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

Jiaxi Ye; Chunji Lv; Guoren Wang; Changsheng Li

cs.LGSep 30, 2026

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

Authors: Jiaxi Ye, Chunji Lv, Guoren Wang, Changsheng Li

Organizations: Beijing Institute of Technology

Abstract

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.

Figures & tables

Rule channel	Violation signal	Purpose
Collision	Insufficient ego–agent clearance	Avoid imminent collisions
Lane	Route-corridor boundary violation	Maintain lane and route compliance
Speed	Speed above the legal limit	Enforce speed-limit compliance
Kinematics	Excess acceleration, braking, or steering	Ensure dynamic feasibility
Comfort	Excess jerk or control variation	Encourage smooth motion
Goal	Insufficient route progress	Preserve planning efficiency

Table 1: Six rule channels for planning and attribution.

Figure 2: Online rule-pressure attribution head.

Split	Planner	Score	Collision	TTC	Drivable	Progress	Speed	Comfort
val14	Diffusion Planner	82.70	92.98	87.84	97.85	96.60	98.29	89.45
val14	RADP(ours)	81.37	94.01	89.53	98.03	94.90	98.87	89.27
test14-random	Diffusion Planner	82.82	94.06	89.66	98.08	97.70	97.07	85.44
test14-random	RADP(ours)	84.48	96.36	91.95	98.08	96.93	97.98	87.36
test14-hard	Diffusion Planner	68.94	86.95	79.78	94.85	92.65	97.39	85.29
test14-hard	RADP(ours)	70.62	92.10	83.46	95.59	90.07	98.29	85.29

Table 2: Closed-loop planning performance with reactive agents.

Type	Planner	Val14-R	Hard-R	Random-R
Expert	Log-replay	80.32	68.80	75.86
Learned	PDM-Open	54.24	35.83	57.23
	UrbanDriver	64.11	49.95	67.15
	GameFormer	8.69	6.69	9.31
	PlanTF	76.95	61.61	79.58
	PLUTO	78.11	59.74	78.62

Table 3: Literature-reported reactive nuPlan scores.

Reactive split	Head–Teacher fidelity			Future-risk alignment
Reactive split	Macro Spearman $\uparrow$	MAE $\downarrow$	Top-1 $\uparrow$	Teacher $\rho_{\mathrm{macro}}$ $\uparrow$	Head $\rho_{\mathrm{macro}}$ $\uparrow$
val14	0.536	0.216	70.6%	0.235	0.207
test14-random	0.570	0.200	71.7%	0.199	0.177
test14-hard	0.554	0.238	71.9%	0.221	0.192

Table 4: Head–Teacher fidelity and future-risk alignment in reactive closed-loop simulation.

Channel	Risk endpoint	Pos. rate	AUPRC $\uparrow$		Lift@10% $\uparrow$		Temporal $\rho$ $\uparrow$		Shuffled $\rho$
Channel	Risk endpoint	Pos. rate	Teacher	Head	Teacher	Head	Teacher	Head	Teacher	Head
Collision	Physical collision	2.37%	0.540	0.514	1.823	1.598	0.234	0.160	0.001	$-0.002$
Collision	TTC risk (aux.)	4.11%	0.555	0.489	1.926	1.610	0.237	0.158	$-0.000$	$-0.000$
Lane	Lane-boundary risk	49.31%	0.911	0.840	1.518	1.340	0.314	0.234	0.001	0.000
Speed	Overspeed risk	6.87%	0.779	0.761	1.890	1.895	0.303	0.297	$-0.001$	$-0.001$
Kinematics	Kinematic risk	0.013%	0.167	0.250	0.000	0.000	0.112	0.159	$-0.000$	0.000

Table 5: Frame-level future-risk alignment on val14-r.

Method	Latency (ms)	Overhead
Planner only	251.05	—
Planner + Head	245.50	$-1.64\%$
Planner + exact Teacher	465.29	$+89.18\%$
Planner + gradient guidance	571.10	$+130.76\%$
Exact Teacher on cached states	62.51	$1.00\times$
Head on cached states	8.18	$7.65\times$ faster

Table 6: Mean inference latency on an RTX 4080.

Panel of Figure 3 — Figure 3: A starting_left_turn case from test14-hard-r. (a) shows the Head’s frame-wise rule pressures. (b) reports front-agent clearance and TTC. (c) shows signed ego-body clearance to the route-corridor boundary.

Panel of Figure 4 — Figure 4: Matched closed-loop views. Baseline and RADP are shown near the two critical interactions; yellow and blue denote the ego vehicle and neighbors.

Setting	Score	Collision	TTC	Drivable	Progress	Speed	Comfort
Collision-Guided Diffusion Planner	59.92	76.65	68.75	90.44	95.96	96.00	60.66
FFN-LoRA (no rules)	69.20	88.42	81.62	95.96	90.44	98.37	86.03
No normalization	67.78	85.11	77.57	93.75	93.38	95.93	84.56
RADP	70.62	92.10	83.46	95.59	90.07	98.29	85.29

Table 7: Rule ablations on test14-hard-r (

\uparrow

). Training variants use the same configuration; collision guidance is applied during DPM sampling.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Rule	Threshold	Physical scale $\sigma$	Weight $w_{i}$	Other constants
Collision	$d_{0}=0.5$ m, $t_{\rm head}=0.8$ s, $a_{\rm brake}=4.0$ m/s 2	$0.5$ m	$2.5$	Active distance $20$ m, risk TTC $4$ s, softmax $\alpha=8$
Lane	Ego-body boundary crossing	$0.5$ m	$0.8$	Centerline weight $0.05$ , center scale $2.0$ m
Speed	$v>v^{\lim}$	$1.0$ m/s	$0.8$	Time steps without a valid speed limit are masked out
Kinematics	$a_{\rm lon}\leq 6$ , $-a_{\rm lon}\leq 8$ , $\|a_{\rm lat}\|\leq 4.5$ , $\|\kappa\|\leq 0.35$	$1,1,1,0.05$	$0.5$	—
Comfort	$\|j_{\rm lon}\|,\|j_{\rm lat}\|\leq 8.37$ , $\|\dot{\kappa}\|\leq 0.30$	$1,1,0.1$	$0.8$	—
Goal progress	Reachable/expert progress deficit	$5.0$ m	$1.5$	Lateral weight $0.1$ , monotonicity weight $0.2$ , stopping buffer $2$ m

Appendix

Table 8: Principal rule constants used in the implementation.

Split	Diffusion Planner	RADP
val14	89.65	88.72
test14-random	88.88	89.46
test14-hard	75.01	74.80

Appendix

Table 9: Closed-loop planning scores with non-reactive agents (

\uparrow

Method	Latency (ms)	Overhead
Planner only	$251.05\pm 39.04$	—
Planner + Head	$245.50\pm 30.43$	$-1.64\%\pm 6.67\%$
Planner + exact Teacher	$465.29\pm 66.46$	$+89.18\%\pm 38.35\%$
Planner + gradient guidance	$571.10\pm 52.64$	$+130.76\%\pm 30.01\%$
Exact Teacher on cached states	$62.51\pm 3.69$	$1.00\times$
Head on cached states	$8.18\pm 1.20$	$7.65\times$ faster

Appendix

Table 10: Inference latency details on an RTX 4080. Values are mean

\pm

standard deviation; lower is better.

Reactive split	Head–Teacher fidelity 95% CI			Future-risk alignment 95% CI
Reactive split	Macro Spearman	MAE	Top-1	Teacher $\rho_{\mathrm{macro}}$	Head $\rho_{\mathrm{macro}}$
val14	[0.525, 0.547]	[0.209, 0.222]	[69.4, 71.8]%	[0.213, 0.256]	[0.183, 0.229]
test14-random	[0.552, 0.588]	[0.188, 0.212]	[69.5, 73.9]%	[0.133, 0.258]	[0.119, 0.233]
test14-hard	[0.537, 0.571]	[0.224, 0.251]	[69.7, 74.0]%	[0.184, 0.255]	[0.151, 0.231]

Appendix

Table 11: 95% confidence intervals for Head–Teacher fidelity and macro-averaged future-risk alignment on reactive splits.

Attribution channel	Risk endpoint	Teacher AUPRC	Head AUPRC	Teacher Lift@10%	Head Lift@10%	Teacher $\rho$	Head $\rho$
Collision	Physical collision	[0.481,0.604]	[0.452,0.578]	[1.388,2.257]	[1.184,2.019]	[0.158,0.302]	[0.077,0.252]
Collision	TTC risk	[0.516,0.598]	[0.450,0.527]	[1.640,2.212]	[1.334,1.896]	[0.196,0.274]	[0.115,0.198]
Lane	Lane-boundary risk	[0.894,0.928]	[0.815,0.864]	[1.422,1.617]	[1.260,1.428]	[0.283,0.345]	[0.206,0.265]
Speed	Overspeed risk	[0.725,0.829]	[0.701,0.816]	[1.553,2.254]	[1.556,2.285]	[0.198,0.402]	[0.200,0.388]
Kinematics	Kinematic risk	[0.167,0.167]	[0.250,0.250]	[0.000,0.000]	[0.000,0.000]	[0.079,0.143]	[0.123,0.194]
Comfort	Comfort risk	[0.162,0.679]	[0.156,0.598]	[0.000,4.375]	[0.000,3.500]	[0.072,0.133]	[0.089,0.155]

Appendix

Table 12: Scenario-bootstrap 95% confidence intervals for rule-wise future-risk alignment on val14-r.

Panel of Figure 5 — Figure 5: Matched collision-avoidance rollouts. Top: a high-speed vehicle interaction (token 3f9e713baeec55a9 ). Bottom: a pedestrian-crossing interaction (token 159942fd13675580 ). The Baseline makes contact in the final column, whereas RADP remains collision-free at the corresponding frame.

Panel of Figure 6 — Figure 6: Additional matched collision-avoidance rollouts. Top: a dense multi-vehicle interaction (token 4f3e807c698a5335 ). Bottom: a left-turn vehicle conflict (token e10289f39c5f5bea ). Identical frame indices are used for Baseline and RADP in every column.

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PC-Diffuser: Path-Consistent Capsule CBF Safety Filtering for Diffusion-Based Trajectory Planner

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Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA

Diffusion Planning Autonomous Driving Trajectory Generation Safety Filters Control Barrier Functions

Open paper AskPDF arXiv

Autonomous driving in complex traffic requires planners that generalize beyond hand-crafted rules, motivating data-driven approaches that learn behavior from expert demonstrations. Diffusion-based trajectory planners have recently shown strong closed-loop performance by iteratively denoising a full-horizon plan, but they remain difficult to certify and can fail catastrophically in rare or out-of-distribution scenarios. To address this challenge, we present PC-Diffuser, a safety augmentation framework that embeds a certifiable, path-consistent barrier-function structure directly into the denoising loop of diffusion planning. The key idea is to make safety an intrinsic part of trajectory generation rather than a post-hoc fix: we enforce forward invariance along the rollout while preserving the diffusion model's intended path geometry. Specifically, PC-Diffuser (i) evaluates collision risk using a capsule-distance barrier function that better reflects vehicle geometry and reduces unnecessary conservativeness, (ii) converts denoised waypoints into dynamically feasible motion under a kinematic bicycle model, and (iii) applies a path-consistent safety filter that eliminates residual constraint violations without geometric distortion, so the corrected plan remains close to the learned distribution. By injecting these safety-consistent corrections at every denoising step and feeding the refined trajectory back into the diffusion process, PC-Diffuser enables iterative, context-aware safeguarding instead of post-hoc repair...

Abstract

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