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Learning to Explain While Planning: Rule-Aligned Diffusion Planning for Autonomous Driving

Jiaxi Ye, Chunji Lv, Guoren Wang, Changsheng Li

arXiv:2609.39995v2cs.LG

TL;DR

Diffusion planners rely mainly on expert demonstrations and lack explanations of which driving rules shape their trajectories. RADP trains with differentiable rules and estimates their optimization pressure online, while a temporal risk-alignment protocol evaluates those attributions. On nuPlan, RADP improves safety metrics in challenging test scenarios while maintaining broadly comparable overall planning performance, and RPA aligns with subsequent rule-specific risks.

  • Problem

    Diffusion planners primarily learn from expert demonstrations, leaving driving rules implicit, and lack explanations of which rules act on trajectories and when.

    Source: §1 · p. 1

  • Method

    RADP incorporates differentiable driving rules into diffusion training, while RPA uses trajectory-gradient supervision to estimate each rule’s optimization pressure online.

    Source: §1 · p. 2

  • Results

    RADP maintains broadly comparable overall planning performance while improving collision and TTC metrics in challenging safety-critical scenarios, and RPA outputs show stable temporal correspondence with subsequent rule-specific risks.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The results support training-time rule integration and show temporal alignment between online rule pressures and subsequent rule-specific risks in closed-loop nuPlan experiments.

    Source: §1 · p. 2

    Simulation results do not establish real-world deployment readiness; deployment would require extensive real-world testing, safety validation, and appropriate human oversight.

    Source: ETHICS STATEMENT · p. 10

Abstract

from arXiv · show

Diffusion planners exhibit strong capabilities in generating multimodal trajectories. However, existing methods primarily rely on expert demonstrations to fit trajectory distributions, learning statistical correlations among scenes, behaviors, and trajectories without explicitly modeling driving rules. In long-tail scenarios where expert data are scarce, the lack of behaviors to imitate may lead to trajectories that violate safety or compliance requirements. Moreover, their generation process lacks rule-level explanations, making it difficult to determine which rules drive trajectory adjustments, when they take effect, and how strongly they act, thereby limiting failure diagnosis, safety validation, and targeted improvement. To address these limitations, we propose the Rule-Aligned Diffusion Planner (RADP), which incorporates differentiable driving rules into the diffusion objective during training, turning rule knowledge into intrinsic behavioral principles beyond finite demonstrations. We further introduce Rule-Pressure Attribution (RPA), which constructs supervision signals from gradients of rule losses with respect to predicted trajectories and employs a lightweight attribution head to estimate the optimization pressure exerted by each rule online. To assess the closed-loop behavioral relevance of these attributions, we propose a temporal risk-alignment protocol that evaluates whether current rule pressures reflect corresponding risks during subsequent closed-loop execution. Experiments on nuPlan show that RADP improves closed-loop planning in challenging safety-critical scenarios, while RPA exhibits consistent temporal alignment with subsequent rule-specific risks, validating both intrinsic rule learning and rule-level interpretability.

1 INTRODUCTION

The paper addresses diffusion planners’ reliance on expert demonstrations and lack of rule-level explanations. It proposes training-time rule integration, online attribution, and a protocol for evaluating whether those attributions align with future closed-loop risks.

1 INTRODUCTION

  • Existing diffusion planners often leave collision avoidance, lane compliance, and speed-limit compliance implicit in demonstrations rather than explicit training objectives.Sparse coverage of complex interactions and long-tail states may leave learned behavior without transferable rule constraints.Source: §1 · p. 1
  • Post-hoc feature explanations do not directly reveal which semantic driving rules drive trajectory optimization or when and how strongly they act.The paper connects this gap to difficulty diagnosing planning failures, validating safety properties, and targeting model improvements.Source: §1 · pp. 1–2
  • RADP jointly trains the diffusion objective with differentiable driving rules, while RPA estimates each rule’s trajectory-optimization pressure online.A lightweight attribution head is supervised by gradients of rule costs with respect to predicted trajectories.Source: §1 · p. 2
  • On nuPlan, RADP improves safety metrics on both test splits while maintaining broadly comparable overall planning performance, and RPA aligns with subsequent rule-specific risks.On val14-r, safety improves but lower progress reduces the aggregate score.Source: §1 · p. 2
  • Temporal risk alignment tests whether higher current rule pressures accompany higher corresponding risks over a future closed-loop rollout window.The protocol evaluates the behavioral relevance of attributions alongside the planner’s closed-loop results.Source: §1 · p. 2

2 RELATED WORK

Prior work uses diffusion models for multimodal planning, adds objectives to guide or constrain sampling, and explains inputs or internal representations. The paper distinguishes its approach by training with semantic driving rules and estimating their corrective pressure on trajectories.

Diffusion Planning

  • Diffusion planning methods mainly learn behavior from demonstrations and do not explicitly represent semantic rules for compliance reasoning or decision explanation.The section describes diffusion models as a framework for multimodal trajectory prediction and planning.Source: §2 · p. 2

Rule and Constraint Integration in Learned Planning

  • Prior generative-planning objectives typically guide or constrain sampling after the diffusion model has been learned, rather than making semantic driving rules part of policy training.The passage surveys reward guidance, differentiable costs, search, semantic constraints, control-barrier conditions, and state or action constraints.Source: §2 · p. 2

Explainable Diffusion Planning

  • Existing explanation methods expose input objects, representations, or visual evidence, but do not directly quantify individual rules’ corrective pressure on a trajectory.The paper uses gradients of differentiable rules with respect to the trajectory as supervision for online rule-pressure estimation.Source: §2 · p. 3

3 METHOD

RADP integrates differentiable driving rules into diffusion-planner training and produces a trajectory with online rule-level attributions. Its staged method defines rule costs, adapts the planner, derives gradient-pressure targets, and trains an attribution head for inference.

3.1 PROBLEM SETUP AND METHOD OVERVIEW

  • RADP maps each scene observation to a future ego trajectory and a six-channel rule-pressure vector within the same planning cycle.The channels represent collision avoidance, lane and speed-limit compliance, kinematic feasibility, comfort, and goal progress.Source: §3.1 · p. 3

3.2 DIFFERENTIABLE DRIVING RULES

  • Each differentiable rule cost aggregates gated local violations over trajectory steps and, for interactive rules, relevant entities.Positive local values denote violations, while nonpositive values indicate satisfaction or remaining safety margin; smooth penalties increase with violation severity.Source: §3.2 · pp. 4–5

3.3 RULE-ALIGNED PLANNER TRAINING

  • The planner is fine-tuned from a diffusion-planner baseline by adding normalized, weighted rule costs to its reconstruction objective.Lightweight LoRA adapters are fine-tuned in the decoder.Source: §3.3 · p. 5

3.4 GRADIENT-PRESSURE TEACHER

  • For each rule, the teacher uses trajectory-gradient magnitude as a local pressure target, then calibrates the rule-specific scale before attribution-head supervision.The calibrated attribution measures rule-specific local trajectory sensitivity.Source: §3.4 · p. 5

3.5 ONLINE ATTRIBUTION HEAD

  • A lightweight head combines generated-trajectory features with scene context to predict rule pressures, trained on cached teacher targets while the planner is frozen.At inference, the head reuses planner features without altering the trajectory or requiring teacher gradients, rule guidance, or trajectory optimization.Source: §3.1 · p. 4, §3.5 · pp. 5–6

4 EXPERIMENTS

RADP’s reactive planning results, attribution evaluations, efficiency measurements, qualitative analysis, and ablations assess both planning behavior and rule-pressure explanations. Across these experiments, RADP improves safety metrics in challenging test splits, while its attribution head tracks teacher pressures and subsequent rule-specific risks.

4.1 EXPERIMENTAL SETUP

  • The evaluation covers reactive nuPlan planning, teacher-fidelity checks, and alignment between rule-specific attributions and future risks in closed-loop rollouts.Six attribution channels are tested against seven future-risk endpoints; TTC is an auxiliary endpoint for collision, not a seventh Head output.Source: §4.1 · p. 6

4.2 PLANNER PERFORMANCE

  • RADP improves reactive scores and safety metrics on both test splits, achieves the highest reported scores on test14-random and test14-hard, and remains competitive on val14.On val14-r, safety improves but lower progress reduces the aggregate score, revealing a safety–efficiency trade-off.Source: Table 2 · p. 6, §4.2 · p. 7, Table 3 · p. 7

4.3 ATTRIBUTION EVALUATION

  • Future-risk targets aggregate rule-specific severity over a rule-specific horizon, with two seconds for collision and TTC and eight seconds for the other listed rules.The severity functions, aggregation operators, horizons, and thresholds are fixed before attribution results are inspected; these risks are evaluation targets, not training labels.Source: §4.3 · p. 7

4.3.1 CLOSED-LOOP HEAD–TEACHER FIDELITY

  • On synchronized reactive frames, the Head tracks the Teacher in pressure ranking, absolute magnitude, and dominant-rule identification, while both align positively with subsequent rule-matched risks.The evaluation measures pressure ordering, numerical agreement, and dominant-rule decisions on the same frame, scene state, and generated trajectory.Source: §4.3.1 · p. 7, Table 4 · p. 7, §4.3 · p. 7

4.3.2 TEMPORAL RISK ALIGNMENT

  • For five endpoints with sufficient events, Head AUPRC exceeds the positive-rate baseline and Lift@10% indicates risk enrichment among high-pressure frames.Positive temporal correlations, alongside near-zero correlations after temporal shuffling, support an association between predicted pressures and subsequent rule-specific risks.Source: §4.3.2 · pp. 7–8, Table 5 · p. 8

4.4 EFFICIENCY

  • Planner-only and planner-plus-Head inference require 251.05 and 245.50 ms per step, respectively, with no measurable end-to-end overhead from online attribution in this evaluation.Exact Teacher computation takes 465.29 ms end to end; on cached planner states, the Head takes 8.18 ms versus 62.51 ms for the Teacher, a 7.65× attribution speedup.Source: §4.4 · p. 8, Table 6 · p. 8

4.5 QUALITATIVE ANALYSIS

  • In the left-turn example, the Head raises collision pressure near two interactions and lane pressure as corridor clearance falls, while RADP maintains greater separation than the baseline.Speed, kinematic, and comfort pressures remain comparatively low in the described scenario.Source: §4.5 · p. 8, Figure 3 · p. 9, Figure 4 · p. 9

4.6 ABLATION STUDY

  • Rule supervision improves planning and safety over rule-free and unnormalized variants, while collision-only inference guidance performs substantially worse.The ablation evaluates rule variants on test14-hard-r.Source: §4.6 · p. 9, Table 7 · p. 9

5 LIMITATIONS AND CONCLUSION

The section identifies fixed rule priorities and a predefined rule set as limitations, and cautions that nuPlan simulation results do not establish real-world deployment readiness. It also documents the diffusion objective, rule-channel semantics, and trajectory processing used in the appendix.

5 LIMITATIONS AND CONCLUSION

  • RADP assumes a predefined rule set and fixed rule weights, so it cannot adapt rule priorities to changing scenarios or preferences.The authors also note that comparisons with other attribution families are non-trivial because their explanations do not align directly with RADP’s rule-specific risk endpoints.Source: §5 · p. 9
  • The authors used generative AI to polish writing and aid related-work retrieval, and reviewed and verified AI-assisted text and references.Source: AI USE STATEMENT · p. 10
  • nuPlan simulation results should not be interpreted as evidence of real-world deployment readiness; deployment would require real-world testing, safety validation, and human oversight.Source: ETHICS STATEMENT · p. 10

A BASELINE DIFFUSION OBJECTIVE

  • The baseline uses a masked reconstruction objective, with the valid set excluding padded agents and unavailable future states.The supplied passages identify this objective but do not provide its full equation.Source: A BASELINE DIFFUSION OBJECTIVE · p. 14

B RULE AND RISK DEFINITIONS

  • The planner rule loss, Teacher targets, and Head outputs share six semantic channels; underspeed and traffic-light costs are not independent channels, and TTC reuses collision pressure.Source: B RULE AND RISK DEFINITIONS · p. 14

B.1 TRAJECTORY DENORMALIZATION AND FINITE DIFFERENCES

  • Rules operate on denormalized trajectories at 0.1 s resolution, with finite differences and masks excluding invalid map points, padded agents, and unavailable future states.Source: §B.1 · p. 14

B.2 COMPLETE INSTANTIATION OF RULE COSTS

This appendix specifies how the differentiable costs and external rollout-risk endpoints are instantiated. It also documents aggregation, normalization, and the temporal windows used to assess risk alignment.

B.2 COMPLETE INSTANTIATION OF RULE COSTS

  • Collision cost combines box separation, closing speed, a 4 s TTC threshold, and safety-distance deficit, with a 20 m cutoff and softmax-weighted mean at temperature 8.The implementation also specifies a 0.8 s reaction time and 4.0 m/s^2 braking acceleration.Source: §B.2 · p. 14
  • Lane cost matches predicted points to the nearest route-polyline point, while a weak centerline regularizer does not replace ego-body boundary constraints.Source: §B.2 · p. 14
  • Speed-limit cost masks steps without a valid route-lane limit and excludes road curvature, low-speed deviation, and free-road status.Source: §B.2 · p. 15
  • Kinematic and comfort costs use acceleration, curvature, longitudinal and lateral jerk, and curvature-rate violations; comfort thresholds include 8.37 for jerk and 0.30 for curvature rate.Source: §B.2 · p. 15
  • Goal progress targets the expert-future endpoint when available; otherwise it uses reachable progress, capped 2 m before an active red-light stop line.Source: §B.2 · p. 15

B.3 RULE CONSTANTS AND AGGREGATION

  • The six rules use fixed physical thresholds; costs are averaged over active elements except collision, and Teacher targets use atomic-cost gradients before weighting or EMA normalization.The principal rule constants are collected in Table 8.Source: §B.3 · p. 15, Table 8 · p. 15

B.4 EXTERNAL ROLLOUT-RISK ENDPOINTS

  • Rollout-risk endpoints are computed from executed ego and agent states, not differentiable training costs; examples include physical overlap, lane-boundary margin, and incomplete route progress.Source: §B.4 · pp. 15–16
  • Collision and TTC risks use 2 s future windows, while lane, speed, kinematics, comfort, and goal use 8 s; temporal Spearman is averaged across eligible scenarios.The shuffled control permutes attribution within each scenario, and confidence intervals use 10,000 scenario-level bootstrap resamples.Source: §B.4 · p. 16

B.5 COMPLETE HEAD–TEACHER FIDELITY METRICS

The supplied metrics cover per-rule correlation and agreement between Head and Teacher outputs.

B.5 COMPLETE HEAD–TEACHER FIDELITY METRICS

  • The fidelity metrics include per-rule correlation and its macro-average.Source: §B.5 · p. 16
  • The section also defines numerical agreement and dominant-rule agreement as fidelity measures.Source: §B.5 · p. 16

B.6 COMPLETE TEMPORAL-ALIGNMENT METRICS

The temporal-alignment metrics evaluate whether rule attributions track future rule-specific risks across scenarios and endpoints. They include correlation and event-retrieval measures, alongside controls and uncertainty estimates.

B.6 COMPLETE TEMPORAL-ALIGNMENT METRICS

  • Continuous temporal alignment is computed per rule and scenario, and the reported macro score averages across seven evaluated endpoints.Source: §B.6 · p. 16
  • AUPRC treats attribution as a continuous event-retrieval score and is macro-averaged over eligible scenarios.Source: §B.6 · p. 16
  • The random-ranking AUPRC baseline equals the positive-event rate; temporal controls permute attribution within scenarios, and confidence intervals use 10,000 scenario-level bootstrap resamples.Source: §B.6 · p. 16

C.1 NON-REACTIVE PLANNING RESULTS

The appendix reports supplementary non-reactive aggregate scores and details planner adaptation, teacher-pressure calibration and caching, and the trajectory-conditioned attribution head.

C.1 NON-REACTIVE PLANNING RESULTS

  • Table 9 reports closed-loop aggregate scores with non-reactive agents as supplementary results to the main text’s reactive evaluation.The supplied passage gives the table’s scope but no score values.Source: §C.1 · p. 16, Table 9 · p. 17

C.2 PLANNER ADAPTATION

  • RADP starts from the released Diffusion Planner checkpoint and restricts LoRA to mlp1 and mlp2 fc1/fc2 modules while keeping other planner components frozen.Twelve linear modules are replaced; the adaptation uses batch size 128 and learning rate 2 × 10^-5.Source: §C.2 · p. 17

C.3 TEACHER CALIBRATION AND CACHING

  • Teacher-pressure calibration uses the 75th percentile of non-negative RMS gradients from 100 training calibration batches for each of six attribution channels.The frozen planner cache contains 100,000 training samples and 20,000 non-overlapping validation samples.Source: §C.3 · p. 17

C.4 TRAJECTORY-CONDITIONED SCENE ATTENTION HEAD DETAILS

  • A trajectory-derived query attends to valid scene tokens, letting the same trajectory retrieve context according to surrounding traffic and road geometry.Planner-side representations are detached and frozen during attribution-head training.Source: §C.4 · p. 17
  • Six independent MLP branches predict non-negative pressures for collision, lane, overspeed, kinematics, comfort, and goal progress.The planner, including its LoRA adapters, remains frozen; the head is supervised by cached gradient-pressure targets, not future rollout risks.Source: §C.4 · pp. 17–18

C.5 EVALUATION REPRODUCIBILITY

The reproducibility details specify synchronized-frame attribution comparisons and fixed evaluation settings, and distinguish end-to-end latency from attribution-only timing.

C.5 EVALUATION REPRODUCIBILITY

  • Attribution fidelity uses synchronized planner, scene, and trajectory frames; future-risk alignment pairs current attribution with risk over the same rollout’s rule-specific horizon.Thresholds, windows, and aggregation operators are fixed before inspecting head results and shared by teacher and head.Source: §C.5 · p. 18

C.6 LATENCY DETAILS

  • Table 10 reports mean ± standard deviation latency on an RTX 4080, separating end-to-end trajectory generation from cached-state attribution computation.End-to-end timing uses five fixed test14-hard-r scenarios; cached-state attribution uses 500 synchronized frames.Source: Table 10 · p. 18, §C.6 · p. 18

C.7 COMPLETE CONFIDENCE INTERVALS FOR MAIN-TEXT ATTRIBUTION RESULTS

The appendix supplies scenario-level confidence intervals for attribution results and additional matched collision-avoidance rollouts.

C.7 COMPLETE CONFIDENCE INTERVALS FOR MAIN-TEXT ATTRIBUTION RESULTS

  • Tables 11 and 12 report 95% confidence intervals for attribution fidelity and future-risk alignment, with scenario-level resampling to account for correlated frames.Table 11 covers reactive splits; Table 12 gives rule-wise future-risk alignment on val14-r.Source: §C.7 · p. 18, Table 11 · p. 19, Table 12 · p. 19

D ADDITIONAL COLLISION-AVOIDANCE CASES

  • Four matched test14-hard-r scenarios show Baseline at-fault collisions where RADP does not, with both planners compared at identical simulation indices through the contact frame.Figure 5 additionally shows Baseline contact and collision-free RADP frames in high-speed vehicle and pedestrian-crossing interactions.Source: D ADDITIONAL COLLISION-AVOIDANCE CASES · p. 20, Figure 5 · p. 20
  • Figure 6 presents matched rollouts for dense multi-vehicle and left-turn conflicts, using identical frame indices for Baseline and RADP in every column.The supplied caption identifies the scenarios and frame matching but does not state their collision outcomes.Source: Figure 6 · p. 21

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