models that begin to internalize the causal structure of the physical world.
Action-conditioned world models (ACWMs) have shown strong promise for video prediction and decision-making. However, existing benchmarks are largely restricted to egocentric navigation or narrow, task-specific robotics datasets, offering only limited coverage of the rich physical interactions required for generalized world understanding. We introduce ACWM-Phys, a new benchmark for evaluating action-conditioned prediction under diverse physical dynamics in a clean, controllable simulation environment with a carefully designed action space. ACWM-Phys contains training and evaluation data spanning rigid-body dynamics, kinematics, deformable-object interactions, and particle dynamics. To evaluate both interpolation and generalization, we design in-distribution and out-of-distribution protocols with controlled shifts in interaction patterns or scene configurations. By building the benchmark in a fully controllable simulator, ACWM-Phys enables precise data collection, reproducible evaluation, and systematic analysis of model capabilities for physically grounded world modeling. Through systematic experiments on ACWM-DiT, we find that OoD generalization depends not only on the physical regime but also on effective task complexity: models generalize well on visually simple, low-dimensional interactions with clear geometric structure, but suffer larger drops on deformable contacts, high-dimensional control, and complex articulated motion. This suggests that the model still relies heavily on visual appearance patterns instead of fully learning the underlying physics. Ablations show that cross-attention improves high-dimensional action conditioning, causal VAEs outperform frame-wise encoders, and larger action spaces are harder to model but can improve generalization by providing richer control signals. These findings guide the design of physically grounded world models.