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Diffusion-2BC: Hybrid Diffusion and Regression Training for Offline Behavior Cloning in Autonomous Driving

Bruno Maciel Machado, Eric Aislan Antonelo

arXiv:2609.38472v1cs.ROcs.LG

TL;DR

Behavior cloning with mean-squared error is poorly suited to demonstrations that contain several valid actions for one observation. Diffusion-2BC adds an auxiliary deterministic regression loss to diffusion training while retaining diffusion-based inference. In the evaluated settings, it improves closed-loop route progress relative to the diffusion baseline and preserves qualitative evidence of varied actions and routes.

  • Problem

    A single observation can admit several valid driving actions, while MSE behavior cloning can represent their conditional mean rather than the distinct modes.

    Source: §1 · p. 1, §3.1 · p. 3

  • Method

    Diffusion-2BC trains a shared visual encoder with diffusion denoising and an auxiliary deterministic regression loss, then uses only the diffusion policy at inference.

    Source: §1 · p. 2, §8 · p. 12

  • Results

    In the evaluated settings, Diffusion-2BC improves closed-loop route progress in CARLA and retains qualitative route variation, while the Claw benchmark supports diffusion and hybrid objectives over deterministic MSE regression for disconnected valid action regions.

    Source: §7 · p. 8, §8 · p. 12

  • Takeaways & Limitations

    Under the evaluated datasets and baselines, an auxiliary regression signal improves diffusion behavior cloning’s closed-loop reliability while preserving multimodal prediction in Claw and qualitative route variation in CARLA.

    Source: §8 · p. 12

    The explanation that regression supplies a lower-variance signal to the shared encoder is plausible, not causal; gradient analysis, representation probes, and a systematic α sweep are absent.

    Source: §7 · p. 8

Abstract

from arXiv · show

Behavior cloning provides an offline route to autonomous-driving policy learning, but mean-squared-error regression is poorly matched to demonstrations in which one observation admits several valid actions. Diffusion policies can represent conditional multimodal action distributions, yet their closed-loop performance may be unstable when visual features and control are learned from limited data. This paper presents Diffusion-2BC, which combines a diffusion denoising objective with an auxiliary deterministic behavior-cloning loss over a shared visual encoder. The auxiliary branch is used only during training; inference remains diffusion-based. The proposed method is evaluated in the controlled Claw environment and in bird's-eye-view CARLA navigation, including route-conditioned driving, route-free navigation through multiple intersections, and cross-map evaluation from Town01 to Town02. In the Claw task, Diffusion-2BC reduced the mean mask-distance error by approximately 10% relative to a diffusion-based behavior-cloning baseline and by 85% relative to standard deterministic behavior cloning. In route-free CARLA, Diffusion-2BC traveled substantially farther before termination under the evaluation protocol than both baselines in Town01 and Town02. Additional qualitative rollouts revealed distinct route choices, showing the multimodal behavior of the proposed diffusion-based agent. The results indicate that an auxiliary regression signal can improve the closed-loop reliability of diffusion behavior cloning while preserving multimodal prediction in the controlled benchmark.

1 Introduction

Driving demonstrations can contain multiple valid actions for the same observation, making ordinary regression an imperfect fit. The paper introduces an offline hybrid objective intended to retain diffusion-based multimodal action generation while improving closed-loop performance.

1 Introduction

  • When demonstrations contain separated valid actions, MSE regression can predict an unsafe conditional mean or collapse to one dominant mode, motivating multimodal policies.Diffusion policies can generate different actions for similar observations, but the paper notes that expressiveness alone does not ensure reliable closed-loop driving.Source: §1 · p. 1
  • Diffusion-2BC shares visual features between a diffusion denoising branch and an auxiliary regression branch used only in training, leaving diffusion-based inference intact.The paper evaluates the approach offline using fixed demonstration datasets.Source: §1 · p. 2, §1.1 · p. 2

1.1 Relation to preliminary work and CarRacing motivation

  • The journal article extends preliminary work with Diffusion-2BC and route-conditioned, route-free, and cross-map CARLA evaluations.The preliminary CarRacing study reported higher aggregate mean reward and lower variability for Diffusion-BC than MSE-BC: 861.35 ± 48.07 versus 638.79 ± 105.20.Source: §1.1 · p. 2

2.1 Behavior cloning for autonomous driving

  • Offline behavior cloning learns from fixed demonstrations, but distribution shift can compound policy errors; this study asks how far fixed datasets can support progress without online relabeling.Conditional imitation learning uses route commands, whereas this work addresses unlabeled valid actions jointly present in demonstrations.Source: §2.1 · p. 2

2.2 Multimodal imitation learning

  • Multimodal behavior-cloning methods include mixture-density, latent-variable, energy-based, and discretized-latent approaches, while the evaluation compares only deterministic BC, diffusion BC, and the hybrid.The paper notes that discretization can introduce quantization and separate coordinated control dimensions.Source: §2.2 · pp. 2–3

2.3 Diffusion models for decision-making and control

  • Diffusion models support multimodal action generation through iterative sampling, which increases inference cost; Diffusion-2BC uses diffusion as the executed policy and regression only as an auxiliary training signal.Unlike Diffusion Model-Augmented Behavioral Cloning, Diffusion-2BC removes its deterministic branch at inference [21].Source: §2.3 · p. 3

3 Background

The background contrasts deterministic behavior cloning with diffusion-based action generation. It describes the forward process as progressively noising actions and the reverse process as generating actions conditioned on observation features.

3.1 Offline behavior cloning

  • For separated action modes, deterministic behavior cloning minimizes toward the conditional mean, which may not match a demonstrated action, or may converge to one mode.The objective is appropriate for a conditional action distribution with one concentrated mode.Source: §3.1 · p. 3

3.2 Forward diffusion process

  • The forward diffusion process adds Gaussian noise so that actions become progressively less distinguishable from noise as the timestep increases.The reparameterized closed form allows a noisy action at any timestep to be sampled directly.Source: §3.2 · p. 3

3.3 Conditional reverse process for behavior cloning

  • The denoising network predicts noise from a noisy action, timestep, and observation features; at inference, reverse updates turn sampled noise into an action estimate.Different initial noise samples can produce different valid actions under the same observation, expressing multimodality.Source: §3.3 · p. 3

4 Proposed Diffusion-2BC Method

Diffusion-2BC retains diffusion-based action generation while adding a deterministic regression signal during training. Its shared visual representation supports both objectives, and useful operation requires both loss terms.

4.1 Design rationale

  • Deterministic BC learns route following but cannot represent conflicting intersection decisions, while Diffusion BC represents left and right turns but is less consistent in route-free navigation.Diffusion-2BC retains diffusion inference and adds a direct regression signal during representation learning.Source: §4.1 · p. 3

4.2 Architecture and objective

  • A shared convolutional encoder feeds a denoising network and an auxiliary action-regression head, whose losses are combined using a fixed or scheduled coefficient.The route-conditioned CARLA experiment uses a fixed coefficient of 0.3; the multi-intersection experiment decays it from 1.0 toward 0.01, without a systematic hyperparameter ablation.Source: §4.2 · p. 4

4.3 Network architecture

  • The visual representation conditions a Transformer denoiser, while a separate fully connected head predicts actions directly; the latter is used only during training.The CARLA regression head maps the 4,608-dimensional representation through hidden widths 2,048, 512, 128, and 32 to two controls.Source: §4.3 · p. 4, Figure 1 · p. 5

4.4 Training and inference

  • Training samples a diffusion timestep and Gaussian noise per action, computes both losses from shared observation features, and combines them before one parameter update.At inference, the auxiliary prediction and regression loss are absent, leaving the same test-time computational structure as Diffusion-BC.Source: §4.4 · p. 5

4.5 Interpretation of the auxiliary loss

  • The regression head provides a direct action-to-feature learning path without arbitrating at inference, where stochasticity is preserved by reverse diffusion.At α = 0 the objective reduces to Diffusion-BC; as α approaches one, denoising is progressively downweighted, and useful operation requires both terms. A full schedule ablation remains future work.Source: §4.5 · p. 5

5 Experimental Methodology

The evaluation progresses from controlled multimodal prediction to route-conditioned and route-free CARLA navigation, with the latter also testing transfer to Town02. The protocols use different observations, termination rules, and distance measures.

5.1 Staged evaluation strategy

  • The staged evaluation assigns Claw to multimodal prediction and CARLA to route following, route-free navigation, route diversity, and cross-map behavior.The organization separates conclusions supported by the controlled environment from the main closed-loop CARLA evaluation.Source: §5.1 · p. 5

5.2 Claw environment

  • Claw images contain toy shapes, and actions are 2D points; images with multiple objects have several disconnected valid action regions.The protocol trains on 20,000 pairs, evaluates 300 sampled actions on each of seven held-out observations, and scores mean distance to the nearest valid mask point; it is also repeated with 90% of the training data.Source: §5.2 · pp. 5–6

5.3 CARLA observations and controls

  • CARLA policies receive four consecutive grayscale BEV frames, with road and lane boundaries encoded visually and a planned-route channel included only when route conditioning is enabled.The BEV representation reduces the perception burden but does not eliminate the need to construct BEV from real sensors in a deployable system.Source: §5.3 · p. 6, Figure 2 · p. 6

5.4 Route-conditioned CARLA protocol

  • Route-conditioned CARLA training uses about 1,900 Town01 PID-expert pairs; evaluation tests ten new routes per model and terminates at an infraction or 3,000 steps.Each architecture is trained three times; reported measures are distance traveled in meters and fraction of the horizon completed. Diffusion-2BC uses fixed α = 0.3.Source: §5.4 · p. 6

5.5 Route-free multi-intersection protocol

  • Route-free training uses 34 Town01 PID-expert routes and omits the route channel; policies are evaluated in Town01 and unseen Town02 using checkpoints selected by Town01 mean distance.Distance is reported in simulator-specific units rather than meters; wrong-lane termination is relaxed, and red-light and stop-sign termination checks are disabled.Source: §5.5 · pp. 6–7

6 Results

Diffusion-2BC preserves diffusion’s multimodal prediction advantage in Claw and records stronger results than both baselines in route-free CARLA evaluations. Route-conditioned results show earlier completion, while computational-cost measurements retain a substantial inference-time trade-off.

6.1 Claw environment results

  • With 90% of Claw training data, fixed-α Diffusion-2BC reached mean distance 0.63, compared with 0.70 for Diffusion-BC.The reported Claw results support the hybrid objective’s preservation of diffusion-based multimodal prediction in this controlled task, not autonomous-driving performance.Source: §6.1 · p. 7

6.2 Route-conditioned CARLA navigation

  • At epoch 150, Diffusion-2BC first completed every route without infraction, versus epoch 300 for Diffusion-BC; it recorded 1498.09 ± 74.81 m and completion 1.00 ± 0.00.Because the intended route is visible, this experiment does not test multimodal route choice.Source: §6.2 · p. 7

6.3 Route-free multi-intersection navigation in Town01

  • 304.697 UoM was Diffusion-2BC’s peak mean distance in Town01, about 2.44 times MSE-BC’s and 5.87 times Diffusion-BC’s.The comparison uses each architecture’s highest-mean-distance checkpoint.Source: §6.3 · p. 7

6.4 Cross-map evaluation in Town02

  • 383.963 UoM was Diffusion-2BC’s highest observed mean in Town02, versus 70.563 UoM for MSE-BC and 165.717 UoM for Diffusion-BC.The Town02 evaluation used Town01-preselected candidates; epoch 50’s clearer distinct-route example was qualitative, not the quantitative optimum.Source: §6.4 · pp. 7–8

6.5 Computational cost

  • Diffusion-BC and Diffusion-2BC each required about 32 seconds per 100 inference steps, versus five seconds for MSE-BC; the auxiliary branch adds no test-time cost over Diffusion-BC.The measurements are implementation- and hardware-dependent and are not normalized by parameter count or optimized sampling steps.Source: §6.5 · p. 8

7 Discussion

The discussion reports gains in route progress and qualitative route variation, while qualifying both the interpretation of the hybrid mechanism and the scope of cross-map evidence. Its evaluation uses bounded protocols that limit the conclusions to the tested settings.

7 Discussion

  • Diffusion-2BC reaches the longest peak route-free trajectories and completes route-conditioned runs earlier than Diffusion-BC, with qualitative route variation in Town01 and Town02.Fig. 5 reports the highest peak mean distance for Diffusion-2BC in Town02.Source: §7 · p. 8, Figure 5 · p. 10
  • The lower-variance regression signal is a plausible explanation for improved reliability, not a causal finding; gradient analysis, representation probes, and systematic α sweeps are absent.Source: §7 · p. 8
  • Route-conditioned curves combine three training runs and ten evaluation routes per model; an infraction ends a rollout before the maximum horizon.The curves show both progress and variability.Source: Figure 4 · p. 9
  • Trajectory spread alone does not establish route diversity; Diffusion-2BC shows distinct intersection choices at selected epochs, while Diffusion-BC lacks a clear alternative route at its peak checkpoint.The discussion proposes route entropy, pairwise trajectory distance, action-distribution calibration, or distinct decision-sequence counts for future evaluation.Source: §7 · p. 9
  • Town02 results are descriptive cross-map evidence: the reported peak is selected from five Town01-preselected checkpoints, not a single checkpoint fixed before transfer.Source: §7 · p. 10, Table 6 · p. 10
  • Residual variance remains a feature of stochastic policies; route conditioning or classifier-free guidance could constrain multimodal actions to designated planner targets.Source: §7 · p. 10

7.1 Scope of Study and Methodological Considerations

  • The scope uses BEV inputs and static urban networks, with Town02 checkpoints transferred without fine-tuning and results aggregated across training instances and repeated rollouts.These choices isolate policy learning and multimodal path selection; dynamic traffic, adverse weather, and V2X interactions remain outside the staged validation.Source: §7.1 · pp. 10–11

8 Conclusions

Diffusion-2BC combines diffusion denoising with an auxiliary regression loss during training while keeping inference diffusion-based. Across the evaluated settings, the results support improved closed-loop reliability alongside multimodal behavior, with further testing proposed under more realistic conditions.

8 Conclusions

  • Diffusion-2BC shares a visual feature extractor between denoising and auxiliary deterministic regression during training, then removes the auxiliary branch at test time.Source: §8 · p. 12
  • The staged evaluation finds reduced Claw error, earlier infraction-free route-conditioned completion, and the greatest peak mean distance in route-free CARLA for Diffusion-2BC.Selected checkpoints also show qualitative route variation in Town01 and Town02.Source: §8 · p. 12
  • Across the evaluated settings, the hybrid method improves closed-loop reliability while preserving multimodal prediction in Claw and qualitative route variation in CARLA.Source: §8 · p. 12
  • Future work includes quantifying route diversity, reducing diffusion inference steps, adding traffic and weather, and integrating real-time sensor-to-BEV perception.Source: §8 · p. 12

Statements and Declarations

The statements report partial CNPq funding, no relevant competing interests, and data and code availability upon reasonable request.

Funding

  • The work was partially funded by CNPq, Brazil, under Grant No. 420148/2025-6.Source: Funding · p. 12

Competing interests

Data and code availability

Supplementary Material

The supplied supplementary-material text contains the paper title and two author names.

Supplementary Material

  • The title identifies the paper as “Diffusion-2BC: Hybrid Diffusion and Regression Training for Offline Behavior Cloning in Autonomous” in the supplied text.Source: Supplementary Material · p. 14
  • The supplied author names are Bruno Maciel Machado and Eric Aislan Antonelo.Source: Supplementary Material · p. 14

Supplementary Note S1: Preliminary CarRacing experiment

This supplementary note documents a preliminary CarRacing experiment comparing only MSE-BC and Diffusion-BC, not the proposed Diffusion-2BC. It records the setup and previously reported aggregate results, and adds qualitative episode curves.

Supplementary Note S1: Preliminary CarRacing experiment

  • The CarRacing experiment predates Diffusion-2BC and compares only MSE-BC with Diffusion-BC, so it is not validation of the proposed method.The note records the protocol and reproduces earlier results, while adding cumulative-reward visualizations.Source: Supplementary Note S1: Preliminary… · p. 14
  • The fixed dataset contains approximately 15,000 observation–action pairs from 20 manually driven expert episodes, each with reward above 900 and expert mean 930.34 ± 7.46.Grayscale observations are stacked with the preceding three frames and normalized to form 96 × 96 × 4 inputs; actions contain steering, acceleration, and braking.Source: Supplementary Note S1: Preliminary… · p. 14
  • Two independently trained models per architecture were evaluated on 100 consecutive random tracks each; reward above 900 denotes expert-level completion.Both policies used the same convolutional feature extractor and were trained for 80 epochs; Diffusion-BC used 50 diffusion timesteps.Source: Supplementary Note S1: Preliminary… · p. 14
  • Reward distributions over 100 randomly generated evaluation tracks for one representative trained model per architecture are reproduced from the conference article.The dashed red line marks reward 900.Source: Figure S1 · p. 15
  • MSE-BC reward curves frequently plateau after missed track tiles, whereas most Diffusion-BC curves continue toward successful completion.The curves show 20 representative evaluation episodes per architecture and provide qualitative context, not evidence about Diffusion-2BC.Source: Figure S2 · p. 15

Supplementary Table S2: Layer-by-layer policy architectures

The supplementary material describes the CARLA policy architectures and principal training and diffusion hyperparameters. It also presents Town01 top-checkpoint distances for comparison with the paper’s prioritized Town02 cross-map results.

Supplementary Table S2: Layer-by-layer policy architectures

  • The CARLA architecture table details components for MSE-BC, Diffusion-BC, and Diffusion-2BC; the four-frame 192 × 192 input yields a 4,608-dimensional visual representation and action dimension d_a = 2.The table expands the architecture summary in the main manuscript; preliminary CarRacing settings are documented separately.Source: Supplementary Table S2: Layer-by-layer… · p. 16, Table S2 · p. 16

Supplementary Table S3: CARLA experimental hyperparameters

Supplementary Fig. S3: Town01 top-checkpoint performance

  • Town01 results show mean distance for the five highest mean-distance checkpoints of one trained model per architecture, with bounds marking rollout minima and maxima.The main manuscript prioritizes Town02 histograms because performance under changed road geometry is more informative than training-map performance.Source: Figure S3 · p. 17, Supplementary Fig. S3: Town01… · p. 17
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