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arxiv: 2506.00560 · v2 · pith:PI6AVQD3new · submitted 2025-05-31 · 💻 cs.RO · cs.CV

Using Ensemble Diffusion to Estimate Uncertainty for End-to-End Autonomous Driving

Florian Wintel , Sigmund H. H{\o}eg , Gabriel Kiss , Frank Lindseth This is my paper

Pith reviewed 2026-05-25 08:16 UTC · model grok-4.3

classification 💻 cs.RO cs.CV
keywords end-to-end autonomous drivingdiffusion modelsensemble methodsuncertainty estimationtrajectory planningCARLA simulatorLAV benchmarkmultimodal prediction
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The pith

Ensemble diffusion generates distributions of trajectories to model uncertainty in end-to-end autonomous driving.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces EnDfuser, an end-to-end driving system that replaces point-estimate trajectory planners with a diffusion model. It fuses camera and LiDAR features through attention pooling inside a diffusion transformer and, from one perception frame, samples 128 candidate trajectories via ensemble diffusion. This produces an explicit distribution that reveals multimodal and uncertain future paths. From the set of trajectories the authors derive a simple safety rule that raises the driving score by 1.7 percent on the LAV benchmark. The central argument is that ensemble diffusion can serve as a drop-in module for uncertainty-aware decision making in closed-loop driving policies.

Core claim

EnDfuser uses a diffusion transformer to combine perception fusion and trajectory planning. Instead of committing to one plan, the model draws 128 trajectories from the posterior distribution in a single forward pass. The resulting set of paths supplies interpretability for uncertain, multimodal spaces and supports a safety rule that improves benchmark performance by 1.7 percent on LAV.

What carries the argument

Ensemble diffusion inside a diffusion transformer module that outputs a distribution of 128 trajectories from fused perception features.

If this is right

  • The full set of candidate trajectories supplies interpretability for multimodal future spaces.
  • A safety rule can be designed directly from observed trajectory spread.
  • Ensemble diffusion can replace traditional point-estimate planners in end-to-end policies.
  • Uncertainty of the posterior trajectory distribution becomes available for downstream decision making.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same sampling approach could be applied to other sensor suites or non-driving control tasks that require multimodal predictions.
  • The 128-sample distribution might support probabilistic collision checks or risk-aware planning beyond the simple rule tested.
  • If the sampled trajectories prove well-calibrated, the method could reduce reliance on hand-crafted uncertainty modules in other autonomous systems.

Load-bearing premise

The trajectories sampled by the ensemble diffusion model accurately reflect real-world uncertainty and the safety rule derived from them improves safety without creating new failure modes.

What would settle it

A closed-loop test in which the safety rule based on trajectory spread produces lower driving scores or additional collisions compared with the baseline point-estimate planner.

Figures

Figures reproduced from arXiv: 2506.00560 by Florian Wintel, Frank Lindseth, Gabriel Kiss, Sigmund H. H{\o}eg.

Figure 1
Figure 1. Figure 1: EnDfuser architecture. (a) The TransFuser++ perception backbone consumes two modalities, RGB images from the ego perspective and a LiDAR birds-eye-view (BEV) image. Transformer-based sensor fusion is performed between the two convolutional branches, after which four auxiliary perception tasks are learned (BEV segmentation, BEV object detection, ego perspective depth estima￾tion and ego perspective segmenta… view at source ↗
Figure 2
Figure 2. Figure 2: We apply attention pooling on the BEV features. (a) TF++ WP relies on learned queries and GRUs. (b) We accomplish similar attention pooling by creating individual waypoint queries that each sample from the noise prior. As we can sample from the noise prior N times, we can denoise an arbitrary number of plans for any given perception frame. three TF++ WP instances. Since we completely replace the planning m… view at source ↗
Figure 3
Figure 3. Figure 3: Uncertainty map in Town02. Areas with a regular occurrence of variance spikes are clearly visible around intersec￾tions and bends. Each town displays the variances of 18 cumula￾tive episodes driven by EnDfuser, downsampled to 2Hz and color coded from low variance ◦ to high variance • in the speed predic￾tions. 4. Experiments and comparison We evaluate our agent on the Longest6 benchmark in CARLA [PITH_FUL… view at source ↗
Figure 4
Figure 4. Figure 4: Categories of uncertain situations. The majority of uncertainty spikes coincide directly with traffic interactions. We investigate the agent’s context in the 100 least certain situations by recording the sensory input of a full Longest6 evaluation (36 episodes) and extracting the 100 sequences with the highest vari￾ance values σˆ 2 (K spd t ). 5. Discussion In the following section, we discuss the observed… view at source ↗
Figure 5
Figure 5. Figure 5: High variance situations. X and Y components represent the posterior trajectory sample Tt, desired speed and yaw angle represent Kt. The selected action is marked in magenta. Most instances of high variane are interactions with dynamic objects, either other agents (a) or traffic signals (b). We attribute such instances to aleatoric uncertainty due to the unpredictable nature of other agents. As Tt represen… view at source ↗
Figure 8
Figure 8. Figure 8: Failure to predict. (a) EnDfuser changes lanes while taking a right turn. It ignores the vehicle to its right and causes a collision. (b) No spike in uncertainty is detectable. addition, EnDfuser is not equipped to distinguish between aleatoric and epistemic uncertainty, since it only produces first-order candidate distributions. Finally, we do not com￾pare ourselves to agents that only target newer, more … view at source ↗
Figure 6
Figure 6. Figure 6: Pre-crash condition. We observe an uncertainty spike before a collision occurs. The ego vehicle is in the process of over￾shooting into the leftmost lane, while another car is approaching fast from behind, leading to a collision. (a) TP • (b) Tt [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Label noise: (a) The prediction horizon extends beyond the target point, forcing the agent to predict positions for which it has no driving instruction. (b) This results in lateral uncertainty in the posterior sample Tt Choosing a different transformation operation, such a mul￾timodal prediction could cause erratic driving behavior. The observation may further offer an explanation why giving the agent two … view at source ↗
read the original abstract

End-to-end planning systems for autonomous driving are rapidly improving, especially in closed-loop simulation environments like CARLA. Many such driving systems either do not consider uncertainty as part of the plan itself or obtain it by using specialized representations that do not generalize. In this paper, we propose EnDfuser, an end-to-end driving system that uses a diffusion model as the trajectory planner. EnDfuser effectively leverages complex perception information like fused camera and LiDAR features, through combining attention pooling and trajectory planning into a single diffusion transformer module. Instead of committing to a single plan, EnDfuser produces a distribution of candidate trajectories (128 for our case) from a single perception frame through ensemble diffusion. By observing the full set of candidate trajectories, EnDfuser provides interpretability for uncertain, multimodal future trajectory spaces. Using this information we design a simplistic safety-rule that improves the system's driving score by 1.7% on the LAV benchmark. Our findings suggest that ensemble diffusion, used as a drop-in replacement for traditional point-estimate trajectory planning modules, can contribute to an uncertainty-aware decision making process in End-to-End driving policies by modeling the uncertainty of the posterior trajectory distribution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes EnDfuser, an end-to-end autonomous driving policy that replaces a point-estimate trajectory planner with an ensemble diffusion transformer operating on fused camera-LiDAR features. From a single perception frame the model samples 128 trajectories; a hand-crafted safety rule derived from this set is reported to raise the driving score by 1.7% on the LAV benchmark. The central claim is that the sampled distribution models posterior trajectory uncertainty and thereby enables more interpretable, uncertainty-aware decision making.

Significance. If the empirical link between the diffusion ensemble and posterior uncertainty were demonstrated, the work would supply a practical drop-in module for uncertainty estimation inside existing end-to-end stacks. The 1.7% gain is modest, however, and the absence of calibration diagnostics or comparisons to other uncertainty estimators limits the immediate significance for safety-critical deployment.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (Experiments): the reported 1.7% LAV improvement is stated without any baseline description, statistical significance test, data-split protocol, or ablation that isolates the contribution of the ensemble diffusion component versus the safety rule itself.
  2. [§3.2 and §4] §3.2 and §4: the assertion that the 128 sampled trajectories “model the uncertainty of the posterior trajectory distribution” is unsupported by any calibration result (e.g., predicted variance versus realized error on held-out data) or comparison against alternative uncertainty estimators; without such evidence the safety-rule benefit cannot be attributed to posterior modeling rather than to the learned data distribution.
minor comments (2)
  1. [§3] Notation for the diffusion transformer and attention pooling is introduced without an explicit equation relating the ensemble members to the final safety rule.
  2. [Figure 3] Figure captions and axis labels in the trajectory visualization panels are too small to read the multimodal spread clearly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We agree that the manuscript requires additional experimental details and supporting analyses for the uncertainty claim. We address each major comment below and commit to revisions that strengthen the paper without overstating current results.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (Experiments): the reported 1.7% LAV improvement is stated without any baseline description, statistical significance test, data-split protocol, or ablation that isolates the contribution of the ensemble diffusion component versus the safety rule itself.

    Authors: We agree this information is missing from the abstract and §4. In the revision we will: describe the point-estimate baseline, report means and standard deviations over multiple random seeds with statistical significance tests, specify the LAV data-split protocol, and add an ablation isolating the ensemble diffusion component from the hand-crafted safety rule. These changes will clarify the source of the reported gain. revision: yes

  2. Referee: [§3.2 and §4] §3.2 and §4: the assertion that the 128 sampled trajectories “model the uncertainty of the posterior trajectory distribution” is unsupported by any calibration result (e.g., predicted variance versus realized error on held-out data) or comparison against alternative uncertainty estimators; without such evidence the safety-rule benefit cannot be attributed to posterior modeling rather than to the learned data distribution.

    Authors: We acknowledge the claim currently lacks direct empirical support. The manuscript relies on the diffusion model's design to approximate a distribution over trajectories. In revision we will add calibration diagnostics (predicted variance vs. realized trajectory error on held-out data) and, space permitting, a brief comparison to other estimators. If the new results do not strongly corroborate posterior modeling, we will qualify the language to emphasize practical diversity sampling rather than strict posterior inference. revision: yes

Circularity Check

0 steps flagged

No circularity; purely empirical proposal with benchmark validation

full rationale

The paper presents EnDfuser as an end-to-end system replacing point-estimate planners with ensemble diffusion to output 128 trajectories, then applies a hand-crafted safety rule yielding +1.7% on LAV. No derivation chain, equations, or first-principles results are claimed; the uncertainty modeling is asserted as an empirical outcome of the trained model rather than reduced to any fitted parameter or self-citation by construction. No self-definitional steps, fitted-input predictions, or load-bearing self-citations appear in the provided text. The central claim remains an empirical observation independent of its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the diffusion model itself is treated as a standard component.

pith-pipeline@v0.9.0 · 5747 in / 989 out tokens · 32034 ms · 2026-05-25T08:16:01.837026+00:00 · methodology

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