cs.CVMar 31, 2026
SaveVideo Models Reason Early: Exploiting Plan Commitment for Maze Solving
Organizations: Princeton University
Abstract
Video diffusion models exhibit emergent reasoning capabilities like solving mazes and puzzles, yet little is understood about how they reason during generation. We take a first step towards understanding this and study the internal planning dynamics of video models using 2D maze solving as a controlled testbed. Our investigations reveal two findings. Our first finding is early plan commitment: video diffusion models commit to a high-level motion plan within the first few denoising steps, after which further denoising alters visual details but not the underlying trajectory. Our second finding is that path length, not obstacle density, is the dominant predictor of maze difficulty, with a sharp failure threshold at 12 steps. This means video models can only reason over long mazes by chaining together multiple sequential generations. To demonstrate the practical benefits of our findings, we introduce Chaining with Early Planning, or ChEaP, which only spends compute on seeds with promising early plans and chains them together to tackle complex mazes. This improves accuracy from 7% to 67% on long-horizon mazes and by 2.5x overall on hard tasks in Frozen Lake and VR-Bench across Wan2.2-14B and HunyuanVideo-1.5. Our analysis reveals that current video models possess deeper reasoning capabilities than previously recognized, which can be elicited more reliably with better inference-time scaling.
Figures & tables
Figure 1: Video diffusion models plan early. Decoded intermediate predictions reveal that the model commits to a trajectory within the first few denoising steps (green box) ; later steps refine visual details but rarely alter the path (blue box) .
Figure 2: Overview of ChEaP. (Left) Early Planning Beam Search scores early plans from partially denoised predictions and selects the most promising candidates for full generation. (Right) Chaining reconditions on the last frame of successful traces to extend reasoning beyond the single-generation horizon.
Figure 3: Early plans stay consistent. (Left) Across multiple settings, the early trajectories emerging from decoded predictions at step 5 match the final trajectory. (Right) Mean trajectory convergence throughout the denoising process. Step 5 already reaches 93%, i.e . trajectories stay converged (over 163 mazes).
Figure 4: Stepwise refinement. Mean pairwise trajectory IoU among re-noised completions at each step , across grid sizes 4–10. Even at , branch trajectories are far more similar to each other than trajectories from different seeds (dashed line), indicating that the route is largely encoded in the initial noise sample.
Figure 5: EPBS finds solutions much more efficiently than best-of- . Accuracy vs Function Evaluations (NFEs) on Frozen Lake mazes across four sizes with Wan2.2-14B. EPBS consistently dominates standard best-of- , with large gains on larger mazes.
Figure 6: EPBS fails beyond the single-generation horizon. While short paths are solved reliably, success drops sharply for trajectories longer than 10–12 steps. This breakdown persists even with strong seed selection, indicating a limitation in executing long plans rather than selecting them.
| Frozen Lake | VR-Bench | |||||||
| Method | NFEs | Easy | Medium | Hard | ||||
| Wan2.2-14B (40 NFEs / full gen) | ||||||||
| BoN | 120 | 61.8 | 24.4 | 14.3 | 7.0 | 38.0 | 10.0 | 0.0 |
| EPBS | 120 | 88.2 | 42.3 | 16.9 | 8.5 | 54.0 | 26.0 | 10.0 |
| BoN | 400 | 86.8 | 43.6 | 22.1 | 9.9 | 56.0 | 28.0 | 10.0 |
| EPBS | 400 | 98.7 | 55.1 | 33.8 | 19.7 | 68.0 | 44.0 | 25.0 |
Table 3: ChEaP substantially improves maze performance. We report pass@2 for best-of- (BoN), EPBS, and ChEaP (EPBS + Chaining) on Frozen Lake and VR-Bench. For Wan2.2-14B, EPBS at 120 NFEs performs on par with BoN at 400 NFEs—a reduction in NFEs—and improves pass rate by 11.9 points on average.
Figure 7: Chaining extends reasoning beyond the single-generation horizon. Wan 2.2 success rates on Frozen Lake mazes by solution length. Chaining provides the most benefit on mazes where the solution length exceeds the generation window ( steps). The largest gain is on long mazes, from to success rate with ChEaP.
Figure 8: Failure mode comparison. Wan2.2 (left) goes from horizon-limited to constraint-dominated as maze size increases. HunyuanVideo (right) is constraint-dominated at all sizes, suggesting that step distillation degrades structural adherence independently of horizon.
Figure 9: The model “cheats” on hard mazes. When the trajectory is too long to complete within the generation window, the model sacrifices structural adherence to fulfill the prompt. Top: the gift teleports from the far corner to an adjacent cell, allowing the agent to “solve” the maze without traversing the full path. Bottom: a second agent spawns near the goal and reaches it, while the original agent remains stranded.
Appendix figures & tables35 assets
Supplementary material from the paper’s appendix.
Appendix
| Parameter | Wan2.2-14B | HunyuanVideo-1.5 |
|---|---|---|
| Resolution | 480p ( ) | |
| Frame count | 81 | 121 |
| FPS | 16 | 24 |
| Guidance scale | 3.5 | 6.0 |
| Scheduler | UniPC | Euler (flow matching) |
| Denoising steps ( ) | 40 | 8 (step-distilled) |
Table 0.A.1: Generation hyperparameters for both video diffusion models.
Figure 0.B.1: Probe step sensitivity. Pass@2 vs. NFE budget for probe steps at beam size , across four grid sizes. All configurations use shared seed pools for fair comparison. provides the best efficiency trade-off for size 4; larger mazes are less sensitive to .
Figure 0.B.2: Beam size ablation. Pass@ vs. NFE budget for beam sizes with fixed probe step ( for sizes 4–6, for sizes 8–10). provides the best trade-off: it reaches peak accuracy at lower budgets than without the probe-count penalty of larger values.
| EPBS @ NFE 120 | Baseline to match | |||||
|---|---|---|---|---|---|---|
| Size | Acc (%) | Time (min) | NFE needed | Time (min) | Speedup | |
| 4 | 5 | 88.2 | 25.9 | 82.0 | 3.2 | |
| 6 | 5 | 42.3 | 25.9 | 320 | 65.6 | 2.5 |
| 8 | 15 | 16.9 | 22.6 | 160 | 32.8 | 1.5 |
| 10 | 15 | 8.5 | 22.6 | 120 | 24.6 | 1.1 |
Table 0.B.1: Wall-clock comparison at matched accuracy. For each grid size, we report EPBS accuracy and wall-clock time at NFE = 120, alongside the baseline NFE and time required to reach the same accuracy. Speedup = baseline time / EPBS time. Sizes 4–6 use ; sizes 8–10 use . All wall-clock estimates include every pipeline component (see text for breakdown).
Figure 0.C.1: Cross-model early plan commitment across all maze sizes. Mean trajectory convergence between intermediate predictions and the final video, plotted against normalized schedule fraction. We compute using the cosine similarity between motion-energy maps, exactly as in the main text. Both Wan2.2-14B ( ) and HunyuanVideo-1.5 ( ) commit to a trajectory within the first 10–15% of their denoising schedules, after which convergence largely plateaus. Despite using different schedulers and step counts, the normalized convergence profiles are similar, suggesting that early plan commitment is a structural property of video diffusion rather than a model-specific artifact.
Figure 0.C.2: Path length is the dominant difficulty axis for both models. HunyuanVideo’s effective planning horizon is shorter: both models solve short paths reliably but diverge sharply beyond 7 cells.
Figure 0.C.3: Diagnostic maze variants. From left to right: Trivial (1–2 moves, ceiling test), Decoy (goal visually adjacent but blocked by lake), Lake-Heavy (>75% lake, single narrow corridor), and Detour (Manhattan distance 2 but 8–12 move path around a lake wall).
Figure 0.C.4: Decoy maze: failure vs. success. Ghost-trail visualizations on a 4 4 decoy maze where the goal is visually adjacent but blocked. Left : the model beelines toward the visible goal through the lake (lake entry). Right : the rare seed that navigates the 5-step detour around the obstruction.
Figure 0.C.5: Lake-heavy maze: failure vs. success. Ghost-trail visualizations on a 6 6 lake-heavy maze (>75% lake). Left : the agent follows the correct corridor but cuts through a single lake cell at step 5 (lake entry). Right : the EPBS-selected seed navigates the full 7-step corridor without constraint violations.
| Category | Size | Path | Per-Seed | EPBS | Dominant Failure Mode |
|---|---|---|---|---|---|
| Trivial | 4 | 1–2 | 60% | 100% | gift mvmt. (33%), wrong path (33%) |
| Decoy | 4–6 | 4–5 | 6% | 25% | lake entry (55%), wrong path (17%) |
| Lake-Heavy | 4–6 | 3–7 | 69% | 100% | lake entry (50%), gift mvmt. (25%) |
| Detour | 4 | 8 | 29% | 100% | gift movement (80%) |
| Detour | 6 | 12 | 0% | 0% | gift mvmt. (36%), lake entry (27%) |
Table 0.C.1: Diagnostic maze results. Per-seed reports the fraction of individual generations that solve the maze; EPBS reports the fraction of mazes for which EPBS finds at least one correct solution across all seeds. Failure modes are assigned by priority (gift movement lake entry wrong path).
Figure 0.C.6: Detour maze: failure vs. success. Ghost-trail visualizations on the same 4 4 detour maze. Left : a typical failure—the agent walks straight toward the goal through the lake (constraint violation). Right : the EPBS-selected success—the agent navigates the 8-step detour around the lake wall. The verifier’s constraint penalty correctly rejects the shortcut and surfaces the rare seed that respects the maze topology.
Figure 0.C.7: Diversity of candidate plans under different noise seeds. We overlay trajectories extracted from multiple samples of the same maze. Incorrect trajectories are shown in gray with reduced opacity, while a successful trajectory is shown in color. Despite sharing identical conditioning, different seeds produce diverse motion plans. Importantly, these plans are distinguishable early in the denoising process, suggesting that inference-time compute should be allocated toward selecting promising trajectories rather than refining all candidates.
Figure 0.D.1: Wan2.2, size 4 (norm). The full solution path is already visible in the prediction; subsequent steps only sharpen the rendering without altering the planned route.
Figure 0.D.2: Wan2.2, size 4 (vary). The planned route is committed to by and maintains it through the final video.
Figure 0.D.3: Wan2.2, size 6 (vary). A longer maze requiring more steps. Despite the increased path complexity, the overall route direction is locked in by .
Figure 0.D.4: Wan2.2, size 8 (vary). Size 8 maze with varied lake ratio. The early prediction captures the general trajectory shape, though fine-grained cell-level details continue to refine through later steps.
Figure 0.D.5: Wan2.2, size 8 (vary), second example. The ghost trail at already traces a path consistent with the final video, demonstrating that early commitment holds across different maze instances.
Figure 0.D.6: Wan2.2, size 10 (vary). The largest maze size. Even for this 10 10 grid, the model’s planned trajectory is apparent by step 5 of denoising.
Figure 0.D.7: HunyuanVideo-1.5, size 8 (vary). HunyuanVideo uses a step-distilled schedule ( ). Despite the shorter schedule, the trajectory is committed by step 3 and remains stable, mirroring the early commitment seen in Wan2.2.
Figure 0.D.8: VR-Bench, maze_4 (easy). Early plan commitment on a VR-Bench maze with a distinct brown/tan texture. The trajectory direction is already visible at and refines through later steps, showing that commitment generalizes beyond the Frozen Lake visual style to procedurally generated maze textures.
Figure 0.D.9: VR-Bench, maze_1 (hard). A harder VR-Bench puzzle on the blue/teal maze_1 texture. Despite higher path complexity, the prediction at already captures the coarse trajectory shape, which persists through to the final generation.
Figure 0.D.10: VR-Bench, maze_2 (easy). The purple/blue maze_2 texture. The ghost trail at is largely noise, but by the planned path is clearly committed and matches the final output.
Figure 0.D.11: Wan2.2 chain, size 6 (norm), lake 20, maze 002. Two-segment chain.
Figure 0.D.12: Wan2.2 chain, size 10 (vary), lake 20, maze 002. Size 10 maze with varied lake ratio. The longer solution path necessitates chaining.
Figure 0.D.13: Wan2.2 chain, size 10 (vary), lake 80, maze 003. High lake density leaves fewer safe cells, creating a narrow corridor that chaining navigates successfully.
Figure 0.D.14: Wan2.2 chain, VR-Bench maze_3_medium, puzzle 0004. Chaining applied to a VR-Bench maze with a different visual texture than Frozen Lake. The agent navigates a medium-difficulty procedurally generated maze across multiple segments.
Figure 0.D.15: Wan2.2 chain, VR-Bench trapfield_2_medium, puzzle 0002. A trapfield environment where the agent must avoid trap cells (analogous to lakes). Chaining enables completion of longer trapfield paths.
Figure 0.D.16: Wan2.2 chain, VR-Bench trapfield_2_medium, puzzle 0005. Another trapfield example showing successful multi-segment navigation through a different puzzle layout.
Figure 0.D.17: HunyuanVideo-1.5 chain, size 4 (vary), lake 65, maze 004. Chaining with HunyuanVideo’s step-distilled schedule ( ). The pivot and chain segments are stitched to form a complete solution.
Figure 0.D.18: HunyuanVideo-1.5 chain, size 6 (norm), lake 65, maze 004. A size 6 maze with 65% lake density. Chaining extends HunyuanVideo’s effective planning horizon beyond a single generation.
Figure 0.D.19: HunyuanVideo-1.5 chain, size 6 (vary), lake 80, maze 009. Despite the constrained environment, chaining produces a valid multi-segment solution.
Figure 0.D.20: Constraint violations — Frozen Lake. Ghost-trail visualizations showing two sub-types: lake entry (the elf crosses into a frozen-lake cell, violating the environment constraint) and gift movement (the goal tile shifts position during generation).
Figure 0.D.21: Constraint violations — VR-Bench. The agent enters a forbidden cell (lake or trap) in procedurally generated mazes and trapfields. Each panel uses a different texture to illustrate that the failure mode is consistent across visual appearances.
Figure 0.D.22: Degenerate failures. The model produces a video with little or no meaningful agent motion. The ghost trail collapses to a single position, indicating that the elf remains static throughout generation.
Figure 0.D.23: Horizon-limited failures. The generated trajectory respects all constraints but fails to reach the goal within the 81-frame budget. Valid stall : the agent follows a correct prefix but stops moving before reaching the goal. Wrong route : the agent takes a legal but sub-optimal path and runs out of frames.
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