Aim Short to Reach Far: Your Frozen World Model Can Plan Better Than You Think
Organizations: Tsinghua University
Abstract
Latent world models plan toward goal images with a frozen pretrained predictor, without task rewards or extra trained heads. However, their planners struggle with long-range goals, and prior work addresses this by training extra components such as value functions or subgoal models. We show that the planning target itself can cause this failure: even with exact dynamics and globally optimal short-horizon search, scoring predictions by their distance to the final goal rejects the first steps of a route that initially moves away from the goal. Building on this insight, we propose Anchored Planning (AP), a training-free method that reuses the world model's own offline trajectories. AP retrieves a segment that leads from the current observation toward the goal and aims the frozen planner at an observation shortly after the segment's start. Across four diverse tasks, AP substantially improves frozen LeWM planners for both action synthesis and action ranking, and it outperforms both additional final-goal search and the LeWM planner on long-range goals.
Figures & tables
| No memory | Observation-only | Recorded actions | |||||||
| Task | Start | LeWM | CEM final | CEM learned | AP-CEM | Direct | Rank final | Rank learned | AP-rank |
| Cube | Standard | 15.6 | 7.0 | 62.5 | 46.9 | 82.0 | 62.5 | 91.4 | 73.4 |
| Perturbed | 12.5 | 2.7 | 38.7 | 29.7 | 47.7 | 41.8 | 50.0 | 45.7 | |
| PushT | Standard | 7.0 | 2.3 | 52.3 | 69.5 | 51.6 | 25.8 | 54.7 | 66.4 |
| Perturbed | 9.4 | 2.7 | 48.8 | 64.8 | 18.0 | 12.9 | 35.5 | 47.7 | |
| Reacher | Standard | 66.4 | 25.8 | 54.7 | 75.8 | 99.2 | 90.6 | 95.3 | 96.9 |
| Successor error | CEM success (%) | |||
|---|---|---|---|---|
| Task | Learned | Observed | Learned | Observed |
| Cube | 19.708 | 63.056 | 62.5 | 46.9 |
| PushT | 3.774 | 10.668 | 52.3 | 69.5 |
| Reacher | 74.724 | 154.351 | 54.7 | 75.8 |
| TwoRoom | 133.857 | 266.676 | 53.1 | 46.9 |
| (a) Target offset and memory size | ||||
|---|---|---|---|---|
| AP-rank | AP-CEM | |||
| Variant | Standard | Perturbed | Standard | Perturbed |
| Target | 69.5 | 61.3 | 43.0 | 37.9 |
| Target | 78.5 | 68.5 | 69.9 | 62.6 |
| Target (default) | 83.8 | 72.3 | 59.8 | 55.1 |
| Target | 81.6 | 68.4 | 54.1 | 52.7 |
| Endpoint error | Selection regret | |||||
|---|---|---|---|---|---|---|
| Task | Start | Predictor | Displ. | Predictor | Displ. | Direct |
| Cube | Standard | 7.538 | 35.344 | 5.332 | 7.535 | 11.375 |
| Perturbed | 37.726 | 66.860 | 8.472 | 11.731 | 14.903 | |
| PushT | Standard | 1.532 | 3.078 | 0.200 | 0.580 | 0.849 |
| Perturbed | 2.980 | 9.562 | 0.753 | 2.418 | 4.449 | |
| Reacher | Standard | 25.243 | 51.917 | 8.644 | 15.058 | 18.640 |
Appendix figures & tables14 assets
Supplementary material from the paper’s appendix.
Appendix
| Task | Cube | PushT | Reacher | TwoRoom |
|---|---|---|---|---|
| 150 | 140 | 150 | 100 | |
| 150 | 280 | 300 | 200 | |
| Memory | 8,000 | 16,688 | 8,000 | 8,000 |
| Task | Width | Output | Best step | Validation MSE |
|---|---|---|---|---|
| Cube | 512 | Absolute | 48,500 | 0.104926 |
| 512 | Residual | 48,500 | 0.104579 | |
| 1024 | Absolute | 41,000 | 0.104422 | |
| 1024 | Residual | 48,500 | 0.102646 | |
| PushT | 512 | Absolute | 48,000 | 0.023950 |
| 512 | Residual | 48,000 | 0.024007 |
| Task | Controller | Standard | Perturbed | ||
|---|---|---|---|---|---|
| Stalling | Detour | Stalling | Detour | ||
| Cube | LeWM | 39.8 (43/108) | 10.5 (2/19) | 48.2 (108/224) | 6.7 (2/30) |
| CEM (final goal) | 100.0 (119/119) | 37.5 (3/8) | 100.0 (249/249) | 40.0 (2/5) | |
| CEM (learned) | 79.2 (38/48) | 60.8 (48/79) | 89.2 (140/157) | 68.0 (66/97) | |
| AP-CEM | 86.8 (59/68) | 66.1 (39/59) | 92.2 (166/180) | 73.0 (54/74) | |
| CEM (transported) | 91.3 (73/80) | 68.1 (32/47) | 95.4 (186/195) | 71.2 (42/59) | |
| Controller | Start | Stalling window | Detour threshold | ||||
|---|---|---|---|---|---|---|---|
| CEM (final goal) | Standard | 55.1 | 53.3 | 49.9 | 68.6 | 30.6 | 29.1 |
| CEM (final goal) | Perturbed | 54.9 | 52.7 | 49.7 | 46.4 | 32.5 | 19.0 |
| CEM (learned) | Standard | 46.1 | 39.9 | 31.4 | 77.6 | 70.0 | 53.7 |
| CEM (learned) | Perturbed | 45.6 | 42.7 | 32.1 | 79.3 | 72.0 | 58.9 |
| AP-CEM | Standard | 51.7 | 49.5 | 40.5 | 90.6 | 84.1 | 70.7 |
| Task | Iterations | Final goal | Learned target | Observed target | |||
|---|---|---|---|---|---|---|---|
| Standard | Perturbed | Standard | Perturbed | Standard | Perturbed | ||
| Cube | 1 | 3.9 | 2.0 | 11.7 | 6.6 | 10.9 | 7.0 |
| 2 | 3.1 | 2.3 | 40.6 | 26.2 | 26.6 | 15.6 | |
| 5 | 3.1 | 2.3 | 52.3 | 34.0 | 36.7 | 26.6 | |
| 10 | 4.7 | 3.9 | 59.4 | 35.2 | 44.5 | 29.7 | |
| 30 | 7.0 | 2.7 | 62.5 | 38.7 | 46.9 | 29.7 | |
| Task | Paper report | LeWM evaluator | Our implementation |
|---|---|---|---|
| Cube | 74.0 | 74.7 | 74.7 |
| PushT | 96.0 | 92.0 | 91.3 |
| Reacher | 86.0 | 80.0 | 80.0 |
| TwoRoom | 87.0 | 87.3 | 87.3 |
| Success (%) | Work ( blocks) | |||
|---|---|---|---|---|
| Task | Standard | Perturbed | Standard | Perturbed |
| Cube | 13.3 | 13.3 | 1,189 | 1,197 |
| PushT | 7.0 | 8.2 | 2,402 | 2,374 |
| Reacher | 73.4 | 77.3 | 1,388 | 1,322 |
| TwoRoom | 27.3 | 25.8 | 1,500 | 1,509 |
| Task | LeWM | Final goal | Learned | AP-CEM | |||||
|---|---|---|---|---|---|---|---|---|---|
| Std. | Pert. | Std. | Pert. | Std. | Pert. | Std. | Pert. | ||
| Cube | 25 | 32.0 | 33.6 | 28.9 | 26.2 | 75.0 | 53.9 | 63.3 | 49.6 |
| 50 | 16.4 | 12.1 | 7.0 | 4.3 | 58.6 | 37.9 | 47.7 | 30.5 | |
| 100 | 18.8 | 13.3 | 8.6 | 9.0 | 55.5 | 34.8 | 32.0 | 25.4 | |
| 150 | 15.6 | 12.5 | 7.0 | 2.7 | 62.5 | 38.7 | 46.9 | 29.7 | |
| PushT | 25 | 60.9 | 57.8 | 51.6 | 46.9 | 91.4 | 75.4 | 91.4 | 87.5 |
| Controller | Cube | PushT | Reacher | TwoRoom | ||||
|---|---|---|---|---|---|---|---|---|
| Std. | Pert. | Std. | Pert. | Std. | Pert. | Std. | Pert. | |
| LeWM | 235.20 | 241.88 | 514.69 | 505.37 | 255.59 | 244.51 | 320.98 | 321.50 |
| CEM (final goal) | 252.62 | 263.17 | 493.56 | 491.10 | 407.76 | 425.31 | 354.95 | 354.95 |
| CEM (learned) | 142.27 | 191.54 | 375.06 | 387.40 | 393.91 | 379.98 | 250.65 | 247.94 |
| AP-CEM | 170.26 | 206.84 | 326.11 | 338.63 | 323.58 | 313.17 | 262.61 | 265.07 |
| CEM (transported) | 193.40 | 223.26 | 347.84 | 393.80 | 306.56 | 310.50 | 289.19 | 291.37 |
| Setting | Cube | PushT | Reacher | TwoRoom | ||||
|---|---|---|---|---|---|---|---|---|
| Std. | Pert. | Std. | Pert. | Std. | Pert. | Std. | Pert. | |
| AP-CEM | ||||||||
| Default | 46.9 | 29.7 | 69.5 | 64.8 | 75.8 | 78.9 | 46.9 | 46.9 |
| 43.8 | 31.3 | 34.4 | 29.3 | 50.0 | 44.9 | 43.8 | 46.1 | |
| 61.7 | 42.6 | 68.8 | 60.9 | 91.4 | 90.6 | 57.8 | 56.3 | |
| 19.5 | 15.6 | 58.6 | 57.4 | 87.5 | 89.8 | 50.8 | 48.0 | |
| Setting | Cube | PushT | Reacher | TwoRoom | ||||
|---|---|---|---|---|---|---|---|---|
| Std. | Pert. | Std. | Pert. | Std. | Pert. | Std. | Pert. | |
| Full key | 73.4 | 45.7 | 66.4 | 47.7 | 96.9 | 95.7 | 98.4 | 100.0 |
| Without distant endpoint | 81.3 | 46.5 | 67.2 | 50.4 | 94.5 | 94.5 | 100.0 | 100.0 |
| Without displacement | 73.4 | 45.7 | 63.3 | 44.9 | 96.1 | 97.7 | 99.2 | 100.0 |
| Fixed span | 4.7 | 3.1 | 0.0 | 0.0 | 12.5 | 19.1 | 21.1 | 23.0 |
| Task | Start | Observed target | Transported target |
|---|---|---|---|
| Cube | Standard | 46.9 | 37.5 |
| Perturbed | 29.7 | 23.8 | |
| PushT | Standard | 69.5 | 61.7 |
| Perturbed | 64.8 | 44.5 | |
| Reacher | Standard | 75.8 | 81.3 |
| Perturbed | 78.9 | 80.5 |
| First-block selector | Cube | PushT | Reacher | TwoRoom | ||||
|---|---|---|---|---|---|---|---|---|
| Std. | Pert. | Std. | Pert. | Std. | Pert. | Std. | Pert. | |
| Direct | 82.0 | 47.7 | 51.6 | 18.0 | 99.2 | 96.9 | 99.2 | 100.0 |
| Predictor / Final | 67.2 | 43.0 | 39.1 | 18.4 | 96.1 | 97.3 | 100.0 | 100.0 |
| Simulator / Final | 73.4 | 44.5 | 43.0 | 19.1 | 96.1 | 97.3 | 99.2 | 99.6 |
| Predictor / Learned | 85.9 | 48.8 | 45.3 | 18.8 | 96.9 | 97.7 | 100.0 | 99.6 |
| Simulator / Learned | 86.7 | 49.2 | 42.2 | 22.3 | 96.9 | 97.7 | 100.0 | 99.6 |
| Task | CEM: Standard | Ranking: Standard | Ranking: Perturbed | |||
|---|---|---|---|---|---|---|
| Final | Observed | Final | Observed | Final | Observed | |
| Cube | 8.6 | 39.1 | 64.8 | 71.1 | 41.4 | 43.4 |
| PushT | 1.6 | 81.3 | 25.8 | 78.1 | 9.0 | 49.2 |
| Reacher | 25.0 | 75.8 | 92.2 | 95.3 | 88.7 | 95.7 |
| TwoRoom | 0.8 | 39.1 | 85.2 | 100.0 | 88.3 | 99.6 |