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

Bruno Maciel Machado; Eric Aislan Antonelo

Method family	Action representation	Handles unlabeled multimodality	Main strength	Limitation relative to this study
MSE behavior cloning	Deterministic point estimate	No	Simple, fast offline training and inference	Conditional averaging or single-mode behavior
Command-conditioned BC	Deterministic action conditioned on a route command	Only after labeling modes	Direct controllability at intersections	Requires reliable command or route labels
Energy-based / implicit BC	Energy over observation-action pairs	Yes	Flexible multimodal scoring	Requires candidate optimization or sampling; not evaluated here
Behavior Transformer	Discrete latent/action representation	Yes	Represents several behavior modes	Quantization and architecture choices differ from continuous diffusion
Diffusion-augmented BC	Conditional BC policy plus joint state–action diffusion model	Potentially	Combines conditional and joint expert modeling	The direct policy, rather than the diffusion model, is the primary action predictor
Diffusion-BC	Conditional generative action model	Yes	Continuous stochastic action generation	Iterative inference and inconsistent closed-loop behavior in the hardest experiment

Table 1 : Qualitative positioning of the methods most directly related to this study. “Unlabeled multimodality” means that several valid actions may appear for similar observations without an explicit command identifying the desired mode

Figure 1 : Diffusion-2BC training architecture. The shared feature extractor processes the observation once. Its representation conditions the denoising branch used to compute

\mathcal{L}_{\mathrm{DBC}}

and feeds an auxiliary deterministic head used to compute

\mathcal{L}_{\mathrm{MSE}}

. Their weighted sum updates the shared representation. The auxiliary head is discarded after training, and test-time actions are generated only by reverse diffusion

Component	MSE-BC	Diffusion-BC	Diffusion-2BC
Visual encoder	Residual CNN	Residual CNN	Shared residual CNN
Executed head	CARLA: MLP $4608$ – $2304$ – $1024$ – $64$ – $2$	Transformer denoiser	Transformer denoiser
Auxiliary head	–	–	CARLA: MLP $4608$ – $2048$ – $512$ – $128$ – $32$ – $2$
Inference	One deterministic pass	$T$ reverse steps	$T$ reverse steps

Table 2 : Compact comparison of the evaluated policy architectures

Figure 2 : Examples of the CARLA observations supplied to the policies. In (a), the yellow planned-route channel identifies the reference path, while blue and magenta encode the drivable road and lane boundaries. In (b), the route channel is omitted, so the policy must choose among locally valid road continuations. In both configurations, black denotes the non-drivable background.

Figure 3 : CARLA demonstration datasets. Each colored line is a PID-expert trajectory recorded with the corresponding observations and controls. The route-conditioned dataset supplies a visible planned-route channel. The route-free dataset omits that channel and includes multiple intersection maneuvers, so similar BEV observations can be associated with different valid actions

Experiment	Dataset	Models	Training	Evaluation	Main metrics	Generalization role
Claw environment	20,000 pairs; also 90% subset	MSE-BC, Diffusion-BC, Diffusion-2BC	Simplified supervised task	300 predictions	Mean mask-distance error	Controlled multimodality
Route-conditioned CARLA	$\sim$ 1,900 pairs from one Town01 route	All three	Three trainings; evaluations every 50 epochs	Ten new random routes; 3,000-step limit	Distance and relative completion	Novel routes in training map
Route-free CARLA	34 Town01 routes; $\sim$ 16,200 pairs	All three	Two trainings; through epoch 700; evaluations every 10	Five repeated rollouts from same start	UoM distance and path diversity	Town01-selected checkpoints transferred to Town02

Table 3 : Summary of experimental protocols

Method	Full dataset	90% dataset
MSE-BC	4.02	4.25
Diffusion-BC	0.68	0.70
Diffusion-2BC, exponential $\alpha$	0.63	0.69
Diffusion-2BC, fixed $\alpha=0.3$	0.61	0.63

Table 4 : Results in the Claw environment. The score is the mean distance to the nearest valid mask region (lower is better), averaged over seven held-out observations with 300 sampled actions per observation

Method	Distance (m)	Relative completion
MSE-BC	$1430.05\pm 580.55$	$0.83\pm 0.26$
Diffusion-BC	$1339.85\pm 150.60$	$1.00\pm 0.00$
Diffusion-2BC	$\mathbf{1498.09\pm 74.81}$	$\mathbf{1.00\pm 0.00}$

Table 5 : Route-conditioned CARLA evaluation at the best completion-oriented checkpoints: epoch 200 for MSE-BC, epoch 300 for Diffusion-BC, and epoch 300 for Diffusion-2BC. Values aggregate three independently trained models, each evaluated on ten random routes; the reported

\pm

values are standard deviations over the resulting 30 rollouts

Figure 4 : Route-conditioned CARLA evaluation during training. Each point combines three training runs and ten random evaluation routes per model. The curves show both progress and variability; an infraction terminates the rollout before the maximum horizon

Figure 5 : Town02 cross-map performance for five checkpoints preselected from Town01 mean-distance performance, using one Town01-trained model per architecture. Bars show mean route-free distance and bounds show the minimum and maximum across repeated rollouts. MSE-BC repeats a single deterministic path, Diffusion-BC has large variability, and Diffusion-2BC achieves the highest peak mean distance

Environment	Metric	MSE-BC	Diffusion-BC	Diffusion-2BC
Town01	Peak mean distance (UoM)	124.945	51.873	304.697
Town01	Reported min–max at peak (UoM)	identical within runs	0.907–121.469	116.741–360.201
Town02	Highest mean in transferred set (UoM)	70.563	165.717	383.963
Town02	Min–max at corresponding candidate (UoM)	identical within runs	7.489–364.232	150.107–429.379

Table 6 : Route-free multi-intersection distance results. All policies are trained in Town01, and Town02 is unseen during training. Town01 candidate checkpoints are selected by mean-distance performance; the Town02 row reports the highest Town02 mean among those five preselected candidates rather than a sweep over all training epochs.

Figure 6 : Route-free rollouts; each panel overlays ten trajectories from the same initial point. The Town01 cross-method panels use the highest mean-distance checkpoint for each architecture (epochs 60, 210, and 330 for MSE-BC, Diffusion-BC, and Diffusion-2BC). The Town02 panels show epochs 220, 230, and 680 from the fixed set of five checkpoints preselected in Town01; these are the highest observed Town02 means within that transferred set, not checkpoints obtained by a new Town02 search. The last row contains additional Diffusion-2BC checkpoints selected only for qualitative inspection of route diversity. These qualitative panels are not used to compute or select the values in Table 6 .

Supplementary Fig. S1. Reward distributions over 100 randomly generated evaluation tracks for one representative trained model of each architecture. The dashed red line marks reward 900. These distributions were previously reported in the conference article and are reproduced here to make the supplementary account self-contained.

Supplementary Fig. S2. Cumulative reward over environment steps for 20 representative evaluation episodes from one trained model of each architecture. These curves were not included in the preliminary conference article. The MSE-BC curves frequently plateau after missed track tiles, whereas most Diffusion-BC curves continue toward successful completion. The plots provide qualitative context for the aggregate statistics and are not evidence about Diffusion-2BC.

Component	Layer sequence and dimensions	Used by
Residual block 1	Two Conv2D layers, kernel $3\times 3$ , stride 1, padding 1, 64 output channels; BatchNorm and GELU after each convolution; residual sum scaled by $1/\sqrt{2}$ ; MaxPool2D $2\times 2$	All policies
Residual block 2	Two Conv2D layers with the same kernel, stride, padding, normalization, activation, and residual scaling; 128 output channels; MaxPool2D $2\times 2$	All policies
Visual projection	AvgPool2D $8\times 8$ , followed by flattening; resulting dimension depends on observation resolution	All policies
Deterministic policy head	Flattened visual vector $\rightarrow 2304\rightarrow 1024\rightarrow 64\rightarrow d_{a}$ with ReLU after the hidden linear layers	MSE-BC
Observation embedding	4,608-dimensional flattened visual vector $\rightarrow 128\rightarrow 128$ with LeakyReLU between the linear layers for CARLA	Diffusion-BC, Diffusion-2BC
Noisy-action embedding	$d_{a}\rightarrow 128\rightarrow 128$ with LeakyReLU between the linear layers	Diffusion-BC, Diffusion-2BC

Supplementary Table S2. Detailed CARLA neural-network components used by MSE-BC, Diffusion-BC, and Diffusion-2BC.

Parameter	Route-conditioned CARLA	Route-free CARLA
Learning rate	$10^{-4}$	$10^{-4}$
Learning-rate schedule	Fixed	Fixed
Feature hidden units	128	128
Batch size	32	32
Optimizer	Adam	Adam
Weight decay	0	0

Supplementary Table S3. Main training and diffusion hyperparameters for the CARLA experiments.

Supplementary Fig. S3. Town01 route-free performance for the five highest mean-distance checkpoints of one trained model per architecture. Bars show mean distance and bounds show the minimum and maximum across repeated rollouts.

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

Abstract

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