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Uncertainty-Aware World Model for Aerial Image-Goal Navigation

Deyi Zhu, Haoyu Fan, Yinan Zhu, Weichen Zhang, Shilin Ma, Xinlei Chen, Yansong Tang

arXiv:2608.05597v1cs.CV

TL;DR

Aerial navigation world models often score trajectories from too few predicted futures to handle substantial future-state uncertainty. UA-NWM models plausible futures with an uncertainty subspace and improves navigation across diverse tasks while preserving low inference latency.

  • Problem

    Existing navigation world models inadequately represent future-state uncertainty when scoring trajectories, particularly in large-scale outdoor aerial scenes with multiple plausible futures.

  • Method

    UA-NWM formulates trajectory scoring as conditional out-of-distribution detection and uses hierarchical error projection to separate uncertainty-explainable deviations from residual errors.

  • Results

    UA-NWM improves navigation performance across diverse tasks while preserving low inference latency, with real-world UAV deployment supporting its practical applicability.

  • Takeaways & Limitations

    Distribution-aware trajectory scoring without stochastic future sampling provides an efficient approach for aerial image-goal navigation.

  • Takeaways & Limitations

    Modeling uncertainty too broadly may absorb true trajectory errors and weaken trajectory scoring, motivating a balance between uncertainty tolerance and trajectory discrimination.

Abstract

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Aerial image-goal navigation requires an unmanned aerial vehicle (UAV) to reach a target location specified by a goal image. Existing world-model-based methods rank candidate trajectories using predicted futures, but typically rely on only one or a few point predictions, which is inadequate for large-scale outdoor environments with substantial future-state uncertainty. To address this limitation, we propose the Uncertainty-Aware Navigation World Model (UA-NWM), an efficient latent world model for aerial image-goal navigation, which formulates trajectory scoring as conditional out-of-distribution detection. UA-NWM represents plausible futures with an uncertainty subspace and decomposes the prediction--goal discrepancy into uncertainty-explainable and unexplainable components. Only the unexplainable residual is used for scoring, enabling robust selection without multiple future samples. Extensive experiments demonstrate that UA-NWM consistently outperforms existing navigation world models while maintaining low inference latency. Real-world UAV experiments further validate its practical applicability. Project page: https://duryi.github.io/UA-NWM-Project-Page

1. Introduction

World-model-based aerial image-goal navigation must account for substantial uncertainty in long-horizon outdoor futures, which existing point-based trajectory scoring handles inadequately. UA-NWM addresses this by formulating scoring as conditional OOD detection and using an uncertainty subspace to isolate unexplained prediction–goal error.

  • Motivation: World models score candidate trajectories by predicting future states and selecting the trajectory most likely to reach the goal.Conventional methods directly predict actions or trajectories, while recent approaches use world models for future-state prediction.
  • Problem: Large-scale outdoor scenes create multiple plausible futures because long-horizon motion and unseen regions make future states uncertain.For example, building occlusion can leave future appearance ambiguous under the same context and actions.
  • Problem: Existing navigation world models compare goals with only one or a few point predictions, causing deterministic models to oversmooth uncertainty and stochastic models to require distribution-level assessment.Deterministic models may predict states outside the true distribution’s high-density region, while stochastic models capture diversity but make goal-membership evaluation challenging.
  • UA-NWM: UA-NWM formulates trajectory scoring as conditional out-of-distribution detection, treating the goal as in-distribution when a candidate trajectory can reach it.The method uses a lightweight deterministic backbone to predict future representations in DINOv3 latent space.
  • UA-NWM: HEP models an uncertainty subspace and decomposes prediction–goal discrepancy into uncertainty-explainable variation and orthogonal unexplained residual error, using only the residual for scoring.This avoids penalizing deviations attributable to plausible future uncertainty.
  • Evaluation: UA-NWM is trained on a high-quality aerial-navigation dataset with staged optimization, and experiments report improved trajectory-scoring accuracy, low inference latency, and real-world UAV effectiveness.The uncertainty-aware HEP consistently improves trajectory-scoring accuracy across offline and online experiments.

2. Related Work

Image-goal navigation has evolved from classical mapping and localization toward learning-based, generative, and world-model approaches. However, UAV methods and existing trajectory-scoring techniques remain limited in long-horizon outdoor planning because they lack reliable multi-step visual prediction and explicit future-state uncertainty modeling.

  • Image-goal navigation: Image-goal navigation supports delivery, inspection, and rescue when precise coordinates are unavailable.The task guides an agent to an image-specified position.
  • Learning-based navigation: Classical navigation relies on mapping or localization, whereas learning-based methods predict actions or waypoints and increasingly model multimodal action or trajectory distributions.Approaches include reinforcement learning, heterogeneous robot data, Transformer policies, LLM backbones, and generative policies.
  • UAV navigation: Recent UAV image-goal navigation methods mainly address indoor exploration, language guidance, or local pose alignment, limiting reliable long-horizon planning outdoors.They generally lack action-conditioned prediction of multi-step visual outcomes for candidate trajectories.
  • Navigation world models: Navigation world models score candidate actions by predicting future visual consequences, extending future-scene imagination from indoor and long-horizon navigation.NWM introduced action-conditioned video prediction for navigation.
  • Uncertainty in trajectory scoring: Existing methods commonly compare trajectories using only one or a few predicted futures, which cannot separate plausible variations from action-inconsistent errors.Deterministic models produce blurry single estimates, while stochastic models are sensitive to sampling variance, motivating explicit future-state distribution modeling.

3. Preliminaries

The preliminaries formulate image-goal navigation as ranking finite candidate action sequences by predicted terminal-goal compatibility. Existing rankers typically use point-to-point distances between predicted futures and the goal, including perceptual pixel-space and feature-space metrics.

  • Image-goal navigation formulation: A world model ranks candidate trajectories over an H-step horizon using the agent’s recent context of C observed images.A proposal policy or sampling-based planner generates a finite candidate set of action sequences.
  • Image-goal navigation formulation: Each candidate action sequence is evaluated through its predicted terminal visual representation and compatibility with the goal image.The formulation uses a frozen visual feature extractor, a future-feature predictor, and a discrepancy measure.
  • Image-goal navigation formulation: The optimal action sequence is selected as the candidate with the lowest world-model trajectory cost.The cost is defined from the predicted future representation and the goal representation.
  • Existing trajectory rankers: Existing world-model rankers typically use point-to-point distances, including LPIPS for generated images and cosine or Euclidean distance in latent feature space.The same cost formulation can support standalone planning with iterative candidate refinement using CEM.

4. Method

UA-NWM scores candidate trajectories by comparing goal features with conditional future-state distributions rather than deterministic predictions alone. Its HEP module constructs hierarchical uncertainty subspaces to isolate unexplainable discrepancy in one forward pass, while a deterministic latent world model supplies the predictions.

  • Uncertainty-aware trajectory scoring: UA-NWM formulates trajectory scoring as conditional OOD detection, modeling each candidate’s plausible future states as an uncertainty subspace around the predicted mean.The goal–prediction discrepancy is decomposed into uncertainty-explainable and unexplainable components.
  • Uncertainty-aware trajectory scoring: Only the unexplainable residual e⊥ determines trajectory cost, yielding low cost for uncertainty-consistent goal differences and high cost for discrepancies outside plausible directions.Trajectories with similar total discrepancy can receive different scores when one discrepancy is explained by occlusion and the other is not.
  • Hierarchical Error Projection: HEP models plausible deviations with multi-scale low-rank subspaces and projects discrepancy hierarchically from coarse to fine using region-specific residual fields.At each scale, it projects cell-level residuals onto learned subspaces, subtracts the explained component, and passes the remainder to finer scales.
  • Hierarchical Error Projection: HEP approximates the conditional future-state distribution around the deterministic prediction and enables uncertainty-aware scoring in one forward pass without sampling multiple future observations.After the finest scale, the remaining residual is e⊥ and the explained component is e∥ = e − e⊥.
  • Deterministic latent world model: The deterministic backbone compresses frozen DINOv3 features into latent tokens, predicts action-conditioned delta tokens with a causal Transformer, and decodes them into future dense feature maps.Training first learns the compressor, fuser, and delta decoder, then freezes them while training the action encoder and Transformer for future latent prediction.

5. Experiments

Experiments introduce AirGoal-10k, a diverse large-scale outdoor UAV image-goal navigation benchmark, and evaluate UA-NWM across offline ranking, standalone planning, and online closed-loop settings. UA-NWM achieves the strongest reported performance, models plausible uncertainty without sacrificing trajectory discrimination, and transfers successfully to real-world UAV deployment.

  • Benchmark: AirGoal-10k provides 11,000 trajectories spanning diverse urban environments, with approximately uniform initial-heading deviations over [0, 90°] and azimuth angles over [0, 360°].The benchmark contains 9000 training, 1000 validation, and 1000 testing trajectories, each pairing 3D waypoints with egocentric RGB observations.
  • Offline evaluation: UA-NWM achieves the lowest ATE and RPE across candidate-set sizes in offline trajectory ranking while remaining substantially faster than previous methods.NoMaD generates 8, 16, or 32 candidate action sequences, and all world-model methods score identical candidate sets.
  • Online evaluation: UA-NWM achieves the best online performance across 100 AirSim episodes under variable-length, long-horizon navigation with unknown goal distances.World-model methods plan with CEM, whereas policy-based methods directly predict trajectories; success requires stopping within 20 meters of the target within the maximum step budget.
  • Qualitative analysis: UA-NWM captures plausible future variations from occlusion ambiguity and long-horizon drift while preserving global geometry for trajectory discrimination.Its uncertainty subspace represents local variations, whereas overly broad uncertainty in NWM and RAE-NWM can absorb true trajectory errors and weaken scoring.
  • Ablation studies: Removing any HEP scale degrades performance, with Scale 14 contributing most and Scale 1 least because explainable errors predominantly arise from fine-grained local variations.The ablation attributes the scale differences to the spatial extent of those variations.
  • Ablation studies: R = 2 performs best across HEP scales, indicating that a low-dimensional subspace captures dominant explainable-error directions while larger ranks may weaken trajectory discrimination.Smaller ranks underrepresent future uncertainty, whereas larger ranks may absorb unexplainable errors.

6. Conclusion

UA-NWM is an uncertainty-aware world model for aerial image-goal navigation that formulates trajectory scoring as conditional OOD detection. It models plausible future variations through an uncertainty subspace, separates uncertainty-induced deviations from unexplained residual errors, and enables efficient distribution-aware scoring without stochastic future sampling.

  • UA-NWM formulates trajectory scoring as conditional OOD detection for aerial image-goal navigation.
  • UA-NWM models plausible future variations through an uncertainty subspace and separates uncertainty-induced deviations from unexplained residual errors.
  • UA-NWM enables efficient distribution-aware trajectory scoring without stochastic future sampling.
  • Experiments show that UA-NWM improves navigation performance across diverse tasks.

Supplementary Material … C. Details of AirGoal-10k Benchmark

The supplementary material contrasts UA-NWM’s future-state uncertainty focus with prior uncertainty and OOD methods, then details its architecture, staged training, inference scoring, and hyperparameters.

  • A.1. Uncertainty-Aware Visual Navigation: Prior visual-navigation methods primarily address uncertainty in current perception, localization, semantic mapping, or planning, whereas UA-NWM models uncertainty over plausible future observations.Given identical visual context and candidate trajectory, multiple future observations may remain plausible.
  • A.2. OOD Detection: World-model OOD methods mainly detect operation outside training distributions, while UA-NWM evaluates whether a goal is compatible with a candidate trajectory’s induced future.This frames trajectory scoring as goal–future compatibility rather than generic world-model reliability detection.
  • B.1. Model Structure: UA-NWM combines a lightweight deterministic latent world model with a Hierarchical Error Projection module that predicts context- and trajectory-conditioned plausible deviation directions.The goal image is excluded from basis prediction, so the uncertainty subspace depends on observation context and candidate trajectory.
  • B.1. Model Structure: The model compresses 196 DINO patch tokens of dimension 768 into 32 latent tokens of dimension 384, then performs action-conditioned autoregressive prediction with six causal Transformer blocks.The predictor uses four compressed context states, yielding 128 context tokens before causal processing.
  • B.1. Model Structure: HEP hierarchically projects normalized goal discrepancies across four spatial scales, subtracting explained components until the finest scale yields the unexplained residual.The scales contain 1, 4, 49, and 196 cells; ridge regularization uses λ = 10^-3.
  • B.2. Training and Inference Procedure: Training proceeds through representation learning, deterministic prediction training with frozen representation modules, and HEP training with the deterministic baseline frozen.Stages 2 and 3 use autoregressive eight-step rollouts, while HEP minimizes normalized orthogonal residual fraction.
  • B.2. Training and Inference Procedure: At inference, HEP scores only the final-step residual energy after rollout; the lowest-cost candidate is selected for offline ranking or CEM planning.HEP does not feed its output back into rollout dynamics, and absolute residual magnitude is retained at test time.
  • B.3. Hyper-parameter Settings: Training uses AdamW, bf16 mixed precision, gradient clipping, warmup, and cosine decay; stage 3 trains HEP for 8k steps with learning rate 5×10^-4.Stage 3 uses batch size 48, an eight-step horizon, and denominator clamp ϵ = 10^-9.

C.1. Dataset Construction … D.2. Offline Experiments

The AirGoal-10k benchmark combines feasible UAV start states, procedurally sampled 3D futures, rendered RGB observations, and automatic quality filtering. Offline evaluation covers candidate trajectory ranking and standalone CEM planning, with matched baselines and ATE/RPE-based assessment.

  • C.1. Dataset Construction: AirGoal-10k learns first-person visual dynamics conditioned on future motion from an AirSim-based UAV image-goal navigation benchmark.
  • C.1. Dataset Construction: Start states are sampled from existing aerial VLN trajectory annotations, then deduplicated by scene, position, and yaw to avoid invalid AirSim viewpoints.
  • C.1. Dataset Construction: Future trajectories sample local-frame target directions, smoothly interpolate segment directions, and update UAV positions by forward integration.The target direction uses dtarget = cos θ ef + sin θ cos φ er + sin θ sin φ eu; θ controls heading deviation and φ controls lateral, vertical, or combined 3D turning.
  • C.1. Dataset Construction: Accepted trajectories are rendered from AirSim’s front RGB camera at 512×512 and filtered using invalid-height, black-frame, and LPIPS-based crash checks.
  • C.2. Task Definition: Both offline tasks use four context RGB frames and a goal image, then compare selected or planned trajectories with ground-truth futures using ATE and RPE.
  • C.2. Task Definition: Trajectory ranking scores 32 shared candidate trajectories branching into 8-step waypoint futures, while standalone planning removes external proposals and uses CEM to search action sequences.CEM uses 32 samples, the top 16 elites, and 3 optimization iterations, producing the final trajectory from the mean parameters.
  • D.1. Baseline Implementation: Baselines are adapted from 2D to 3D action spaces, trained to convergence on AirGoal-10k, and matched by parameter count where model-size options differ.NWM and MWM use CDiT-B/2; RAE-NWM uses CDiT-B/2 and DINOv2-B.
  • D. Experimental Details: Offline experiments run on four NVIDIA RTX 4090 GPUs, with speed tests using one GPU and the same batch size; ranking additionally reports random and oracle references.Oracle selection chooses the candidate with the smallest ATE relative to the ground-truth trajectory.

D.3. Online Simulation Experiments … E. Additional Ablation Studies

Online simulation evaluates UA-NWM on 100 AirSim episodes using success and path-efficiency metrics, while real-world experiments test deployment on a custom quadrotor under visual and sensing constraints. Additional passages describe latent-space visualization and plausible-state sampling procedures.

  • D.3. Online Simulation Experiments: Online navigation is evaluated on 100 AirSim start–goal pairs, with an average three-dimensional distance of 57 m.The dataset includes 57 AerialVLN episodes and 43 OpenFly episodes; 76% of distances lie between 45 m and 60 m.
  • D.3. Online Simulation Experiments: An episode succeeds when the UAV terminates within 20 m of the ground-truth goal, while observation-capture failures and collisions are tracked separately.The evaluation reports Success Rate (SR) and Success weighted by Path Length (SPL).
  • D.3. Online Simulation Experiments: SPL uses initial start-to-goal distance as the reference and accumulated flown distance as the executed path length.Runtime is measured as average planner time per online step, excluding simulator startup, environment reset, and scene-switching overhead.
  • D.4. Real-world Experiments: Real-world deployment uses a custom quadrotor equipped with an NVIDIA Jetson Orin NX, forward-facing RGB camera, Livox Mid-360 LiDAR, and MicoAir NxtPX4v2 controller.The RGB camera supplies visual observations, while the Jetson provides onboard computing and communication.
  • D.4. Real-world Experiments: The distributed system connects the UAV, a Windows ground station, and a battery-powered MacBook Air M4, where world-model inference and high-level planning run locally.A mobile-phone hotspot provides communication; the ground station manages missions and supervises flights.
  • D.4. Real-world Experiments: UA-NWM makes high-level navigation decisions without directly accessing LiDAR, IMU states, FAST-LIO poses, ground-truth goals, or ground-truth goal distances.FAST-LIO is reserved for low-level state estimation and flight control, while mobile-phone goal images create camera-parameter and viewpoint gaps.
  • D.5. DINO Latent Visualization: Trajectory scoring is performed directly in DINOv3 latent space, while RAEv2-decoded RGB images are used only for qualitative visualization.The RAEv2 checkpoint is fine-tuned on AirGoal-10k to improve reconstruction quality, but decoded images may omit information in predicted latents.
  • E. Additional Ablation Studies: Sampling other plausible states within the predicted subspace is discussed in Section H.The supplied passages do not provide a separate result for Additional Ablation Studies.

E.1. Rollout Steps for Training · E.2. Staged Training and Delta Representation · E.3. Number of Compressed and Delta Tokens

The ablations show that longer autoregressive training rollouts improve robustness, while staged training, delta prediction, and moderate token capacity strengthen future prediction and navigation performance. The best compressed-and-delta token configuration is K = 32 and M = 32 across candidate-set sizes.

  • E.1. Rollout Steps for Training: Longer autoregressive rollouts generally improve navigation performance.The model averages losses across rollout steps and is exposed to its own intermediate predictions during training, better matching autoregressive inference and mitigating error accumulation.
  • E.1. Rollout Steps for Training: Autoregressive rollout training improves robustness to accumulated prediction errors.Rollouts are used in stages 2 and 3, with losses averaged across all rollout steps.
  • E.2. Staged Training and Delta Representation: The staged strategy first learns compact representations and latent transitions before future prediction.The deterministic backbone follows this sequence, while delta representation encodes changes between adjacent visual representations.
  • E.2. Staged Training and Delta Representation: Delta prediction estimates changes between adjacent frames rather than the full next-frame representation.This design follows DeltaWorld [25] and is ablated alongside the staged training strategy.
  • E.2. Staged Training and Delta Representation: End-to-end training without staging degrades performance.Pretraining the compressor, fuser, and delta decoder provides a more stable and effective initialization for future prediction.
  • E.2. Staged Training and Delta Representation: Directly predicting the full next-frame representation causes a larger performance drop than removing staged training.The comparison is conducted across different numbers of candidate trajectories.
  • E.3. Number of Compressed and Delta Tokens: K = 32 and M = 32 achieves the best performance across all candidate-set sizes.Deviating from this configuration in either direction consistently produces inferior results, suggesting that moderate capacity benefits both representations.

F. Performance on 2D Navigation Benchmarks · G. Further Analysis of HEP · G.1. Residual Energy as a Conditional Compatibility Score

On RECON and GO Stanford, UA-NWM consistently outperforms NWM and RAE-NWM when ranking shared NoMaD candidate trajectories. HEP explains its score probabilistically as penalizing goal discrepancy primarily outside a predicted uncertainty subspace, under a high-anisotropy assumption.

  • F. Performance on 2D Navigation Benchmarks: UA-NWM is evaluated on RECON and GO Stanford against NWM and RAE-NWM using identical NoMaD-generated candidate trajectory sets.NWM uses 250 diffusion steps, while RAE-NWM uses 50 flow-matching ODE steps under official inference settings.
  • F. Performance on 2D Navigation Benchmarks: UA-NWM consistently outperforms both baselines across both 2D datasets and all candidate-set sizes.
  • G. Further Analysis of HEP: The HEP analysis uses a probabilistic view to justify unexplained residuals as trajectory-goal compatibility scores and explains the coarse-to-fine projection.It also examines how training encourages predicted bases to capture residual directions recurring under similar context-action conditions.
  • G.1. Residual Energy as a Conditional Compatibility Score: For a context and candidate action sequence, UA-NWM compares the deterministic DINO feature prediction µ with the goal feature x_g = ϕ(o_g).
  • G.1. Residual Energy as a Conditional Compatibility Score: Plausible residual variation is modeled as E = V a + ξ, where V a lies in an R-dimensional uncertainty subspace and ξ lies outside it.The model assumes a ∼ N(0, τ^2I) and ξ ∼ N(0, σ^2I), with V's columns orthonormal.
  • G.1. Residual Energy as a Conditional Compatibility Score: The Gaussian negative log-likelihood weights residual components through e^TΣ^-1e, while its log-determinant term is constant for fixed R, τ, and σ.Decomposing e into components parallel and orthogonal to the subspace yields distinct penalties for explainable and unexplained variation.
  • G.1. Residual Energy as a Conditional Compatibility Score: UA-NWM uses ||e_⊥||^2 as its dominant criterion when τ^2 ≫ σ^2, treating within-subspace variation as acceptable and penalizing unexplained discrepancy.If τ^2 is not substantially larger than σ^2, the score is a conservative approximation because it omits a non-negligible penalty on e_∥.

G.2. What the Hierarchical Projection Computes · G.3. Why the Training Objective Learns Plausible Residual Directions

HEP hierarchically removes regularized, cell-wise residual components from coarse to fine, approximating plausible residual subspaces without a global joint projection. Its normalized residual objective learns low-rank, conditional basis directions that capture recurring and spatially coherent future deviations.

  • G.2. What the Hierarchical Projection Computes: HEP builds a multi-scale approximation over DINO patch residuals using grid scales G = {1, 2, 7, 14} and cell-average residuals.Residuals are initialized by r1,i = ei, and each scale partitions the patch grid into cells.
  • G.2. What the Hierarchical Projection Computes: For each cell, HEP predicts a local basis and ridge-projects the cell-average residual onto its span before subtracting that projection from every patch.The cell-average is computed across all patches in the cell rather than from a single patch.
  • G.2. What the Hierarchical Projection Computes: Regularization improves numerical stability and prevents unstable coefficients when predicted basis vectors are correlated, while λ = 0 recovers ordinary least squares.The projected vector is subtracted from every patch in the cell at that scale.
  • G.2. What the Hierarchical Projection Computes: Coarse scales remove broad spatially coherent deviations, finer scales remove localized deviations, and the finest 14×14 scale performs patch-wise residual projection.At the finest scale, each cell contains one DINO patch.
  • G.2. What the Hierarchical Projection Computes: HEP is a greedy coarse-to-fine residual decomposition, not a single exact orthogonal projection, because earlier components are not jointly re-optimized.If scale-wise subspaces are mutually orthogonal, the sequential procedure is equivalent to exact orthogonal projection.
  • G.3. Why the Training Objective Learns Plausible Residual Directions: The normalized residual loss trains predicted bases to explain recurring residual directions under the same context and action while reducing the unexplained component.For a fixed basis span S, the cell-average residual decomposes into PS¯rg,c and (I − PS)¯rg,c.
  • G.3. Why the Training Objective Learns Plausible Residual Directions: Minimizing empirical unexplained energy is equivalent to maximizing expected explained energy, so the optimal low-rank subspace contains principal residual directions of plausible futures.The objective is interpreted over transitions sampled from the training distribution.
  • G.3. Why the Training Objective Learns Plausible Residual Directions: HEP learns conditional local bases rather than memorizing arbitrary residuals, constrained by R directions, spatial coherence at coarse scales, and a frozen deterministic baseline.Because R ≪ D, each cell cannot explain all channel-space errors; the baseline remains fixed during HEP training.

H. Further Discussions and Future Work … I.6. Real-world UAV Navigation

UA-NWM visualizes and exploits uncertainty-subspace futures for projection-based goal matching, while revealing limitations in random sampling and uncertainty representation. Qualitative evaluations across offline, simulated online, and real-world settings show robust trajectory ranking, planning, closed-loop approach, and sim-to-real generalization.

  • H. Further Discussions and Future Work: UA-NWM predicts deterministic future state µ and uncertainty subspace S, then samples plausible future states within S.The predicted subspace is intended to represent alternative conditional futures.
  • H. Further Discussions and Future Work: Projecting the goal state onto S yields xP_g = µ + e∥, typically reducing the goal gap while preserving plausible appearance.Hierarchical error projection explains residuals along plausible uncertainty directions, and the unexplained residual decreases progressively during projection.
  • H. Further Discussions and Future Work: Random samples from S show meaningful diversity and reasonable global layouts, but can lack spatial coherence, producing inconsistent appearance across regions.The limitation reflects S being a low-dimensional, local approximation rather than a complete conditional future-state distribution.
  • H. Further Discussions and Future Work: Goal-oriented sampling uses visually distinct, contextually plausible pseudo-goals whose projections remain close to compatible goals while staying constrained by S when goals are incompatible.This strategy is proposed to obtain more interpretable plausible samples and supports UA-NWM as an efficient stochastic generator as well as a navigation discriminator.
  • I.2. Uncertainty Subspace: Additional uncertainty-subspace visualizations identify two alternative plausible samples per case, capturing future-state diversity from occlusion ambiguity or long-horizon drift.These visualizations provide qualitative evidence that the predicted subspace represents meaningful alternatives.
  • I.3. Offline Trajectory Ranking: When ranking 32 candidates, UA-NWM uses the unexplained residual to produce more robust rankings than NWM [5] under future-state uncertainty.NWM [5] is described as susceptible to error accumulation and sampling variability, whereas UA-NWM favors candidates closer to the ground-truth trajectory.
  • I.4. Offline Standalone Planning: Under the same CEM planning framework, UA-NWM identifies the direction toward the goal through iterative sampling, prediction, and optimization, whereas NWM [5] often fails to recover the correct path.This result comes from qualitative comparisons on the offline standalone planning task.
  • I.5. Online Simulation / I.6. Real-world UAV Navigation: UA-NWM progressively approaches unknown-distance targets through multi-step closed-loop CEM planning in online simulation and transfers robustly across real-world weather and times of day.Real-world evaluations cover sunny, cloudy, and post-rain conditions as well as morning, afternoon, and dusk.
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