Object-centric world models forecast future videos by evolving a set of entity slots, but the variables receiving dynamics supervision are often unconstrained visual features. We introduce \method{}, a mask-grounded soft-Hamiltonian world model that makes its position-like state explicitly depend on slot-owned image support. A frozen video-slot encoder produces slots and masks; spatial moments of mask-owned support form a canonical state Q, temporal differences form P, and a learned energy supplies a soft directional bias to a bounded learned increment. Decoder-relevant appearance and identity are stored separately in a causal visual context. A gated composer and bounded residual then combine this context with the propagated phase state to reconstruct decoder-compatible slots. On OBJ3D, given six observed frames and evaluated over the following 30 frames, \method{} reduces LPIPS by 25.0% and spatial MSE by 33.7% relative to the strongest object-centric baseline. On CLEVRER, given six observed frames and evaluated over the following ten frames, the corresponding reductions are 14.5% and 18.7%. Horizon-resolved visual and object-state measurements show that the complete model accumulates error more slowly throughout the 30-frame closed-loop rollout. Project page:https://github.com/moshwm-anon/-moshwm-anon.github.io.
Figures & tables
Figure 1: Mask grounding and long-horizon prediction on OBJ3D. Owned masks expose object support. SlotFormer matches the immediate future but drifts over closed-loop rollout; MOSH-WM better preserves object identity and scene layout.
Figure 2: MOSH-WM pipeline. A frozen SAVi interface supplies visual slots and decoded masks. Mask-owned pooling extracts Q , raw temporal differences provide P , and causal slots provide C . The SoftHamiltonian update propagates (Q,P) ; a gated composer and bounded spatiotemporal residual return to decoder-compatible slot space. Dashed arrows denote direct state propagation and autoregressive context update.
Figure 3: Long-sequence prediction on OBJ3D. Two observation frames and six future frames are shown at a larger scale than a full-frame strip. All rows use the same six-frame context and independently exported 30-frame closed-loop predictions. Under repeated feedback, MOSH-WM better retains object identity, color, and relative layout.
Figure 4: SlotPi-style scene decomposition by the frozen SAVi observer on OBJ3D. Each row is one observation time. The mask uses a black background and mutually exclusive colors; slots 1–6 are independently decoded RGB components on near-white backgrounds. Fixed columns expose temporal slot consistency and the support used to construct Q .
Reconstruction
LPIPS ↓
PSNR ↑
SSIM ↑
MSE ↓
Frozen SAVi
0.0286
41.05
0.9826
0.376
Phase composer
0.0288
40.81
0.9820
0.395
Table 1: OBJ3D reconstruction quality before rollout. The phase-to-slot composer remains close to the frozen-interface upper bound.
Method
Mean@10
Mean@30
Final@30
MOSH-WM
.0381
.0858
.1744
SlotFormer
.0540
.1144
.2063
SAVi-dyn
.0559
.1197
.2065
Table 3: OBJ3D mean LPIPS up to increasing horizons and LPIPS at the final predicted frame.
Figure 5: OBJ3D closed-loop error accumulation. (a) Mean LPIPS over increasing horizons. (b) Per-frame centroid error. (c) Per-frame pairwise-distance error. All curves use the same six observations.
Variant
LPIPS ↓
MSE ↓
Slot@30 ↓
MOSH-WM ( α=0.5 )
0.0858
4.718
0.02608
residual only
0.1665
8.468
0.08405
physics only
0.1037
5.840
0.04212
w/o context
0.1437
8.595
0.04799
re-encode state
0.1122
6.259
0.06985
α=0.1
0.0964
5.154
0.02970
Table 4: OBJ3D component and mixing-coefficient ablation. All entries use the same six-input, 30-prediction evaluator. Bold identifies each column minimum.
Figure 6: Physion transfer through frozen STEVE. Slot MSE remains lowest for the complete model throughout the 35-step closed-loop rollout.
Appendix figures & tables10 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 7: Validation Slot@30 during the main OBJ3D training run. The curve is used for checkpoint selection.
Attention blocks
LPIPS ↓
MSE ↓
Slot@30 ↓
1
0.1863
9.945
0.06165
2 (default)
0.0873
4.789
0.02755
3
0.1251
6.856
0.03984
Appendix
Table 5: Capacity sensitivity under the shared short-budget protocol.
Figure 8: Additional OBJ3D 6-to-30 rollout on test video 125. Columns show future horizons and rows compare ground truth with three predictors under the same closed-loop protocol.
Figure 9: Compact OBJ3D ablation summary. The plot shows relative error increases when the physical, context, or residual pathway is removed.
Figure 10: Physion slot error over the prediction horizon. The complete model remains lowest throughout the rollout.
Symbol
Shape
Meaning
Xt
H×W×3
video frame
St
N×ds
observer slot tokens
Mt
N×H×W
soft slot masks
Qt
N×dq
mask-grounded coordinate
Pt
N×dq
temporal phase difference
Ct
context-dependent
causal visual memory
Appendix
Table 6: Notation and tensor roles used in the implementation.
Method
@1
@3
@5
@10
@20
@30
Residual-only
.0296
.1215
.2500
.6331
1.3689
1.9220
Hamiltonian-only
.0541
.0620
.0674
.0758
.0858
.0932
MOSH (full)
.0126
.0187
.0230
.0290
.0362
.0422
Appendix
Table 7: Physion test slot MSE over the closed-loop rollout.
Figure 11: Physion qualitative transfer. Ground truth, MOSH prediction, and absolute reconstruction error are shown at horizons 1, 10, 20, and 30. Pixel quality is limited by the frozen STEVE decoder; the experiment is primarily a slot-dynamics transfer test.
Scenario
MOSH @30
Collide
0.0546
Contain
0.0341
Dominoes
0.0403
Drape
0.0683
Drop
0.0321
Link
0.0362
Appendix
Table 8: Scenario-level Physion slot MSE at horizon 30.