BridgeGuard: Explicit Safety Drift for Diffusion-based Autonomous Driving

1 INTRODUCTION

• Existing safety strategies rely on proposal coverage, informative cost gradients along sampling paths, or accurate scene geometry, while direct driving adaptations of MBM face scene- and horizon-dependent constraints and waypoint distortion.Learning expert behavior alone does not ensure safety under limited data coverage or distribution shift.Source: §1 · p. 1
• BridgeGuard adapts MBM with a learned scene- and horizon-dependent distance field, supervised on safe and unsafe regions beyond expert paths, and applies its gradients through low-dimensional curve corrections.The pretrained backbone and planner remain frozen.Source: §1 · pp. 1–2
• The terminal-safety guarantee holds only for an idealized continuous-time bridge under stated assumptions and does not directly extend to the learned field and discretized corrections.The paper establishes sufficient conditions for terminal safety in that idealized setting.Source: §1 · p. 2
• On Bench2Drive, BridgeDrive driving score rises from 87.99 to 90.88 and success rate from 74.99% to 76.36%; DiffusionDrivegeo rises from 80.79 to 90.46 and 58.18% to 74.09%.The results demonstrate cross-model generalization.Source: §1 · p. 2

2.1 DIFFUSION MODELS IN TRAJECTORY PLANNING

• Diffusion planners generate waypoint trajectories through reverse-time denoising; DiffusionDrive refines candidates around multiple anchors, while BridgeDrive selects an anchor and uses a diffusion bridge.The planners retain their waypoint representations, and geometric variants can separately predict target speed.Source: §2.1 · pp. 2–3
• A diffusion bridge conditions generation on a fixed endpoint x_T, with scheduler coefficients defining its Gaussian bridge kernel.The preliminaries also refer to reverse SDE and ODE formulations.Source: §2.1 · pp. 2–3

2.2 CONSTRAINED DIFFUSION AND MANUALLY BRIDGED MODELS

• An Ω-bridge modifies reverse dynamics so terminal samples lie in constraint set Ω with probability one.The definition applies to a constraint set Ω and a modified reverse process.Source: §2.2 · p. 3
• Manually Bridged Models add a time-weighted negative gradient of an Ω-distance to the score, downweighting violations; this alone does not guarantee terminal constraint satisfaction.Sufficient conditions for an Ω-bridge are given by Wu et al. (2022).Source: §2.2 · p. 3

3.1 SAFETY DOMAIN AND DISTANCE FUNCTION

• BridgeGuard evaluates obstacle constraints at fixed physical horizons, mapping planner outputs into time-indexed positions and correcting fitted curves while keeping auxiliary predictions fixed.Its safety domain is defined over the time-indexed positions; correction parameters are resampled into the planner’s original waypoint representation.Source: §3.1 · pp. 3–4, §3.3 · p. 5

3.2 THEORETICAL ANALYSIS

• Under the stated expected gradient-dominance and terminal-domination assumptions, the idealized continuous-time manual bridge places the terminal trajectory in the prescribed safe set almost surely.The guarantee applies to the idealized process, not the approximate curve-space correction.Source: §3.2 · p. 4

3.3 SAFETY INJECTION

• DistanceFieldNet supplies scene- and horizon-dependent gradients, and low-dimensional curve updates refine denoised trajectories without directly distorting waypoint geometry.Training queries sampled from planner trajectories or anchors cover safe and dangerous regions beyond expert paths; Figure 2 contrasts narrow expert-only coverage with broader anchor-based coverage.Source: §3.3 · p. 5, Figure 2 · p. 5

3.4 TRAINING OBJECTIVE AND INFERENCE

• A finite score-level schedule strengthens safety corrections toward the end of denoising, while curve fitting and discretized updates remain approximations without a terminal-safety guarantee.The learned field is trained while the perception backbone and diffusion planner remain frozen.Source: §3.4 · p. 6

3.5 MODEL ARCHITECTURE

• DistanceFieldNet conditions shared BEV features on waypoint positions and physical horizons, then aggregates query outputs into a trajectory-level safety objective whose gradients update curve parameters.The field is coupled to the planner while the pretrained backbone and selected planner remain frozen.Source: §3.5 · pp. 6–7

4.1 CLOSED-LOOP EVALUATION IN CARLA SIMULATOR

• Evaluation uses 220 safety-critical CARLA routes on Bench2Drive; training uses CARLA Garage data, and only DistanceFieldNet is trained while the planner and perception backbone remain frozen.Source: §4.1 · pp. 7–8
• BridgeGuard reaches 90.88 DS and 76.36% SR on BridgeDrive; gains are 2.89 DS/1.37% SR over BridgeDrive and 9.67 DS/15.91% SR over DiffusionDrivegeo.Source: Table 1 · p. 8, §4.1 · p. 8

4.2 ABLATION STUDY AND QUALITATIVE ANALYSIS

• Allowing the third curve coefficient improves DS from 88.65 to 90.88 and SR from 73.18% to 76.36%, while mean ability rises from 64.77% to 69.74% and merging falls from 75.00% to 73.75%.Source: §4.2 · p. 8, Table 2 · p. 9
• Sampling 20 points from two anchors yields the best mean DS (90.96) and SR (75.23%); increasing to 100 points from ten anchors provides no further improvement.Source: §4.2 · p. 8, Table 3 · p. 9
• In the unprotected left-turn and multi-lane-change examples, BridgeDrive collides or enters an occupied lane, while BridgeGuard avoids the conflict and yields safely.Source: §4.2 · p. 8, Figure 4 · p. 9, Figure 5 · p. 9

• The eighth-order superellipse distance function can have small gradients deep inside unsafe regions, weakening correction and making the idealized bridge’s gradient-dominance condition harder to satisfy.Source: §5 · p. 9
• Low-dimensional curve corrections promote geometric coherence but restrict correction directions and may not capture the full diversity of drivable, dynamically feasible trajectories.Source: §5 · p. 9

6 CONCLUSION

• BridgeGuard improves driving score and success rate for both BridgeDrive and DiffusionDrivegeo on Bench2Drive, while its terminal-safety guarantee is limited to an idealized continuous-time bridge.The guarantee does not directly extend to the learned field and discretized corrections.Source: §6 · p. 9

A.1 GENERATIVE MODELS FOR END-TO-END AUTONOMOUS DRIVING

• BridgeGuard complements diffusion-bridge planning with an explicit safety-correction mechanism in the reverse process.Diffusion planners model distributions over trajectories; BridgeDrive refines anchors through a diffusion bridge.Source: §A.1 · p. 13

A.2 SAFETY-GUIDED AND CONSTRAINED TRAJECTORY GENERATION

• BridgeGuard adapts constrained-domain bridges by learning a scene- and horizon-dependent distance field and correcting trajectories in low-dimensional curve space.Sufficient conditions establish terminal membership in the feasible set for the idealized continuous-time full-space process, not its learned and discretized approximations.Source: §A.2 · p. 13

B DIFFUSION MODELS AND DIFFUSION BRIDGE MODELS

• Unlike ordinary diffusion models, diffusion bridges model paired endpoints and condition the reverse process on terminal information.Discarding the terminal endpoint reduces the formulation to the ordinary diffusion-model setting.Source: B DIFFUSION MODELS AND DIFFUSION… · p. 14

C DERIVING ENDPOINT CORRECTIONS FROM SCORE CORRECTIONS

• The paper derives an equivalent endpoint correction for the manual-bridge score adjustment by evaluating the original and corrected scores at the same current state.For the bridge planner, the anchor and scene context remain fixed during this derivation.Source: C DERIVING ENDPOINT CORRECTIONS FROM… · p. 15

D LOW-DIMENSIONAL CONSTRAINED CORRECTION

• Safety correction maps planner waypoints to physical-horizon positions and restricts updates to representable curve changes.The pulled-back gradient gives a descent direction when nonzero, but finite-step objective reduction depends on step magnitude.Source: D LOW-DIMENSIONAL CONSTRAINED CORRECTION · pp. 15–16

E QUERY-CONDITIONED DISTANCE FIELD NETWORK

• DistanceFieldNet predicts per-waypoint distance values conditioned on query location and prediction time, then sums them into a trajectory-level safety objective.Gradients through waypoint coordinates and the trajectory parameterization provide the curve-space correction direction.Source: E QUERY-CONDITIONED DISTANCE FIELD… · pp. 16–17

F IMPLEMENTATION CONFIGURATION

• The implementation configuration summarizes DistanceFieldNet architecture and training and sensor settings in Tables 4 and 5.The query encodings use 256 dimensions, with a convolutional gate and DistanceFieldHead.Source: F IMPLEMENTATION CONFIGURATION · pp. 17–18, Table 4 · p. 18, Table 5 · p. 18
• The pretrained perception backbone and diffusion planner remain frozen; safety injection refines the path while keeping target speed fixed, and a PID controller produces control commands.The planner outputs ten geometric waypoints and a scalar target speed.Source: F IMPLEMENTATION CONFIGURATION · p. 17
• Training labels extrapolate annotated obstacle positions with constant headings, use no additional safety margins, and supervise queries at uniform times over 0.5 s.At inference, field predictions use observed BEV features and waypoint–horizon queries without explicit obstacle dimensions or ground-truth geometry.Source: F IMPLEMENTATION CONFIGURATION · p. 17
• Curve refinement fits y(x) = η1x+η2x2+η4x4 with three parameters; the quadratic ablation removes the quartic term and uses two.Corrected curves are resampled at approximately 1 m arc-length intervals.Source: F IMPLEMENTATION CONFIGURATION · p. 17

G.1 CURVE DIMENSIONALITY: FULL RESULTS

• 20.00% to 30.00% giving way and 60.00% to 68.89% overtaking accompany mean ability rising from 64.77% to 69.74%, despite merging falling from 75.00% to 73.75%.The quartic representation also improves DS and SR and four of five ability metrics.Source: Table 6 · p. 19, §G.1 · p. 19

G.2 EVALUATION WITH LEAD TRAINING

• BridgeGuard achieves state-of-the-art Bench2Drive performance when trained with LEAD, where the performance gap between baselines becomes smaller.The authors attribute the reduced margin to LEAD’s higher quality and fewer safety-critical failure cases for existing baselines.Source: §G.2 · p. 19, Table 7 · p. 19

H SUPPLEMENTARY VIDEOS

• Six supplementary videos pair BridgeDrive and BridgeGuard across two lane changes and one unprotected left turn.Each scenario includes one video for each model.Source: H SUPPLEMENTARY VIDEOS · p. 19

I SUFFICIENT CONDITIONS FOR Ω-BRIDGE

• The sufficient-condition appendix specializes the analysis in Naderiparizi et al. (2025), Appendix C.1, to autonomous driving.Source: I SUFFICIENT CONDITIONS FOR Ω-BRIDGE · p. 19

• Condition 1 requires the expected Polyak–Łojasiewicz condition for the Ω-distance at each fixed diffusion time.Source: §I.1 · p. 20
• Condition 2 requires the integrating factor to dominate the initial value and accumulated drift, time-variation, and diffusion-curvature terms.Source: §I.1 · p. 20
• The section keeps Condition 1 unchanged and replaces the less transparent asymptotic Condition 2 with assumptions interpreted for trajectory planning.Source: §I.1 · p. 20

I.2 A TERMINAL-DOMINATION CONDITION FOR TRAJECTORY PLANNING

• For t in (0, δ], A1–A5 require time-invariant distance, bounded gradient and curvature, controlled drift and diffusion, singular terminal guidance, and well-behaved coefficients away from the endpoint.Source: §I.2 · p. 20
• Under A1–A5, terminal domination implies the original Condition 2.Source: §I.2 · p. 20
• Under Condition 1 and Assumptions A1–A5, the manual bridge term is an Ω-bridge.Source: §I.2 · p. 21

I.3 INTERPRETATION OF CONDITION 1 AND ASSUMPTION A3

• Condition 1 and A3 are the verification challenges because they involve expectations under the reverse-SDE marginal; A3 controls the original reverse dynamics along that law.Source: §I.3 · pp. 21–22
• Condition 1 is distributional gradient dominance: expected distance must be no greater than expected squared gradient norm; a pointwise inequality on reachable states is a stronger sufficient condition.Source: §I.3 · p. 21
• A finite constant in the pointwise inequality can be absorbed by rescaling the potential and inversely rescaling its guidance coefficient.Source: §I.3 · p. 21
• No nonzero globally bounded C1 distance satisfies pointwise PL inequality over all of Rd, but the expected condition can hold if the marginal assigns little mass to such regions.Source: §I.3 · p. 22
• The remaining A3 requirement, boundedness of g2, follows from the chosen analytic diffusion schedule in both VP and VE cases.Source: §I.3 · p. 22