MomADv2: Reliable Temporal Memory for End-to-End Autonomous Driving

• Long-horizon planning depends on temporally consistent planning states; MomAD (Song et al. 2025) uses historical planning queries to reduce mode instability and trajectory jitter.Such planning supports anticipation of future behaviors and proactive risk perception in complex traffic interactions.Source: Introduction · p. 1
• Because scene changes, temporal discontinuities, and command shifts can make history unreliable, MomADv2 selectively retains useful memory and suppresses invalid or command-inconsistent information.This addresses the risk that blindly reused history may mislead planning.Source: Introduction · p. 1
• MomADv2 combines SSM-Q, which filters historical queries and models planning intentions, with FM-Ref, which learns residual trajectory corrections while preserving anchor-based planning stability.SSM-Q selects command-relevant modes using temporal continuity and command consistency; FM-Ref learns a continuous correction field from refined output toward the expert trajectory.Source: Introduction · pp. 1–2
• 15.6% lower 6-second collision rate than MomAD, with experiments also reporting improved long-horizon planning consistency and trajectory accuracy.Evaluations span closed-loop NAVSIM and Bench2Drive and open-loop nuScenes.Source: Introduction · p. 2

End-to-End Autonomous Driving

• E2E-AD studies cover unified planning, efficient decoding, generative trajectories, planning optimization, large-model cognition, and world models, yet temporal-memory reliability is overlooked.Representative work includes Hu et al. 2023; Jiang et al. 2023, 2026; Jia et al. 2023, 2025; Sun et al. 2024; Li et al. 2024; Liao et al. 2025; Xing et al. 2025; Liu et al. 2025b; Song et al. 2026b; Shang et al. 2025; Zheng et al. 2026; Zhou et al. 2025; and Song et al. 2026a. Reused history can conflict with current scenes or commands and cause negative interference, motivating selective retention of reliable memory and suppression of invalid history.Source: End-to-End Autonomous Driving · p. 2

State Space Models for Autonomous Driving

• SSMs support long-range sequence modeling with selective state transitions and linear-complexity computation, but SSM-based E2E-AD work leaves historical-memory reliability in long-horizon planning underexplored.SSMs have also been applied to visual representation learning, occupancy prediction, and E2E-AD.Source: State Space Models for Autonomous… · p. 2

Overview of MomADv2

• MomADv2 encodes multi-view images into sparse scene representations, then uses an anchor-based decoder to produce multi-modal motion predictions and initial ego-planning candidates.It adds a selective state-space memory module and a flow-matching residual refiner to this planning pipeline.Source: Overview of MomADv2 · p. 2

Selective State-Space Planning Memory Query

• SSM-Q retrieves command-consistent, temporally continuous historical queries, aligns candidates by trajectory similarity, and selectively models planning-intention evolution.A token-keyed bank stores raw queries and baseline command-specific trajectories, avoiding recursive storage of SSM-corrected outputs. Reliability-aware aggregation weights valid history by trajectory similarity and temporal decay; memory activates only when enough valid, consistent history is available. A selective state-space encoder processes the sequence, and a reliability-gated, norm-constrained residual update limits perturbations to the current query.Source: Selective State-Space Planning Memory… · pp. 3–4

Flow-Matching Trajectory Residual Refiner

• FM-Ref learns a query-conditioned residual velocity field from planner-refined candidates toward expert trajectories, then applies gated residual corrections during inference.Training uses flow-matching supervision and a regression loss for the flow-refined trajectory alongside planner and SSM objectives; inference integrates the field with two Euler steps while bounding residual strength to preserve anchor-based stability.Source: Flow-Matching Trajectory Residual… · pp. 4–5

Datasets and Metrics

• Experiments cover open-loop nuScenes and closed-loop Bench2Drive and NAVSIM, using L2 displacement error and collision rate, DS and SR, and closed-loop planning metrics, respectively.The nuScenes evaluation uses multi-view images; Bench2Drive uses 1,000 base-split training clips and 220 evaluation routes, while NAVSIM uses non-reactive simulation.Source: Datasets and Metrics · p. 5

Main Results

• MomADv2 records a 1.21 m average L2 error and 0.76% collision rate on 6-second nuScenes planning, improving these metrics by 11.7% and 11.6% over the strongest prior method.It achieves the best performance across all reported timestamps.Source: Table 1 · p. 6, Main Results · p. 6
• On Bench2Drive, MomADv2 reaches 78.82 DS and best Comfortness of 31.23, improving MomAD from 47.91 to 52.32 DS and from 18.11% to 24.24% SR.The comparison uses the base training set.Source: Table 2 · p. 6, Main Results · p. 6
• On NAVSIMv1 navtest, MomADv2 achieves 99.0 NC, 97.1 DAC, 95.5 TTC, 83.2 EP, and 89.9 PDMS.The passage reports competitive safety, progress, and planning stability.Source: Table 3 · p. 6, Main Results · pp. 6–7

Implementation Details

• The experiments use ResNet-50 for nuScenes, Adv-nuSc, and Bench2Drive, and ResNet-34 with the same perception modules as TransFuser for NAVSIM.Training uses 8 RTX 4090 GPUs; the batch sizes are 48 for nuScenes and Bench2Drive and 64 for NAVSIM, with 20, 2, and 100 epochs, respectively.Source: Implementation Details · p. 6

Main Results

• On NAVSIMv2, MomADv2 achieves best EPDMS of 39.5 on navhard and 87.9 on navtest, ranking first on navtest DDC, EP, and EC.On navhard it maintains strong Stage-2 performance, especially on DAC and TTC.Source: Table 4 · p. 6, Table 5 · p. 6, Main Results · p. 7

Ablation Studies

• SSM-Q raises PDMS from 84.0 to 86.9, FM-Ref further raises it to 89.9, selective memory yields the lowest collision rate at 0.76%, and K=4 achieves best PDMS of 89.9.Longer histories gradually degrade performance; the full selective strategy outperforms naive fusion and partial filtering variants.Source: Ablation Studies · p. 7, Table 6 · p. 7, Table 7 · p. 7

Visualization

• MomADv2’s consecutive trajectories across t−1, t, and t+1 are more temporally consistent and closer to ground truth than MomAD’s.Figure 4 visualizes the comparison with MomAD and MambaFlow on nuScenes.Source: Figure 4 · p. 7, Visualization · p. 7

Conclusion

• MomADv2 consistently improves long-horizon planning accuracy, temporal consistency, and driving safety on NAVSIM, Bench2Drive, and nuScenes.The conclusion reports these results across the three benchmarks.Source: Conclusion · p. 7
• The Selective State-Space Planning Memory Query Module filters historical queries for temporal continuity and command consistency, selects command-relevant modes, and models planning-intention evolution.It selectively preserves useful history while suppressing stale or command-inconsistent memory.Source: Conclusion · p. 7
• The Flow-Matching Trajectory Residual Refiner learns a continuous correction field to mitigate local trajectory deviations and accumulated planning errors while preserving anchor-based planning stability.Source: Conclusion · p. 7

Limitation and Future Work

• MomADv2 relies on predefined driving commands and does not explicitly model uncertainty in future scene evolution; future work targets command-free intention inference, uncertainty-aware memory selection, and world-model-based reasoning.Source: Conclusion · p. 7

A.1 Broader Impacts

• MomADv2 may improve autonomous-driving safety and reliability by enhancing long-horizon planning consistency and suppressing unreliable temporal memory.The proposed capabilities may support safer interactions and more stable decision-making in complex traffic environments.Source: §A.1 · p. 10
• Its selective state-space memory mechanism preserves useful historical context for planning.This is intended to suppress unreliable temporal memory.Source: §A.1 · p. 10
• Its flow-matching trajectory refiner improves trajectory accuracy and smoothness.Source: §A.1 · p. 10
• These capabilities may support safer interactions in autonomous driving.Source: §A.1 · p. 10
• MomADv2 may enable more stable decision-making and greater robustness in complex traffic environments.Source: §A.1 · p. 10
• The reliable temporal modeling paradigm may benefit sequential decision-making systems in robotics and embodied intelligence.Source: §A.1 · p. 10

• MomADv2 selectively preserves useful temporal information and suppresses stale or command-inconsistent memory to improve long-horizon planning consistency, trajectory stability, and robustness.Source: §A.2 · p. 10
• SSM-Q retrieves historical planning queries using command consistency, temporal continuity, and trajectory-level alignment, then models planning-intention evolution with a selective state-space mechanism.Source: §A.2 · p. 10
• FM-Ref learns a conditional residual velocity field to progressively correct local trajectory deviations while preserving anchor-based planning stability.Source: §A.2 · p. 10

NAVSIM

• NAVSIM evaluates standard driving scenes on navtest and safety-critical long-tail scenes on navhard, using PDMS for NAVSIM-v1 and EPDMS for NAVSIM-v2.NAVSIM-v2 navhard uses two stages: evaluation on the original observation, then re-evaluation with synthesized future observations around the Stage-1 endpoint; scores are percentages, with higher values better.Source: §A.3 · p. 10

Bench2Drive

• Bench2Drive tests closed-loop driving on 220 short routes across 44 interactive scenarios, reporting driving, success, efficiency, comfort, and five advanced-ability metrics.The five abilities are Merging, Overtaking, Emergency Brake, Give Way, and Traffic Sign; open-loop evaluation on logged data additionally reports average L2 displacement error and trajectory diversity.Source: §A.3 · p. 10

nuScenes

• nuScenes open-loop evaluation uses 1,000 real-world scenes to measure short-horizon planning at 1–3 seconds and long-horizon planning at 4–6 seconds.Metrics include L2 displacement error, collision rate, and trajectory diversity for multi-mode planners; predictions do not affect subsequent scene evolution.Source: §A.3 · p. 10

PDM and PDMS

• NAVSIM’s PDMS simulates candidate trajectories and combines hard collision and drivable-area penalties with soft progress, time-to-collision, and comfort objectives.An at-fault collision or leaving the drivable area makes its corresponding subscore zero; non-at-fault collisions are ignored in the non-reactive setting.Source: §A.4 · pp. 10–11

EPDMS

• NAVSIM-v2’s EPDMS adds driving-direction, traffic-light, lane-keeping, history-comfort, and extended-comfort terms to the PDMS metrics.Human filtering ignores a violation also committed by the human trajectory in that scene, reducing penalties from annotation noise or contextually necessary maneuvers; default weights are βEP = 5, βTTC = 5, and βLK = βHC = βEC = 2.Source: §A.4 · p. 11

NAVSIM-v2 Navhard

• NAVSIM-v2 navhard multiplies the original-observation score by a Gaussian-weighted score aggregated across synthetic observations around plausible future ego states.Its two-stage pseudo-simulation assesses immediate planning and robustness to future observation shifts, making it stricter than NAVSIM-v1 PDMS or NAVSIM-v2 navtest.Source: §A.4 · p. 11

Bench2Drive Metrics

• Bench2Drive (Jia et al. 2024) reports closed-loop route success, driving score, efficiency, comfortness, and ability-wise scores across five interactive abilities.Success Rate is the proportion of routes completed on time without traffic violations; Driving Score combines route completion and infraction penalties, while Multi-Ability is the arithmetic mean of the five ability scores. Open-loop evaluation also reports average L2 displacement error and trajectory diversity.Source: §A.4 · pp. 11–12

nuScenes Metrics

• On open-loop nuScenes (Caesar et al. 2020), evaluation reports average L2 displacement error and collision rate for the selected ego trajectory.Collision rate counts samples where the predicted oriented ego footprint overlaps a surrounding actor, estimating heading from consecutive trajectory points; lower displacement error and collision rate indicate more accurate and safer planning.Source: §A.4 · p. 12
• For multi-mode planners, time-conditioned Div(t) measures normalized pairwise distance between trajectory modes, with higher values indicating greater diversity and values near zero indicating mode collapse.Average diversity is computed over reported future timestamps; the metric is applicable only to multi-mode planning methods (Song et al. 2026b).Source: §A.4 · p. 12

Temporal-Link Construction and Memory Reset

• The temporal-continuity token is a frame-level predecessor identifier used only for memory indexing and hard validity masking, while memory resets at sequence or scene boundaries and invalid frame intervals.During a sequence’s first K frames, only valid available entries are used; without valid history, the temporal residual is zero and planning falls back to the single-frame branch.Source: §A.5 · p. 12

Memory Contents and Causal Update

• The FIFO memory stores at most K=4 entries under frame and command keys, retrieves only command-matched history, and writes the current entry after producing the planning result.Only pre-enhancement queries and baseline trajectories are stored; read-before-write prevents self-retrieval, and enhanced queries and flow-refined trajectories are not written back.Source: §A.5 · p. 12

Temporally Shifted Trajectory Distance

• SSM-Q aligns historical and current candidate trajectories over shared future times by removing elapsed waypoints, transforming ego coordinates, and interpolating noninteger temporal offsets before distance comparison.This alignment accounts for trajectories having different temporal origins, so matching driving intentions are not treated as inconsistent solely because their predictions began at different times.Source: §A.5 · pp. 12–13

Handling Inaccurate Baseline Candidates

• Minimum shifted-distance associations determine similarity and reliability; entries with no overlapping horizon, temporal discontinuity, command mismatch, or poor alignment are suppressed, leaving the current query unchanged if none survive.Baseline trajectories serve as association cues rather than being directly propagated as the final output.Source: §A.5 · p. 13

Causal Online Inference

• Causal inference evaluates perception once, then runs baseline planning, memory retrieval and alignment, SSM query enhancement, planning refinement, and flow refinement with S=2 Euler evaluations.Parameters remain fixed during inference; only the explicit memory state changes, making this online stateful inference rather than test-time optimization or adaptation.Source: §A.5 · p. 13

A.6 Implementation Details

• MomADv2 is trained in two stages: baseline pretraining followed by adaptation that freezes most pretrained components and optimizes the new temporal-memory and trajectory-refinement modules.The second stage runs for 10 epochs at 3 × 10^-6 learning rate; the approach is intended to limit interference, stabilize integration, and improve training efficiency. It uses ResNet-50, 256×704 inputs, a 55 m detection radius, a 60×30 m mapping range, six trajectory modes, and 8 RTX 4090 GPUs.Source: §A.6 · p. 13

A.7 More Planning Results

• MomADv2 reaches a 49.02% mean with expert distillation, outperforming DriveAdapter and DIVER by 16.5% each; without distillation, it ranks first across abilities, raising mean score from 22.67% to 25.84% over DIVER.With expert distillation, it leads on Merging and Traffic Sign; without it, the reported ability gains include merging, overtaking, emergency braking, and traffic-rule compliance.Source: Table 9 · p. 14, §A.7 · p. 14
• MomADv2 lowers nuScenes TPC error by 12.6% at 4 seconds and 9.0% at 5 seconds versus MomAD, matches the best baseline at 6 seconds, and reduces average TPC error by 6.6%.Its TPC errors are 1.04 m and 1.32 m at the 4- and 5-second horizons, respectively, and 1.61 m at 6 seconds.Source: Table 10 · p. 14, §A.7 · p. 14
• MomADv2 reduces average collision rate from 0.09% to 0.07% and 3-second collision rate from 0.22% to 0.18%, while its average L2 error of 0.54 m improves on MomAD by 10.0%.Its average collision rate of 0.07% matches DIVER and GuideFlow, and its average L2 error improves on GraphWorld by 5.3%; SSR has lower displacement error but a higher average collision rate.Source: Table 11 · p. 14, §A.7 · pp. 14–15

A.8 More Ablation Results

• SSM-Q consistently reduces trajectory error and collision rate across horizons; adding FM-Ref yields L2 errors of 1.32, 1.82, and 2.40 m and collision rates of 0.72%, 1.33%, and 2.03% at 4, 5, and 6 seconds.The ablation reports complementary benefits from selective temporal memory and flow-matching residual refinement.Source: Table 12 · p. 14, §A.8 · p. 15
• Selective SSM/Mamba achieves the best planning accuracy and collision performance among the compared temporal memory methods, while Vanilla SSM offers a better efficiency-performance trade-off than Concat + MLP, GRU/LSTM, and Transformer.Concat + MLP lacks temporal modeling ability, while GRU/LSTM and Transformer improve planning performance at higher latency.Source: Table 13 · p. 14, §A.8 · p. 15
• Euler improves PDMS from 89.0 to 89.9 and FPS from 38 to 43 versus Heun, providing a better planning-quality and inference-efficiency trade-off for FM-Ref.The results indicate that the simple Euler solver is sufficient for residual trajectory refinement.Source: Table 14 · p. 14, §A.8 · p. 15

A.9 More Qualitative Study of Planning Results

• Qualitative examples show smoother, more temporally coherent MomADv2 trajectories that better follow lane and drivable-area constraints and maintain stable intentions in long-horizon turns and dense traffic.The NAVSIM comparison with GuideFlow depicts safer interactions and fewer aggressive deviations; the nuScenes 6-second visual attributes stability to retaining reliable history, suppressing stale or command-inconsistent memory, and refining local deviations.Source: Figure 5 · p. 15, §A.9 · pp. 15–16, Figure 6 · p. 16