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AUGUstus: Autonomous Driving VLA Model with Unified Generation and Understanding
Yuqi Ye, Caigao Jiang, Zhuonan Wang, Congyuan Pei, Chao Qu, Changhao Peng, Junhong Lin, Qize Yu, Zetian Song, Guangzhao Fu, Chongruo Wu, Shiyu Huang, Shuchang Zhou, Honggou Yang, Wei Gao
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Abstract
Abstract:Vision-language-action (VLA) models show strong potential for end-to-end autonomous driving by leveraging world knowledge and understanding to excel in long-tail scenarios. However, current VLAs have two limitations: 1) Degeneration into vision-action (VA) models. For low latency, regression/flow-based methods directly generate actions but underuse VLM understanding, causing unsafe, unexplainable actions. 2) Autoregressive high latency. Autoregressive methods sequentially generate chain-of-thought (CoT) and action tokens, fully leveraging VLM understanding, but high latency hinders deployment. To enable low-latency deployment while using CoT to assist action generation, we propose AUGUstus, an Autonomous-driving VLA model with Unified Generation and Understanding. We unify diffusion-based action generation and autoregressive CoT understanding in one model, where understanding only serves generation. Joint CoT supervision preserves VLM spatial understanding in shared representation for safer, more accurate trajectories. AUGUstus-mode orders action generation before CoT, so CoT supervises reliable actions during training while inference needs only action output, enabling low latency. AUGUstus-GRPO, a unified GRPO algorithm, jointly optimizes action and CoT, improving action performance. Experiments show AUGUstus achieves 94.6 PDMS on NAVSIMv1 and 90.7 EPDMS on NAVSIMv2, SOTA planning without scorer module. On nuScenes, it achieves average L2 error 0.27 m and average collision rate 0.05%, best among compared methods. To validate AUGUstus practicality, we train on in-house data with 512 NVIDIA H800 GPUs for ~2 days, evaluate on an internal 1,000 km dataset, and preliminarily deploy on a real vehicle, achieving 12 Hz operation. Project page: this https URL
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- Source: https://arxiv.org/abs/2610.16985v1
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AUGUstus: Autonomous Driving VLA Model with Unified Generation and Understanding Yuqi Ye 1,∗ , Caigao JIANG 2,‡ , Zhuonan Wang 3 , Congyuan Pei 2 , Chao Qu 3 , Changhao Peng 1 , Junhong Lin 1 , Qize Yu 1 , Zetian Song 1 , Guangzhao Fu 2 , Chongruo Wu 2 , Shiyu Huang 2 , Shuchang Zhou 2 , Honggou Yang 2 , Wei Gao 1,† 1 Peking University, 2 XPeng Motors, 3 Fudan University ∗ First author, ‡ Project lead, † Corresponding author Vision-language-action (VLA) models have shown strong potential for end-to-end autonomous driving by leveraging world knowledge and understanding to achieve great performance in long-tail scenarios. However, current VLAs suffer from two major limitations: 1) Degeneration into vision-action (VA) models. To achieve low latency, regression-based and flow-based methods directly generate actions, yet they do not sufficiently leverage the VLM’s understanding, leading to unsafe and unexplainable actions. 2) Autoregressive high latency. Autoregressive methods sequentially generate chain-of-thought (CoT) and action tokens, fully leveraging the VLM’s understanding, but high latency makes deployment difficult. To enable low-latency deployment while properly using CoT to assist action generation, we propose AUGUstus 1 , anAutonomous- driving VLA model withUnifiedGeneration andUnderstanding. Specifically, we first unify diffusion-based action generation and autoregressive CoT understanding in a single model, where understanding is optimized only to serve generation. More concretely, joint CoT supervision preserves the VLM’s spatial understanding in the shared representation and keeps it useful for safer and more accurate trajectories. Second, we propose AUGUstus-mode, which orders the action generation before the CoT so that the CoT supervises the reliable action during training while inference needs only the action output, enabling low latency. Finally, we introduce AUGUstus-GRPO, a unified GRPO algorithm that jointly optimizes the action and CoT, further improving action performance. Extensive experiments demonstrate that AUGUstus achieves 94.6 PDMS on NAVSIMv1 and 90.7 EPDMS on NAVSIMv2, establishing state-of-the-art (SOTA) planning performance without scorer module. On nuScenes, our method achieves an average L2 error of 0.27 m and an average collision rate of 0.05%, both the best among the compared methods. To validate the practicality of AUGUstus, we train it on our in-house dataset using 512 NVIDIA H800 GPUs for approximately two days, then evaluate it on an internal 1,000 km dataset and preliminarily deploy it on a real vehicle, achieving 12 Hz operation. Project Page: https://augustus-ad.github.io Code: https://github.com/haha-yuki-haha/AUGUstus Model: https://huggingface.co/yuki-hahaha/AUGUstus 1 Introduction Autonomous driving has gradually moved from modular stacks for perception, prediction, and planning toward end-to-end models to reduce error accumulation, including ST-P3 (Hu et al., 2022), UniAD (Hu et al., 2023), and VAD (Jiang et al., 2023). Yet their limited model capacity and training data restrict the world knowledge available to the policy, making long-tail scenes and semantically complex interactions difficult to handle reliably. To address long-tail scenarios, many recent studies have explored large vision-language models (VLMs) as a promising foundation model for autonomous driving, leveraging their large-scale pre-training to supply broad visual concepts, language priors, and reasoning capabilities (Zhao et al., 2026; Xiong et al., 2026; Zhou et al., 2026b; Ye et al., 2026b). However, current mainstream autonomous driving VLA architectures still exhibit three limitations: 1) Regression head: Despite low latency, these methods (Zhao et al., 2026; Li et al., 2025) produce no action distribution, making RL post-training difficult; moreover, 1 AUGUstus refers to Augustus (Octavian), the first Roman emperor, whose consolidation of Roman authority symbolizes unification. Here, it denotes a unified generation and understanding VLA model. 1 arXiv:2610.16985v1 [cs.CV] 12 Oct 2026 Images Vision Language Model (VLM) Ego Status Image Token Text Token Action Text (c) VLM+CoT/Latent CoT (AutoVLA, OneVL) ... CoT/Latent CoT Having distribution, RL friendly Autoregression, high latency Sufficiently using VLM knowledge ... Images Vision Language Model (VLM) Ego Status Image Token Text Token Action Text (c) VLM+CoT/Latent CoT (AutoVLA, OneVL) ... CoT/Latent CoT Having distribution, RL friendly Autoregression, high latency Sufficiently using VLM knowledge ... Images Vision Language Model (VLM) Ego Status Image Token Text Token Action Query Action Value (a) Query-based/Regression (PWM) ... No distribution, RL unfriendly Regression, low Latency Lacks explicit VLM knowledge Images Vision Language Model (VLM) Ego Status Image Token Text Token Action Query Action Value (a) Query-based/Regression (PWM) ... No distribution, RL unfriendly Regression, low Latency Lacks explicit VLM knowledge Images Vision Language Model (VLM) Ego Status Image TokenText Token Gaussian Noise (b) VLM+Diffusion (ReCogdrive) Diffusion / Flow Matching ... ... Lacks explicit VLM knowledge Having distribution, RL friendly Few-steps denoise, low latency Images Vision Language Model (VLM) Ego Status Image TokenText Token Gaussian Noise (b) VLM+Diffusion (ReCogdrive) Diffusion / Flow Matching ... ... Lacks explicit VLM knowledge Having distribution, RL friendly Few-steps denoise, low latency ... CoT/Latent CoT AUGUstus (Unify Generation and Understanding) Images Ego Status Image Token Text Token (d) Unify Architecture (Ours) ... Gaussian Noise CoT CoT Having distribution, RL friendly 1/Few-steps denoise, low latency Sufficiently using VLM knowledge Inference Only Action! AUGUstus (Unify Generation and Understanding) Images Ego Status Image Token Text Token (d) Unify Architecture (Ours) ... Gaussian Noise CoT CoT Having distribution, RL friendly 1/Few-steps denoise, low latency Sufficiently using VLM knowledge Inference Only Action! Action Value Action Value Action Text Figure 1 The difference between AUGUstus and other autonomous-driving VLA paradigms. Our method unifies generation and understanding under AUGUstus-mode, so that joint CoT supervision preserves the VLM’s under- standing in the shared representation, yielding safer, more accurate actions with an RL-friendly action distribution and low-latency deployment. they do not fully leverage VLM knowledge, resulting in low-quality generated actions (Fig. 1a). 2) Diffusion or flow-matching expert: To address the lack of action distribution for RL algorithm, some VLA methods (Xiong et al., 2026) adopt diffusion or flow-matching experts for action generation, but they still do not fully exploit the VLM’s spatial understanding, thereby producing unsafe and unexplainable actions (Fig. 1b). 3) Autoregressive decoding: To make full use of VLM understanding for action generation, some VLAs (Zhou et al., 2026b; Ye et al., 2026b) serially generate CoT and action, which incurs high latency and makes real-time deployment difficult (Fig. 1c). Overall, current VLAs struggle to reconcile the VLM’s understanding with low-latency control. This raises a key question: can we design an architecture that keeps this action-relevant understanding while remaining low-latency and easy to deploy? We argue that these limitations lie in the separation between VLM-based understanding and action generation, rather than treating them as a unified process. Autonomous driving requires understanding and action generation to work in synergy, where accurate spatial understanding enables reliable action generation. However, conventional approaches decouple them: direct regression and diffusion/flow experts degenerate into Vision-Action (VA) models that produce unsafe and unexplainable actions, whereas autoregressive CoT leverages understanding but serializes reasoning before action, causing high latency. Accordingly, we reconsider the role of CoT understanding in autonomous driving. Rather than treating CoT as an independent reasoning stage or a serial prefix to actions, CoT should be jointly optimized with action generation within a unified architecture, where action generation is the core and CoT serves to improve it. Such a unified formulation keeps VLM spatial understanding coupled to and useful for the action policy, while inference only outputs actions, preserving an RL-friendly action distribution and low latency. To address above fundamental limitations, we propose AUGUstus, anAutonomous-driving VLA model withUnifiedGeneration andUnderstanding (Fig. 1d). Our objective is action-centric: understanding is not trained for its own sake but to generate a safer and more accurate trajectory. Specifically, (1) we unify diffusion-based action generation and autoregressive CoT understanding in a single model, where joint CoT supervision preserves the VLM’s spatial understanding in the shared representation for better action generation; (2) we propose AUGUstus-mode, an action-first and CoT-second ordering. This forces the model to learn a CoT that benefits action performance, while inference only needs the action output, thereby maintaining low latency. We explore various CoT designs and find that a CoT describing the specific positions and future orientations of other agents in the scene is most effective for action; and (3) we also introduce AUGUstus-GRPO, a unified GRPO algorithm that jointly optimizes the continuous action and CoT streams so that reasoning serves planning, further improving planning capabilities. We extensively evaluate AUGUstus on closed-loop NAVSIM and open-loop nuScenes. AUGUstus achieves 94.6 PDMS on NAVSIMv1 and 90.7 EPDMS on NAVSIMv2, without a scorer module. On nuScenes, our method achieves an average L2 error of 0.27 m and an average collision rate of 0.05%, both the best among the compared methods. To validate the practicality of AUGUstus, we train it on our in-house dataset 2 using 512 NVIDIA H800 GPUs for approximately two days, then evaluate it on an internal 1,000 km dataset and preliminarily deploy it on a real vehicle, achieving 12 Hz operation. These results show that the shared model preserves the VLM’s spatial understanding, improving action generation while meeting the latency requirements of real-time planning. The main contributions of this paper are summarized as follows: 1.We propose AUGUstus, a unified VLA that integrates diffusion-based action generation and autoregressive CoT understanding in one transformer. The shared model preserves the VLM’s spatial understanding for action generation, avoiding VLA-to-VA degeneration. AUGUstus-mode orders action before CoT to ensure low-latency inference. 2.We introduce AUGUstus-GRPO, a unified GRPO algorithm that jointly optimizes action and CoT. It combines JaT-GRPO, which uses closed-form Gaussian importance sampling ratios and KL terms, with CoT-GRPO, which uses token-level GRPO. The reasoning stream is rewarded for serving planning, thereby further improving action performance. 3. We demonstrate that AUGUstus achieves state-of-the-art performance on multiple autonomous driving benchmarks, underscoring the effectiveness and generality of our approach. It also demonstrates practical scalability through large-scale training, validation on an internal driving dataset, and real-vehicle deployment. 2 Related Work VLA models for autonomous driving. Recent driving VLAs follow three designs. Query-based policies (Zhao et al., 2026; Liu et al., 2026b; Shao et al., 2026) are low-latency but without action distribution for RL and weakly leveraging VLM semantics, which can yield unsafe and unexplainable actions. External flow-matching experts (Xiong et al., 2026) model continuous action distributions but keep the generator outside the VLM, weakening VLM semantics. Autoregressive policies (Zhou et al., 2026b; Ye et al., 2026b; Wang et al., 2026) expose semantic reasoning but serialize CoT and action tokens, incurring high latency. These designs struggle to trade off VLM understanding and low latency. AUGUstus unifies continuous action tokens and CoT understanding in one transformer under AUGUstus-mode, where understanding is trained to serve action generation rather than to maximize its own output quality, and deployment outputs actions directly. Reinforcement learning for driving VLAs. Driving-oriented VLMs increasingly adopt GRPO-style post- training, such as AutoVLA, AutoDrive-R 2 , AutoDrive-P 3 , and RecogDrive (Zhou et al., 2026b; Yuan et al., 2026; Ye et al., 2026b; Xiong et al., 2026). RecogDrive directly supervises actions but lacks explicit CoT supervision, making it prone to reward hacking. Other autoregressive methods supervise token-level outputs, which slows both training and inference. In contrast, AUGUstus-GRPO jointly optimizes CoT and action under a shared group-relative advantage, with CoT further improving action performance. 3 Methodology This section introduces AUGUstus framework, which unifies generation and understanding within a single transformer. First, we unify continuous, flow-based action generation with autoregressive, token-based CoT understanding in one transformer. Second, we propose AUGUstus-mode, an action-first, CoT-second training scheme in which the CoT stream is optimized to supervise and improve action generation. At inference, only the action stream is evaluated, ensuring low-latency deployment. Finally, we introduce AUGUstus-GRPO, a unified reinforcement learning algorithm that further improves the VLA’s planning capability. 3.1 Unified framework As shown in Fig. 2, for vision-based end-to-end driving, each sample contains camera video푆, ego state퐸, route command퐶, and history trajectory퐻, which we write compactly as the driving context 푐 =(푆,퐸, 퐶, 퐻). During training, as summarized in Algorithm 1, the model additionally receives a noised trajectory푥 푡 and the teacher-forced prefix푦 <푘 CoT and predicts both a clean trajectory estimate and the next CoT token: 푐, 푥 푡 , 푦 <푘 ↦−→ ˆ 푥 0 , 푝 휃 푦 푘 | 푐, 푥 푡 , 푦 <푘 .(1) 3 Language Tokenizer Vision Encoder Ego Status visual input text noise action action value chain-of-thought text Driving Video Training: Vision + Language -> Action + CoT Inference: Vision + Language -> Action Language Tokenizer LM Head Noise Action CoT(bounding box + future position) Action Projector Action Decoder As an expert driving...Ego Future Action is GO FORWARD.Ego current stateis vx: 5.82 m/s, vy: -0.03 m/s, ax: -1.48 m/s², ay: -0.23 m/s², and the historical trajectory ... Predict the future trajectory for the next 4 seconds (8 points). <prediction>```json [ "bbox_2d": [418, 274, 661, 378], "future_position": "middle, left", ... ```</prediction> Time Modulation VL A L t=0 t~[0,1] Layer 1 Layer 2 Layer n-1 Layer n AUGUstus(Unify Generation & Understanding) VLAAL V L A A L L L V L VL V L A A V L VLAAVL ... Figure 2 Overview of AUGUstus. AUGUstus takes video and ego status as input and uses one shared transformer to first generate clean action and then understand a CoT containing key-object bounding boxes and future position. Action tokens use bidirectional attention and cannot attend to the CoT tokens. At inference, AUGUstus directly outputs the action to ensure low latency. Algorithm 1 AUGUstus training Require: Context 푐, trajectory 푥 0 , CoT 푦. Ensure: ˆ 푥 0 , CoT probabilities, updated 휃. 1: Noise the target: 푥 푡 =(1− 푡)푥 0 + 푡휀. 2: Joint forward: context, noisy action, teacher-forced CoT. 3: Predict ˆ 푥 0 and the next CoT tokens. 4: Update with flow-matching and CoT losses. Algorithm 2 AUGUstus inference (1-step denoise) Require: Context 푐, noise 푥 1 , step budget 푁. Ensure: Trajectory ˆ 푥 0 ; optional post-hoc CoT. 1: Cache the causal context prefix. 2: Denoise the action block in 푁 evaluations. 3: For 푁 = 1, return ˆ 푥 0 directly. 4: Skip CoT at inference; decode it afterward only if requested (e.g., during RL rollout sampling). Here푥 0 ∈ R 푇×3 is the continuous target trajectory, with each waypoint represented by planar position and heading.푦is an autoregressive token sequence describing key objects with bounding box and future position. At inference, as summarized in Algorithm 2, only context푐is provided. The initial noise state 푥 1 is denoised in one or few steps denoising to generate ˆ 푥 0 , and CoT decoding is optional to ensure low latency. We denote this action-first, CoT-second ordering as AUGUstus-mode. As shown in Fig. 2, its attention design is: context tokens are causal; action tokens form a bidirectional block attending to the full context and to each other; and CoT tokens are causal and additionally attend to the complete action block, while action tokens cannot attend to CoT tokens. Complete procedures are provided in Appendix D.3. 3.2 Supervised Fine-Tuning for AUGUstus As summarized in Algorithm 1, supervised fine-tuning for AUGUstus jointly trains conditional flow matching for actions and teacher-forced language modeling for CoT. Let푥 0 be the clean trajectory, 휀∼풩(0, 퐼) the initial noise, and 푡 ∈[0, 1] the flow time: 푥 푡 =(1− 푡)푥 0 + 푡휀, ˆ 푥 0 = 푓 휃 (푥 푡 ,푡, 푐).(2) Here푓 휃 is AUGUstus model, which directly predicts the clean trajectory ˆ 푥 0 rather than a velocity, similar to (Li and He, 2025) which predicts the clean image in the image domain. This푥 0 parameterization makes the deployed endpoint explicit, since one Euler step at푡 = 1returns ˆ 푥 0 exactly, supporting both few-step sampling and a genuine one-step policy. The supervised objective combines flow matching for continuous action reconstruction with teacher-forced 4 Gaussian Noise Action Value Denoising N steps Text Token Autoregression CoT ... ... Group Advantage Update Stage1 (Run Phase): Focus on Progress Stage2 (Walk Phase): Focus on Safety High Progress, but No Safety High Progress, and Safety Reward Function 1 R 2 R G R ... 3 R G1 R − GRPO JaTGRPOCoTGRPO AUGUstus J λ J − − − = + Figure 3 The pipeline of AUGUstus-GRPO. Paired푥 0 actions and autoregressive CoTs share a group-relative advantage, with closed-form JaT-GRPO and token-level CoT-GRPO. Stage I focuses on progress via PDMS reward, while Stage I focuses on safety via terminal and safety rewards. Algorithm 3 AUGUstus-GRPO: Stage I Require: SFT policy and contexts. Ensure: Progress-tuned policy 휋 ∗ I . 1: Sample paired action and CoT rollouts. 2: Compute 푅 pred,푖 ; set 푅 plan,푖 = PDMS 푖 . 3: Normalize the shared group advantage 퐴 푖 . 4: Jointly update JaT-GRPO and CoT-GRPO. Algorithm 4 AUGUstus-GRPO: Stage I Require: Stage-I policy 휋 ∗ I and contexts. Ensure: Safety-refined policy 휋 ∗ I . 1: Sample paired action and CoT rollouts. 2: Keep 푅 pred,푖 ; set 푅 plan,푖 = 푅 end,푖 + 푅 safe,푖 . 3: Normalize the shared group advantage 퐴 푖 . 4: Jointly update JaT-GRPO and CoT-GRPO. CoT entropy minimization under the same context 푐 and noise action 푥 푡 : ℒ SFT = 휆 FM E 푡,휀 [∥ ˆ 푥 0 − 푥 0 ∥ 1 ] | z flow matching loss −휆 CoT E h Õ 퐿 푘=1 log푝 휃 (푦 푘 | 푦 <푘 , 푐, 푥 푡 ) i | z CoT likelihood .(3) During SFT, we note that CoT for prediction, i.e., predicting the bounding boxes and future positions of key objects, is more beneficial for safe and efficient actions than CoT for perception or planning reasoning; additional CoT experiments are provided in the supplementary material. 3.3 Reinforcement Learning for AUGUstus To further improve the VLA’s planning capability, we introduce AUGUstus-GRPO, a unified RL method for continuous action and autoregressive CoT. As illustrated in Fig. 3, each rollout produces a paired action and CoT, and the two streams share a normalized group-relative advantage. JaT-GRPO applies GRPO to the continuous action branch under the푥 0 parameterization, while CoT-GRPO optimizes the CoT branch with token-level likelihoods. Unified GRPO objective. For each context, the behavior policy samples퐺paired rollouts. In stage 푠 ∈1, 2,푅 pred,푖 evaluates the CoT and푅 (푠) plan,푖 denotes the corresponding planning reward. We define the shared reward and normalized advantage as 푅 (푠) 푖 = 푅 pred,푖 + 푤 plan 푅 (푠) plan,푖 , 퐴 푖 = 푅 (푠) 푖 − mean 푗 (푅 (푠) 푗 ) std 푗 (푅 (푠) 푗 )+ 휖 0 .(4) For each branch, we compute the importance sampling ratio between 휋 휃 and 휋 old : 푟 (action) 푖,푞 = 휋 휃 (푥 푖,푡−Δ푡 | 푥 푖,푡 , 푐 푖 ) 휋 old (푥 푖,푡−Δ푡 | 푥 푖,푡 , 푐 푖 ) , 푟 (CoT) 푖,푞 = 휋 휃 (푦 푖,푘 | 푦 푖,<푘 , 푐 푖 , 푥 푖 ) 휋 old (푦 푖,푘 | 푦 푖,<푘 , 푐 푖 , 푥 푖 ) .(5) Both branches are optimized with the same clipped GRPO objective, 풥 푚 = E 1 퐺 퐺 Õ 푖=1 1 |ℐ 푚 푖 | Õ 푞∈ℐ 푚 푖 min 푟 (푚) 푖,푞 퐴 푖 , clip(푟 (푚) 푖,푞 , 1− 휖, 1+ 휖)퐴 푖 ,(6) 5 where푚 ∈ action, CoT, andℐ action 푖 andℐ CoT 푖 index the denoising steps and CoT token positions, respectively. Combining the two branches, the overall objective is ℒ AUGUstus-GRPO =−풥 action + 훽 action KL act | z JaT-GRPO on 푥 0 +훼 CoT −풥 CoT + 훽 CoT KL CoT | z CoT-GRPO on language .(7) Closed-form JaT-GRPO. The action-policy derivation starts from the linear conditional-flow path푥 푡 = (1− 푡)푥 0 + 푡휀, with휀∼풩(0, 퐼). Following Flow-GRPO (Liu et al., 2026a), we adopt its reverse transition: 푥 푡−Δ푡 = 푥 푡 − 푣 휃 + 푔(푡) 2 2푡 푥 푡 +(1− 푡)푣 휃 Δ푡+ 푔(푡) √ Δ푡 푧, 푧 ∼풩(0, 퐼).(8) Here 푣 휃 is computed by our predicted clean trajectory ˆ 푥 휃 0 (푥 푡 ,푡, 푐) through: 푣 휃 (푥 푡 ,푡, 푐) = 푥 푡 − ˆ 푥 휃 0 (푥 푡 ,푡, 푐) 푡 .(9) Using Eq. (9) and푔(푡) 2 = 휆푡in Eq. (8) yields a transition with mean휇 휃 = 푐 푥 푥 푡 + 푐 0 ˆ 푥 휃 0 and variance휎 2 푠 퐼. Only ˆ 푥 휃 0 is policy-dependent, and the covariance is fixed. Thus, the휋 휃 ,휋 old , and휋 ref policies induce Gaussian transitions with the same covariance휎 2 푠 퐼and means휇 휃 ,휇 old , and휇 ref , respectively. With 훿 old = ˆ 푥 휃 0 − ˆ 푥 old 0 and 훿 ref = ˆ 푥 휃 0 − ˆ 푥 ref 0 , the importance ratio and KL simplify to: log푟 (action) 푡 = 푐 0 휎 푠 ⟨훿 old , 푧⟩− 푐 2 0 2휎 2 푠 ∥훿 old ∥ 2 2 ,KL act = 푐 2 0 2휎 2 푠 ∥훿 ref ∥ 2 2 . (10) With the closed-form solution, we plug resulting ratios and KL terms into Eq. (6), enabling optimization with few-step and single-step denoising. The complete derivation is in Appendix B. Two-stage RL. AUGUstus-GRPO uses a two-stage training procedure inspired by Run-then-Walk schedul- ing (Ye et al., 2026a). As summarized by Algorithms 3 and 4, Stage I starts from the SFT policy and, following Eq. 4, sets the planning reward푅 (1) plan,푖 = PDMS 푖 while keeping푅 pred,푖 . This encourages assertive progress and aligns the policy with the benchmark objective. Stage I starts from the Stage-I checkpoint and sets푅 (2) plan,푖 = 푅 end,푖 + 푅 safe,푖 , preserving the same푅 pred,푖 . It therefore retains the progress learned in Stage I while refining the trajectory toward accurate endpoints and safe behavior. In both stages, the shared reward and advantage in Eq. 4 jointly update JaT-GRPO and CoT-GRPO; only planning reward is different. 4 Experiments 4.1 Benchmarks and Baselines Public benchmarks. Following (Zhou et al., 2026b; Xiong et al., 2026; Ye et al., 2026b), we evaluate on the NAVSIM (Dauner et al., 2024) and nuScenes (Caesar et al., 2020) benchmarks. For both benchmarks, the input is a 2-second, 4-frame clip from the front, front-left, and front-right cameras at2048×512. AUGUstus predicts 8 waypoints over a 4-second horizon for NAVSIM, and 6 waypoints over a 3-second horizon for nuScenes. For NAVSIM, we report the official PDMS on NAVSIMv1 and EPDMS on NAVSIMv2. For nuScenes, following the ST-P3 protocol (Hu et al., 2022), we report L2 error and collision rate. In-house benchmarks and driving test. To validate the practicality of AUGUstus, we train it on in-house dataset without using any public dataset, using 512 NVIDIA H800 GPUs for approximately two days with a global batch size of 2048. We first evaluate it on in-house 1,000 km driving set covering safety, comfort, efficiency, and compliance metrics, and then deploy the model on a real vehicle for a preliminary driving test in Guangzhou, China. Baselines. We use Qwen3.5-2B (Qwen Team, 2026) as the base model. On public datasets, we compare against mainstream approaches, including end-to-end small planners and representative autoregressive, regression-based, and diffusion-based VLA planners. On the in-house dataset, we compare AUGUstus with diffusion-based and regression-based architectures. Note that, considering the real-time requirements for deployment, unless otherwise specified, inference in this paper refers to 1-step denoising without the subsequent CoT generation. 6 Table 1 Performance comparison on NAVSIMv1 benchmark. MethodRefRL NC↑ DAC↑ EP↑ TTC↑ Comf.↑PDMS↑ Human-✗ 100.0 100.0 87.5 100.0 100.094.8 End-to-end small models TransFuser (Chitta et al., 2022)TPAMI’23✗ 97.8 92.6 78.9 92.9 99.983.9 PARA-Drive (Weng et al., 2024)CVPR’24✗ 97.9 92.4 79.3 93.0 99.8 84.0 Hydra-MDP (Li et al., 2024)CVPR’24✗ 98.3 96.0 78.7 94.6 100.086.5 WoTE (Guan et al., 2025)ICCV’25✗ 98.5 96.8 81.9 94.9 100.0 88.3 Regression-based VLA planners ImagiDrive (Li et al., 2025)ICRA’26✗ 97.9 95.5 80.7 93.1 99.986.4 PWM (Zhao et al., 2026)NeurIPS’25✗ 98.6 95.9 81.8 95.4 100.0 88.1 DriveVLA-W0 (Li et al., 2026)ICLR’26✔ 98.7 99.1 83.3 95.3 99.390.2 Autoregressive VLA planners AutoVLA (Zhou et al., 2026b)NeurIPS’25✔ 98.4 97.5 81.9 98.0 99.989.1 AdaThinkDrive (Luo et al., 2025)ICRA’26✔ 98.4 97.8 84.4 95.2 100.090.3 AutoDrive-R 2 (Yuan et al., 2026)ICLR’26✔ 98.5 95.9 82.7 95.4 100.089.1 AutoDrive-P 3 (Ye et al., 2026b)ICLR’26✔ 98.9 97.7 83.7 96.6 99.990.2 VGGDrive (Wang et al., 2026)CVPR’26✗ 98.6 96.3 82.9 95.6 100.0 88.8 Flow-matching VLA planners ReCogDrive (Xiong et al., 2026)ICLR’26✔ 98.1 97.7 86.5 94.9 100.090.6 AUGUstus (Ours, 1-step denoising)-✔ 98.6 98.7 91.4 96.6 100.094.0 AUGUstus (Ours, 3-step denoising)-✔ 98.9 98.9 91.9 97.1 100.094.6 Table 2 Performance comparison on NAVSIMv2 benchmark. MethodNC↑ DAC↑ DDC↑ TLC↑ EP↑ TTC↑ LK↑ HC↑ EC↑ EPDMS↑ False / True Human100.0 100.0 99.8 100.0 87.4 100.0 100.0 98.1 90.190.3 / 94.5 Ego Status MLP93.1 77.9 92.7 99.6 86.0 91.5 89.4 98.385.464.0 / – Transfuser (Chitta et al., 2022)96.9 89.9 97.8 99.7 87.1 95.4 92.7 98.387.276.7 / 84.0 Hydra-MDP++ (Li et al., 2024)97.2 97.5 99.4 99.6 83.1 96.5 94.4 98.2 70.981.4 / – DiffusionDrive (Liao et al., 2025)98.2 96.2 99.5 99.8 87.497.3 96.998.4 87.784.7 / 88.2 WoTE (Guan et al., 2025)98.5 96.8 98.8 99.8 86.1 97.9 95.5 98.382.984.2 / 87.7 ReCogDrive (Xiong et al., 2026)98.2 97.7 98.4 100.0 89.9 97.4 90.8 97.7 26.882.7 / – AutoDrive-P 3 (Ye et al., 2026b)98.997.698.9 99.8 86.8 98.5 95.4 98.380.685.2/ 88.7 AUGUstus (Ours, 1-step denoising) 99.0 97.9 99.7 99.987.3 98.498.0 98.387.287.1 / 90.7 4.2 Main Results Public benchmark results. As shown in Table 1, AUGUstus reaches 94.0/94.6 PDMS with 1/3-step denoising on NAVSIMv1, only 0.2 below human performance (94.8), while only generating a single trajectory without any scorer module. On NAVSIMv2, as shown in Table 2, AUGUstus obtains the SOTA performance, 90.7 EPDMS with the human-penalty filter (87.1 without it) with only 1-step denoising. On nuScenes, as shown in Table 3, our method with only 1-step denoising achieves 0.27m average L2 error and 0.05% average collision rate. In-house benchmarks and real driving test. Beyond public benchmarks, we evaluate VLM+flow matching, VLM+regression, and AUGUstus on an internal 1,000 km driving dataset. We report macro-averages across safety, comfort, efficiency, and compliance, where positive values indicate worse performance and AUGUstus is fixed at 0%. AUGUstus performs best in safety, comfort, and efficiency, with the largest gaps in safety and comfort; the flow-matching baseline is slightly better in compliance (Table 4). As shown in Table 5, AUGUstus achieves 13.6 Hz on a single H800 and 12.0 Hz on the real vehicle in our preliminary assisted driving tests. Figs. 4 and 5 further visualize its qualitative behavior on the in-house evaluation 7 Table 3 Performance comparison on nuScenes benchmark. MethodRef L2 (m)↓Collision (%)↓ 1s 2s 3sAvg. 1s 2s 3sAvg. ST-P3 (Hu et al., 2022)ECCV’22 1.33 2.11 2.902.11 0.23 0.62 1.270.71 VAD (Jiang et al., 2023)ICCV’23 0.17 0.34 0.600.37 0.07 0.10 0.240.14 UniAD (Hu et al., 2023)CVPR’23 0.44 0.67 0.960.69 0.04 0.08 0.230.12 GPT-Driver (Mao et al., 2023)arXiv’23 0.20 0.40 0.700.44 0.04 0.12 0.360.17 DriveVLM (Tian et al., 2024)CoRL’25 0.18 0.34 0.68 0.40 0.10 0.22 0.450.27 RDA-Driver (Huang et al., 2024)arXiv’24 0.17 0.37 0.690.40 0.010.05 0.260.10 OmniDrive (Wang et al., 2024)CVPR’25 0.14 0.29 0.550.330.010.040.270.11 OpenDriveVLA (Zhou et al., 2026a) AAAI’26 0.14 0.30 0.550.330.02 0.07 0.220.10 AutoVLA (Zhou et al., 2026b)NeurIPS’25 0.25 0.46 0.73 0.48 0.07 0.07 0.260.13 AutoDrive-R 2 (Yuan et al., 2026)ICLR’26 0.35 0.49 0.62 0.49 0.13 0.44 0.870.48 AutoDrive-P 3 (Ye et al., 2026b)ICLR’26 0.16 0.31 0.560.34 0.00 0.040.200.08 AUGUstus (Ours, 1-step denoising)-0.14 0.24 0.420.27 0.010.02 0.130.05 Table 4 In-house 1,000 km evaluation. Category VLM+Flow VLM+Reg.AUGUstus Safety+18.4% +15.1%0.0% Comfort+8.2%+8.2%0.0% Efficiency+3.0%+3.9%0.0% Compliance-0.5%+0.1%0.0% Table 5 Inference time. Module/systemTime (ms) Vision Encoder Stage40.2 VLA Stage (1-step denoising)33.2 Total (Locally, no CoT)73.6 (13.6 Hz) Real vehicle total83.0 (12.0 Hz) front leftfrontfront right rear leftrearrear right 100102030 BEV 0 Ego Agent History trajectory GT trajectory Ours trajectory FM trajectory RH trajectory Figure 4 In-house evaluation visualization. front leftfrontfront right rear leftrearrear right 10010203040 BEV 0 lateral (m) [left +] Ego Agent History trajectory Predict trajectory Figure 5 Real driving test visualization. Table 6 Ablation Study of CoT and AUGUstus-mode. SettingPDMS↑ NC↑ DAC↑ DDC↑ EP↑ TTC↑ Comf.↑ ADE (m)↓ Time (ms)↓ No CoT, Only Action89.2 98.8 96.8 98.4 83.5 95.8 100.00.53073.60 CoT first, Action second90.6 99.1 97.8 98.6 84.2 96.6 100.00.5214587 AUGUstus-mode (Ours)90.6 99.0 97.9 98.5 84.2 96.5 100.0 0.52073.60 and real driving test. Further details and supplementary videos are provided in the supplementary material. 4.3 Ablation Study 4.3.1 Ablation Study of AUGUstus-mode and CoT As shown in Table 6, we ablate CoT and AUGUstus-mode on SFT with NAVSIMv1. With AUGUstus-mode, adding CoT to training makes driving safer and further improves performance. Compared with CoT-first, 8 Table 7 Ablation Study of AUGUstus-GRPO. SettingPDMS↑ NC↑ DAC↑ EP↑ TTC↑ Comf.↑ SFT with AUGUstus-mode90.6 99.0 97.9 84.2 96.4 100.0 + AUGUstus-GRPO Stage I 94.0 98.6 98.7 91.4 96.6 100.0 + AUGUstus-GRPO Stage I94.6 98.9 98.9 91.9 97.1 100.0 + JaT-GRPO, without CoT-GRPO 92.6 98.0 97.6 91.8 94.1 100.0 raw frame (+GT boxes + GT path)AUGUstus action attention in-box 46% AUGUstus CoT attention in-box 0% w/o CoT training, action attention Figure 6 CoT attention visualization. CoT supervision anchors the action-relevant attention on the nearby risk object (46% in-box), whereas the no-CoT model misses it (0%). � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Figure 7 Visualization. Left: Trajectory visualization with and without CoT. Right: Trajectory visualization compared with other methods. AUGUstus-mode achieves comparable performance while preserving real-time inference, making the architecture deployable. Overall, our proposed AUGUstus-mode and unified CoT training prove effective. 4.3.2 Ablation Study of AUGUstus-GRPO As shown in Table 7, with our proposed AUGUstus-GRPO, jointly optimized with JaT-GRPO and CoT- GRPO, stage I improves PDMS by +4 and stage I further improves it by +0.6, achieving a SOTA PDMS of 94.6. These results demonstrate the effectiveness of our proposed unified AUGUstus-GRPO algorithm. 4.4 Visualization As shown in Fig. 7, the no-CoT model fails to yield to the nearby agent and collides, whereas CoT supervision produces a safer trajectory. Compared with other methods on the same scene, AUGUstus avoids collision while maintaining high progress. 5 Conclusion and Future Work In this work, we propose AUGUstus, a deployable unified VLA that integrates diffusion-based action generation and autoregressive CoT understanding in a single transformer, with AUGUstus-mode ordering for low-latency inference and AUGUstus-GRPO for joint optimization. Experiments on NAVSIMv1/v2 and nuScenes show state-of-the-art performance: AUGUstus achieves 94.6 PDMS on NAVSIMv1 and 90.7 EPDMS on NAVSIMv2 without a scorer module, and on nuScenes it achieves an average L2 error of 0.27 m and an average collision rate of 0.05%, both the best among the compared methods. To validate 9 its practicality, we train it on our in-house dataset with a large-scale GPU cluster, then evaluate it on an internal driving dataset and preliminarily deploy it on a real vehicle, achieving real-time operation. In future work, we will conduct more extensive real-vehicle tests to further validate the architecture and attempt to apply it to robot VLA. Acknowledgments Yuqi Ye completed this project as the first author during an internship at XPeng. We extend special thanks to Caigao Jiang, the project lead, for his leadership, invaluable guidance, and sustained support throughout the project. 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In International Conference on Learning Representations, volume 2026, pages 134129–134150, 2026. Xingcheng Zhou, Xuyuan Han, Feng Yang, Yunpu Ma, Volker Tresp, and Alois Knoll. Opendrivevla: Towards end-to-end autonomous driving with large vision language action model. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 40, pages 13782–13790, 2026a. Zewei Zhou, Tianhui Cai, Seth Zhao, Yun Zhang, Zhiyu Huang, Bolei Zhou, and Jiaqi Ma. Autovla: A vision-language-action model for end-to-end autonomous driving with adaptive reasoning and reinforcement fine-tuning. Advances in Neural Information Processing Systems, 38:27920–27956, 2026b. 11 Linear Linear SiLU Linear c Time Emb. Action Projector A 푡~ [0,1] 푥 푡 ∈푅 8×3 푒 푎푐푡 ∈푅 8×퐷 noise action Concatenate Time Emb. Sin/Cos 풆 풂풄풕 : Action token embedding풉 풂풄풕 : Action token hidden state + Residual Add visual input textchain-of-thought text A V L Linear SiLU Linear SiLU 푐표푛푑∈푅 퐵×푆×퐷 Time Emb. AdaRMSNorm Attention AdaRMSNorm MLP ℎ 푎푐푡 ∈푅 8×퐷 푥∈푅 퐵×푆×퐷 푐표푛푑∈푅 퐵×푆×퐷 RMSNorm (normalize x) Linear scale shift 푥 푛표푟푚 표푢푡∈푅 퐵×푆×퐷 푤 푠∈푅 퐵×푆×퐷 푏∈푅 퐵×푆×퐷 c 푥 c + + VVVLL A L t=0t=0t~[0,1]t=0 Transformer Decoder Layer x N AUGUstus AdaRMSNorm VL L A L Input Sequence (tokens) Time Modulation VL A L LayerNorm Linear SiLU Linear LayerNorm Action Decoder ℎ 푎푐푡 ∈푅 8×퐷 ො푥 0 ∈푅 8×3 풄풐풏풅: Time condition풔/풃:Adaptive scale/shift풘: RMSNormweight 풙 풏풐풓풎 (ퟏ+풘)(ퟏ+풔)+풃 Figure 8 Detailed AUGUstus module. Left: Action Projector. A normalized noisy trajectory푥 푡 ∈ R 8×3 and a sinusoidal time embedding are projected, concatenated, and passed through Linear–SiLU layers to form푒 act ∈ R 8×퐷 . Center: shared decoder. Visual tokens푉, input text퐿, noisy action tokens퐴, and CoT text share the transformer; the action block is bidirectional, and the segment-specific time modulation uses푡=0for context/CoT and the sampled푡for action tokens. Each layer contains attention, MLP, residual additions, and AdaRMSNorm. The inset expands the adaptive scale/shift푠,푏and the pretrained RMSNorm weight푤. Right: Action Decoder. LayerNorm–Linear–SiLU– LayerNorm–Linear decoding maps ℎ act ∈ R 8×퐷 to ˆ 푥 0 ∈ R 8×3 . A Supplementary Architecture Details A.1 Backbone and action projections Action-module data path. Given a normalized noisy trajectory푥 푡 ∈ R 8×3 and flow time푡 ∈ [0, 1], the module produces a clean trajectory estimate ˆ 푥 0 ∈ R 8×3 through three stages: an Action Projector, the shared transformer action-token block, and an Action Decoder. The eight rows always correspond to the eight future waypoints; all linear maps are shared across waypoint positions, while positional information is carried by the backbone’s continued token positions. Action Projector. In the left block of Fig. 8, each waypoint is first mapped from three coordinates to the hidden width by a linear layer. In parallel, the scalar flow time is encoded with a sinusoidal sine/cosine embedding. The two representations are concatenated row-wise and passed through a Linear–SiLU–Linear MLP, yielding action-token embeddings푒 act ∈ R 8×퐷 . Thus the time condition is available at the input of every action token without changing the dimensionality of the pretrained language-vision stream. Shared action-token block. The embeddings푒 act are inserted as an eight-token action block after the multimodal context. In AUGUstus-mode, the action block reads the cached video, ego-state, route, and language context and is bidirectional within itself; the subsequent causal CoT block may read the action states, but action tokens cannot read CoT tokens. The action states therefore receive scene information from the shared trunk while remaining independent of the optional autoregressive decoding path. During training, this is also the route by which the CoT loss can shape the action representation; during deployment, only the action block is evaluated. Segmented input sequence and transformer layer. The center of Fig. 8 expands one forward pass into its token segments: visual tokens푉, input-language tokens퐿, noisy action tokens퐴, and causal chain-of-thought tokens퐿. The action segment is a single bidirectional block, while the language and CoT segments retain their autoregressive masks. Every decoder layer applies the same residual pattern, AdaRMSNorm→ Attention→ Add→ AdaRMSNorm→ MLP→ Add, to the shared hidden states. The time condition is segment-specific: visual and input-language tokens use푡=0, the noisy action tokens use the sampled푡 ∈[0, 1], and the CoT tokens again use푡=0. This keeps the diffusion state from contaminating the language stream while allowing every action layer to adapt to the denoising point. Action Decoder. The right block of Fig. 8 maps the final action hidden statesℎ act ∈ R 8×퐷 back to waypoint coordinates. It applies LayerNorm, a linear projection, SiLU, a second LayerNorm, and a final linear projection to three channels, producing ˆ 푥 0 ∈ R 8×3 . The output is inverse-normalized to metric푥,푦, and heading coordinates before being sent to the planner. At푡 = 1, the푥 0 -parameterization makes this decoder output the deployed one-step trajectory directly; for a multi-step ODE/SDE rollout, the output is re-embedded as the next noisy action state and the same shared module is applied again. No separate action transformer or scorer is introduced. 12 Table 8 Kernel coefficients per schedule (Eq. (8); one reverse step푡 → 푡−Δ푡). The first row names each method and the second row gives its diffusion schedule 푔(푡) 2 ; the remaining rows give the induced kernel coefficients and endpoint behavior. †Flow-GRPO implementations substitute a clamp 휎 max for 휎 푠 near 푡=1. Flow-GRPO (Liu et al., 2026a) DanceGRPO (Xue et al., 2025)JaT-GRPO (ours) 푔(푡) 2 푎 2 푡 1−푡 휂 2 휆푡 푐 푥 1− Δ푡 푡 1+ 푎 2 2(1−푡) 1− Δ푡 푡 1+ 휂 2 2푡 1− Δ푡 푡 1+ 휆 2 푐 0 Δ푡 푡 1+ 푎 2 2 Δ푡 푡 1+ 휂 2 (1−푡) 2푡 Δ푡 푡 1+ 휆(1−푡) 2 휎 푠 푎 q 푡 Δ푡 1−푡 휂 √ Δ푡 √ 휆푡 Δ푡 푡=1, Δ푡=1푐 푥 →−∞, 휎 푠 →∞ † 푐 푥 =− 휂 2 2 , 푐 0 =1, 휎 푠 =휂 푐 푥 =− 휆 2 , 푐 0 =1, 휎 푠 = √ 휆 single-step policyundefined풩( ˆ 푥 0 − 휂 2 2 푥 1 , 휂 2 퐼)풩( ˆ 푥 0 − 휆 2 푥 1 , 휆퐼) terminal state 푡=0clean+풩(0, 휂 2 Δ푡 퐼) corruptionclean Flow time is injected with per-segment AdaRMSNorm. For hidden state ℎ and condition 푞, we use AdaRMSNorm(ℎ; 푞) = RMSNorm(ℎ)⊙(1+ 푤)⊙(1+ 푠(푞))+ 푏(푞), [푠(푞),푏(푞)] = 푊 푞 푞, (11) where푤is the pretrained RMSNorm weight. Context, language, and boundary tokens use a zero-time condition, while action tokens use the sampled flow time. The positional indices continue from the multimodal context into the action and CoT blocks, so the pretrained positional statistics are preserved. B Algorithmic Details for JaT-GRPO B.1 Reverse-time SDE kernel in x0-parameterization With the convention푡=1pure noise,푡=0data, the forward CFM interpolation푥 푡 =(1− 푡)푥 0 + 푡휀defines the probability-flow ODE ¤ 푥 푡 = 푣 휃 (푥 푡 ,푡) in the direction of decreasing푡. Adding Langevin diffusion with coefficient푔(푡)(the Flow-GRPO construction (Liu et al., 2026a)) gives the reverse-time SDE; its Euler–Maruyama step of size Δ푡 > 0 (from 푡 to 푡− Δ푡) is 푥 푡−Δ푡 = 푥 푡 − h 푣 휃 + 푔(푡) 2 2푡 푥 푡 +(1− 푡)푣 휃 i Δ푡+ 푔(푡) √ Δ푡 푧,(12) where− 1 푡 (푥 푡 +(1− 푡)푣)is the score∇ log푝 푡 of the linear interpolation path. Substituting the푥 0 - parameterized velocity 푣 휃 =(푥 푡 − ˆ 푥 휃 0 )/푡 and collecting 푥 푡 and ˆ 푥 휃 0 yields the kernel of Eq. (8) with 푐 푥 = 1− Δ푡 푡 1+ 푔(푡) 2 2푡 , 푐 0 = Δ푡 푡 1+ 푔(푡) 2 (1− 푡) 2푡 ,휎 푠 = 푔(푡) √ Δ푡. For푔(푡) 2 = 휆푡these reduce to푐 푥 = 1− Δ푡 푡 (1+ 휆 2 ),푐 0 = Δ푡 푡 (1+ 휆(1−푡) 2 ),휎 푠 = √ 휆푡Δ푡; at푡=1,Δ푡=1:푐 푥 =−휆/2, 푐 0 = 1, 휎 푠 = √ 휆, hence Eq. (16). The action-transition schedules used by GRPO are summarized in Table 8. The proposed schedule is finite at the pure-noise endpoint and vanishes at the clean endpoint, so it supports both one-step deployment and a clean terminal trajectory. The schedule enters the exact ratio and KL only through푐 0 and휎 푠 , so the same implementation covers all three alternatives. B.2 Closed-form log-ratio and KL Both kernels share variance 휎 2 푠 퐼, so with 푧 =(푥 푡−Δ푡 − 휇 old )/휎 푠 : log 휌 푡 =− 1 2휎 2 푠 푥 푡−Δ푡 − 휇 휃 2 − 푥 푡−Δ푡 − 휇 old 2 (13) = 1 휎 2 푠 ⟨휇 휃 − 휇 old , 푥 푡−Δ푡 − 휇 old ⟩− 1 2휎 2 푠 휇 휃 − 휇 old 2 = 푐 0 휎 푠 ⟨훿, 푧⟩− 푐 2 0 2휎 2 푠 ∥훿∥ 2 .(14) 13 SinceE[푧] = 0,E[log 휌 푡 ] =− 푐 2 0 2휎 2 푠 ∥훿∥ 2 =−KL(휋 old ∥휋 휃 )(equal-covariance Gaussian KL). The same derivation applies per coordinate푑when휎 푠 and푧are diagonal per-dimension quantities – the form used in our implementation with multivariate noise levels 휆 푥,푦,휓 . The corresponding reference-policy KL and deployed one-step policy are KL act = 푐 2 0 2휎 2 푠 ∥ ˆ 푥 휃 0 − ˆ 푥 ref 0 ∥ 2 2 .(15) 휋 휃 (푥 0 | 푥 1 , 푐) =풩 ˆ 푥 휃 0 − 휆 2 푥 1 , 휆퐼 (푡 = 1,Δ푡 = 1).(16) Scalar parametric form. Writing푚 = 훿/푡(the velocity-space prediction difference) and defining the schedule coefficient 휅 ≜ 푐 0 푡/휎 푠 , Eq. (14) factorizes per element into the compact quadratic form log 휌 = 휅⟨푚, 푧⟩− 1 2 휅 2 ∥푚∥ 2 ,KL = 1 2 휅 2 ∥푚∥ 2 ,휌≤ exp ∥푧∥ 2 /2 , with equality of the bound at푚 = −푧/휅– the quadratic dependence of휌 max on the exploration noise is a second, independent motivation for two-sided PPO clipping. For the constant-휂schedule, 휅 = √ Δ푡(휂 −1 + 휂(1−푡) 2푡 ); at 푡=1 this stays finite (휅 = √ Δ푡/휂). B.3 Gradient decomposition and comparison Writing 휙(휃) ≜ log 휌 푡 and differentiating Eq. (14): ∇ 휃 휙 = 푐 0 휎 푠 ⟨∇ 휃 ˆ 푥 휃 0 , 푧⟩− 푐 0 휎 푠 ⟨∇ 휃 ˆ 푥 휃 0 , 훿⟩ ,(17) i.e. an advantage-weighted noise-following term (move ˆ 푥 0 along푧when퐴 푖 > 0) and a trust-region-like term pulling ˆ 푥 0 back toward ˆ 푥 old 0 , which vanishes at the behavior policy; on-policy,E 푧 ∇휙 = 퐴 푖 푐 0 휎 푠 푧, equivalent to minimizingℒ equiv =− Í 푡 퐴 푖 푐 0 휎 푠 ⟨푧, ˆ 푥 휃 0 ⟩ . This contrasts with DiffusionNFT (Zheng et al., 2026), whose gradient follows the velocity difference direction with a built-in trust region of radius∝ 퐴 푖 /훽; Flow-GRPO coincides direction-wise with our first term but has no closed-form KL and a diverging 푡=1 schedule. B.4 Necessity of 휆 > 0 for Single-Step GRPO When푁 = 1, all rollouts in a group share the same initial condition푥 1 , so they can differ only in the noise variable푧. If휆 = 0, the kernel collapses to a point mass. Consequently, all퐺samples are identical, std 퐺 (푅) = 0, and the advantages are undefined or zero. Therefore,휆 > 0is necessary. Sufficiency follows because풩(휇, 휆퐼) has full support. B.5 Exploration Noise Engineering Per-dimension levels and trajectory smoothing. Exploration noise is applied in the quantile-normalized action space, with per-dimension levels(휆 푥 , 휆 푦 , 휆 휓 ). The injected noise is smoothed along the trajectory, keeping perturbed trajectories kinematically plausible. The group shares the initial푥 1 state so that advantages compare like-for-like trajectories. 휎-sensitivity of heteroscedastic noise. For fixed prediction shift훿 푑 in dimension푑, Eq. (15) gives per-step KL∝ 훿 2 푑 휆 −1 푑 , while the induced update drift of dimension푑scales as∇ ∝ 훿 푑 휆 −1 푑 (gradient) and the post-update KL as∝ 휆 −2 푑 ; with per-dimension noise levels spanning∼2.5×and time-scaled reweighting across waypoints, the effective step-size ratio across dimensions blows up to∼10 3 in drift terms, collapsing the effective sample size of the group to a few near-deterministic slots. As a result, we set noise level 5×10 −2 and groups with 퐺=8. C More detail about CoT This appendix complements the main-text CoT ablation with the complete CoT-content metrics and supervision templates (Table 9) and additional CoT-vs-no-CoT attention statistics. To avoid duplicate reporting, the metric table and the format table are merged: each CoT variant is listed once with its supervision template and full PDMS sub-metric breakdown. 14 Table 9 CoT content ablation (complete metrics and supervision formats). All variants share the Section 4.1 protocol and are evaluated with the deterministic one-step evaluator on the full navtest split; only the CoT content changes. PDMS is reported together with its full sub-metric breakdown: NC, DAC, DDC, EP, TTC, Comfort, and ADE. NC: no-collision, DAC: drivable-area compliance, DDC: driving-direction compliance, EP: ego progress, TTC: time-to-collision, Comfort: comfort, ADE: average L2 displacement. The default prediction CoT (risk-object boxes + future positions) is bolded; the last row is the CoT-first ordering control (identical recipe and prediction content, reverse token order). Inference time is reported once for the shared 73.60 ms action-only path and separately for the CoT-first path. CoT typeTemplate PDMS↑ NC↑ DAC↑ DDC↑ EP↑ TTC↑ Comf.↑ ADE↓ Time (ms) No CoT action-only training 89.2 98.8 96.8 98.4 83.5 95.8 100.0 0.530 Planning slow, keep lane, pass after crossing 90.1 98.9 97.4 98.5 83.8 96.1 100.0 0.522 Reasoning perception + future bins + maneuver 89.6 98.7 96.9 98.4 83.4 96.1 100.0 0.534 Perception car [x1,y1,x2,y2]; ped. [x1,y1,x2,y2] 90.3 98.9 97.5 98.6 84.3 96.1 100.0 0.517 73.60 Perception + Prediction boxes + future bins, no maneuver sentence 90.3 98.9 97.6 98.6 84.1 96.3 100.0 0.513 Short- prediction atomic vocabulary encoding 89.1 98.7 96.7 98.3 83.1 95.4 100.0 0.559 Prediction car [box] -> near-front; ped. [box] -> far-left 90.6 99.0 97.9 98.5 84.2 96.5 100.0 0.520 CoT first same as Prediction, CoT tokens precede action 90.6 99.1 97.8 98.6 84.2 96.6 100.0 0.521 4597 CoT content (Table 9). Removing CoT costs 1.4 PDMS (89.2 vs. 90.6), concentrated in drivable-area compliance (−1.1DAC) and ego progress (−0.7EP). This ablation directly tests the VLA-to-VA hypothesis: CoT is useful only when its content is action-relevant and its supervision reaches the shared action representation. Among CoT types, prediction beats perception (+0.3), planning (+0.5), and their union (+0.3): future-position labels carry the operative information, and stacking perception on top adds tokens without information. Free-form reasoning is worse (89.6), and a 2573-token-vocabulary atomic short-prediction encoding (∼14tokens per scene,7×shorter than the default) even falls below the no-CoT baseline (89.1 vs. 89.2) – aggressive CoT compression trades away the planning gain entirely. Order analysis confirms the “pre>per/perpre>pla” ranking. The CoT-first ordering control (last row) reaches the same 90.6 PDMS as the action-first default, confirming that the quality gain comes from the CoT supervision itself rather than the ordering; the ordering decides only the deployment cost, as reported in Fig. 6 (left). C.1 CoT content and supervision formats C.1.1 What each CoT teaches Our CoT ablation is a comparison of three alternative supervision targets, not a three-stage pipeline: every variant is trained on the identical scene and action, and only the content of the single CoT block differs. We take the three task-oriented CoT definitions from AutoDrive-P 3 (Ye et al., 2026b) – Perception CoT (the 2-D boxes of relevant agents), Prediction CoT (each box plus a discretized future-position label, such as near-frontorfar-left), and Planning CoT (textual ego waypoints or maneuvers) – and ask which one makes the action head plan best, since only one of them is emitted per sample. We do not chain them, and the model never consumes its own perception output to produce a prediction or a plan; the three streams are competing ways of describing the same scene, and Table 9 reports the outcome (prediction CoT wins). A fourth variant, reasoning CoT, concatenates the three signals into a compact approximately 100-token 15 explanation: it first names the relevant agents, then states their future bins, and finally gives the resulting ego maneuver. This is intentionally shorter and more structured than unconstrained free-form reasoning. Figure 9 instantiates the three variants on one NAVSIM right-turn scene, using the ground-truth annotation of the released evaluation split. The three panels share the identical scene and the identical agent ordering, so the figure isolates exactly what each CoT content contributes. All coordinates below are reported on the deployment canvas (2048× 512), matching the model input coordinate system. (a) Perception CoT: what is where. This variant emits a 2-D bounding box and a semantic class for every agent that can influence ego motion. Here the annotation contains five agents—two vehicles (one in the left lane, one far ahead in the center) and three vulnerable road users (two pedestrians and one cyclist on the right sidewalk)—each drawn with a class-colored box and a label tag in Figure 9(a). The complete answer field is <perception >["bbox_2d ":[0 ,265 ,146 ,509] ," l a b e l ":" v e h i c l e " , "bbox_2d ":[994 ,222 ,1085 ,329] ," l a b e l ":" v e h i c l e " , "bbox_2d ":[1954 ,259 ,2018 ,378] ," l a b e l ":" pedestrian " , "bbox_2d ":[1676 ,262 ,1740 ,372] ," l a b e l ":" pedestrian " , "bbox_2d ":[1728 ,283 ,1807 ,366] ," l a b e l ":" b i c y c l e "]</ perception > All five boxes are the salient agents that can influence ego motion: the two vehicles lie along the ego path, and the three vulnerable road users stand on the sidewalk that the right turn sweeps past. The ego vehicle is moving at10.35m/s, so the pedestrians and the cyclist are the agents whose distance the maneuver changes most rapidly. This variant carries location but no motion: it tells the planner where the conflicts currently are, not where they will be. (b) Prediction CoT: where each agent will be. This variant keeps the same boxes and assigns each of them a coarse future relative position over the next 4 s (e.g. near, right / far, front / behind), drawn as a directional arrow and a text tag on every box in Figure 9(b): <prediction >["bbox_2d ":[0 ,265 ,146 ,509] ," future_position ":" behind " , "bbox_2d ":[994 ,222 ,1085 ,329] ," future_position ":" far , front " , "bbox_2d ":[1954 ,259 ,2018 ,378] ," future_position ":" near , right " , "bbox_2d ":[1676 ,262 ,1740 ,372] ," future_position ":" near , right " , "bbox_2d ":[1728 ,283 ,1807 ,366] ," future_position ":" near , right "]</ prediction > The boxes share the same order as the perception variant. The vehicle in the adjacent left lane drops to behind, the lead vehicle stays far, front, and all three vulnerable road users remain near, right—the right-side road users are the safety-critical agents for this maneuver. This variant is the one our default model uses: it adds the future bearing of each conflict to its current location, and Table 9 shows that this extra content, and not merely the presence of language, is what lifts PDMS from 89.2 to 90.6. (c) Planning CoT: what the ego does. This variant instead describes the ego maneuver itself, as eight waypoints(푥, 푦, 휃)at0.5s intervals over a4s horizon. Figure 9(c) projects the ground-truth trajectory (green) back onto the camera strip and shows the complete top-down arc in a BEV inset; note that the inset is drawn with ego-left on the left, so the right turn bends to the right of the star: <planning >["x_y_radian " : [ 5 . 2 2 , 0 . 0 , - 0 . 0 1 ] , " l a b e l ":"0.5 s " , "x_y_radian " : [ 1 0 . 5 8 , - 0 . 0 7 , - 0 . 0 2 ] , " l a b e l ":"1.0 s " , "x_y_radian " : [ 1 6 . 0 4 , - 0 . 2 8 , - 0 . 0 5 ] , " l a b e l ":"1.5 s " , "x_y_radian " : [ 2 1 . 5 5 , - 0 . 6 , - 0 . 0 7 ] , " l a b e l ":"2.0 s " , "x_y_radian " : [ 2 7 . 0 6 , - 1 . 0 2 , - 0 . 0 9 ] , " l a b e l ":"2.5 s " , "x_y_radian " : [ 3 2 . 5 7 , - 1 . 5 5 , - 0 . 1 ] , " l a b e l ":"3.0 s " , "x_y_radian " : [ 3 8 . 0 9 , - 2 . 1 1 , - 0 . 1 ] , " l a b e l ":"3.5 s " , "x_y_radian " : [ 4 3 . 7 6 , - 2 . 6 9 , - 0 . 1 ] , " l a b e l ":"4.0 s "]</ planning> The eight waypoints trace a gentle, high-speed right curve that advances from(5.2, 0.0)m to(43.8,−2.7)m while the heading rotates from−0.01to−0.10rad, keeping a lateral offset from the sidewalk agents on the right. Because this variant describes the answer rather than the evidence, it is farther from the visual input than (a) and (b): its90.1PDMS sits below prediction CoT, consistent with the view that the most useful CoT content is the one that supplies the action head with the operative scene information. Prediction CoT is the most useful target because it supplies the action head with both the current conflict location and its likely future bearing. Perception alone gives the object but not its motion, while planning text is farther from the visual evidence. Free reasoning is less stable under teacher forcing, and aggressive atomic compression removes useful spatial context. The supervision templates and the complete PDMS sub-metric breakdown (NC, DAC, DDC, EP, TTC, Comfort, and ADE) are reported together in Table 9. 16 (a) Perception 2D bounding box + semantic class vehicle veh. ped. ped. bike GT Perception answer (2048x512 canvas) [ "bbox_2d": [0, 265, 146, 509], "label": "vehicle", "bbox_2d": [994, 222, 1085, 329], "label": "vehicle", "bbox_2d": [1954, 259, 2018, 378], "label": "pedestrian", "bbox_2d": [1676, 262, 1740, 372], "label": "pedestrian", "bbox_2d": [1728, 283, 1807, 366], "label": "bicycle" ] (b) Prediction future relative position + motion arrow behind far front near right near right near right GT Prediction answer (2048x512 canvas) [ "bbox_2d": [0, 265, 146, 509], "future_position": "behind", "bbox_2d": [994, 222, 1085, 329], "future_position": "far, front", "bbox_2d": [1954, 259, 2018, 378], "future_position": "near, right", "bbox_2d": [1676, 262, 1740, 372], "future_position": "near, right", "bbox_2d": [1728, 283, 1807, 366], "future_position": "near, right" ] (c) Planning ground-truth 4 s trajectory 202 y (m, left+) 0 20 40 x (m, forward) BEV GT Planning answer (metric, 0.5 s per waypoint) [ "x_y_radian": [5.22, 0.0, -0.01], "label": "0.5s", "x_y_radian": [10.58, -0.07, -0.02], "label": "1.0s", "x_y_radian": [16.04, -0.28, -0.05], "label": "1.5s", "x_y_radian": [21.55, -0.6, -0.07], "label": "2.0s", "x_y_radian": [27.06, -1.02, -0.09], "label": "2.5s", "x_y_radian": [32.57, -1.55, -0.1], "label": "3.0s", "x_y_radian": [38.09, -2.11, -0.1], "label": "3.5s", "x_y_radian": [43.76, -2.69, -0.1], "label": "4.0s" ] Figure 9 The three CoT contents compared on one NAVSIM right-turn scene (ground-truth annotations). The three rows are three alternative supervision targets, not a serial pipeline: each is trained alone on the same scene and action, and the model never consumes one row’s output to produce another’s. One pastel outer frame encloses the title, annotated scene, and JSON answer of each CoT variant. (a) Perception CoT: a 2-D box and a class label for every salient agent (vehicle: blue, bicycle: orange, pedestrian: violet) on the2048× 512deployment canvas. (b) Prediction CoT: each box is annotated with its future relative position and a motion arrow; this is the default target. (c) Planning CoT: the ground-truth4s trajectory (green) projected onto the camera strip, with a BEV inset (ego-left on the left) showing the top-down right-turn arc. C.2 CoT attention visualization We visualize the last-frame attention from the final full-attention layer, as shown in Figure 10. With prediction-CoT supervision, the action queries consistently concentrate on nearby vehicles and vulnerable road users that constrain the maneuver, rather than spreading attention over the whole image. More 17 importantly, we observe a clear qualitative difference between models trained with and without CoT. Without CoT supervision, the attention is dominated by the lead vehicle that the ego car is following, while surrounding vehicles receive little attention. This narrow focus becomes problematic in cluttered or safety-critical scenes: nearby hazardous vehicles can be overlooked, which in turn prevents the policy from reacting safely. In contrast, adding CoT supervision broadens the attention of the VLA to a larger set of task-relevant objects, including adjacent vehicles, pedestrians, and cyclists that may affect the maneuver. As a result, the model acquires more comprehensive spatial awareness and produces safer driving strategies. These observations are consistent with the quantitative gains in NC and DAC reported in Table 9. raw frame (+GT boxes + GT path)AUGUstus action attention in-box 58% AUGUstus CoT attention in-box 1% w/o CoT training, action attention raw frame (+GT boxes + GT path)AUGUstus action attention in-box 66% AUGUstus CoT attention in-box 2% w/o CoT training, action attention raw frame (+GT boxes + GT path)AUGUstus action attention in-box 59% AUGUstus CoT attention in-box 9% w/o CoT training, action attention raw frame (+GT boxes + GT path)AUGUstus action attention in-box 62% AUGUstus CoT attention in-box 3% w/o CoT training, action attention raw frame (+GT boxes + GT path)AUGUstus action attention in-box 48% AUGUstus CoT attention in-box 0% w/o CoT training, action attention raw frame (+GT boxes + GT path)AUGUstus action attention in-box 60% AUGUstus CoT attention in-box 1% w/o CoT training, action attention Figure 10 CoT attention visualization. After prediction-CoT supervision, action tokens attend more to key objects across these scenes. 18 C.3 Trajectory visualization: collision reduction The attention evidence is reflected in the trajectories. Training CoT reduces collisions and improves the safety terms in Table 9: NC rises from98.8to99.0, DAC from96.8to97.9, and TTC from95.8to96.5. The following three collision cases show the qualitative counterpart: the no-CoT policy enters the conflict region, whereas the CoT-trained policy identifies the nearby agent and keeps a feasible clearance, as shown in 11. � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Figure 11 Collision cases. Each row compares the no-CoT and prediction-CoT trajectories in the same scene. CoT redirects the action away from the conflict agent, consistent with the improved NC, DAC, and TTC values in Table 9. C.4 Trajectory visualization: progress preservation Safety does not come from stopping. The prediction-CoT model also improves ego progress (EP 83.5→ 84.2) and the aggregate PDMS (89.2→ 90.6) in Table 9, while retaining full comfort. The three progress cases, as shown in 12, below show that the CoT policy avoids the conflict and continues along the route instead of replacing unsafe motion with an overly conservative halt. 19 GTw/o CoT trainingw/ CoT training 100102030 Lateral (m) 10 0 10 20 30 Longitudinal (m) GT PDMS 0.85 EP 0.63 Human reference 100102030 Lateral (m) w/o CoT training PDMS 0.65 EP 0.15 Low progress 100102030 Lateral (m) w/ CoT training PDMS 0.83 EP 0.59 High progress GTw/o CoT trainingw/ CoT training 100102030 Lateral (m) 10 0 10 20 30 Longitudinal (m) GT PDMS 0.93 EP 0.83 Human reference 100102030 Lateral (m) w/o CoT training PDMS 0.90 EP 0.76 Low progress 100102030 Lateral (m) w/ CoT training PDMS 1.00 EP 1.00 High progress GTw/o CoT trainingw/ CoT training 100102030 Lateral (m) 10 0 10 20 30 Longitudinal (m) GT PDMS 1.00 EP 1.00 Human reference 100102030 Lateral (m) w/o CoT training PDMS 0.90 EP 0.77 Low progress 100102030 Lateral (m) w/ CoT training PDMS 1.00 EP 1.00 High progress Figure 12 Progress-preserving cases. Prediction CoT keeps the route-directed motion while avoiding the nearby agent. The qualitative cases complement the EP and PDMS gains reported in Table 9; they are representative examples rather than a pointwise guarantee. D Algorithmic Details: SFT, AUGUstus-GRPO D.1 Reward Design Details and Curriculum Rationale Prediction (CoT) reward. Predicted boxes are greedily matched to ground-truth boxes by descending IoU at threshold0.5;푟 det = Í IoU/max(#pred, #gt)is a soft F1 (penalizing both misses and hallucinations), and푟 fp is the fraction of matched boxes whose future-position label agrees;푟 pred = 푟 det ·푟 fp . A strict format gate requires exactly one<prediction>...</prediction>block with clean JSON content and no surrounding text or code fences; violations zero 푟 pred (and only 푟 pred ). Planning reward. Stage I uses푅 = 푟 pred + 5· PDMS. Stage I uses푅 = 푟 pred + 5(푟 endpoint + 푟 safe ), where 푟 endpoint maps the final-waypoint deviation to1, .8, .6, .4, .2over progressively looser L1 thresholds (the 20 softest of four tested “soft-error” shapings worked best), and 푟 safe = ( mean TTC, DAC ,min 푚∈풢 subscore 푚 > 0 0otherwise, 풢 =NC, DAC, TTC, EP. with the hard gate additionally zeroing the whole planning term. PDMS is deliberately removed from the stage-I reward for two reasons: (i) late-stage PDMS becomes near-constant within a group (std∼0.02), so its group-relative advantage is dominated by noise, a measured failure mode of dense-score rewards; (i) direct PDMS optimization slightly trades NC/TTC for EP. The endpoint-plus-shield shaping preserves a dense informative signal (waypoint geometry) but re-imposes safety ceilings; PDMS remains the validation/model-selection metric throughout, so there is no metric/reward mismatch risk in checkpoint choice. D.2 Implementation details D.2.1 SFT Training Detail We adopt Qwen3.5-2B backbone network. The action sequence consists of 8 action tokens with hidden dimension퐻=2048. The ActionEncoder is a 3-layer SiLU MLP with concatenated sinusoidal time embedding푡. The ActionDecoder follows the structureLN→ Lin→ SiLU→ LN→ Lin(3)and uses a near-zero final initialization. Each layer applies per-norm modulation projections that map퐻to 2퐻, corresponding to a DiT variant with approximately8M additional parameters. We apply quantile normalization with(푞 01 , 푞 99 )per action dimension. Training uses DeepSpeed ZeRO-2 with bf16 precision. The loss weights are 휆 diff =10 and 휆 lm =1. The main model uses dimension weights(1, 1, 1). For every training example we sample a flow time푡and noise휀, construct푥 푡 =(1− 푡)푥 0 + 푡휀, and run one joint AUGUstus-mode forward. The action head predicts ˆ 푥 0 while the language head teacher-forces the structured CoT 푦. The complete objective is ℒ SFT = 휆 diff ℒ 푥 0 + 휆 lm ℒ CE ,(18) whereℒ 푥 0 is the dimension-normalized flow-matching L1 loss. We use휆 diff =10and휆 lm =1in the default recipe. The CoT labels are generated from the same scene annotation as the action target. Teacher forcing is used only during SFT: the action tokens are visible to the CoT stream, whereas the action tokens never read CoT tokens. Consequently,ℒ CE back-propagates through the action states and the shared trunk, but does not create an inference-time dependency on generated text. D.2.2 RL Training Detail We perform synchronous rollouts based on Verl, where a unified actor serves both rollout generation and policy updates. Each iteration uses 32 prompts with퐺=8rollouts per prompt, resulting in 256 sequences. The rollout uses a 3-step SDE with per-dimension diffusion coefficients푔 푑 (푡) 2 = 푎 2 푑 푡, where 푎 푑 ∈(0.05, 0.05, 0.02). All rollouts in a group share the same initial state푥 1 . During rollout, the prefix KV is frozen, and the behaviour policy output ˆ 푥 0 as well as the CoT token log-probabilities are recorded. For the update, we use a single PPO mini-batch that is fully on-policy, with a learning rate of10 −6 , a clipping threshold of 0.2 for both heads, and a gradient clipping norm of 1.0. For a context group푐we draw one shared initial noise state푥 1 and퐺independent transition-noise sequences. Each rollout returns an action trajectory 푥 푖 and a CoT sequence 푦 푖 . Its scalar reward is 푅 푖 = 푅 pred (푦 푖 )+ 휆푅 plan (푥 푖 ), 퐴 푖 = 푅 푖 − mean 푗 (푅 푗 ) std 푗 (푅 푗 )+ 10 −6 ,(19) where we set휆 = 5. The same outcome signal trains both modalities. Stage I sets푅 plan = PDMS; Stage I replaces this saturating score by the endpoint-plus-safety shaping in Appendix D.1.The action objective is the clipped JaT-GRPO surrogate, and the language objective is token-level clipped CoT-GRPO: 풥 푎 = E min(휌 푎 퐴, clip(휌 푎 , 1− 휖, 1+ 휖)퐴) ,(20) 풥 푐 = E " 1 |푦| Õ 푘 min(휌 푐,푘 퐴, clip(휌 푐,푘 , 1− 휖, 1+ 휖)퐴) # .(21) 21 The update maximizes풥 푎 + 훼 푐 풥 푐 while adding the exact action KL in Eq. (15) and a token-level reference KL for CoT. Thus CoT-GRPO is ordinary PPO on the discrete suffix, but its advantage is tied to the same simulator outcome as the continuous action head. Algorithm 5 AUGUstus supervised fine-tuning: complete procedure Require: Pretrained parameters 휃; training samples풟 =(푐, 푥 0 , 푦); loss weights and optimizer. Ensure: Cold-start policy 휋 SFT with action and prediction-CoT outputs. 1: for each supervised training iteration do 2: Sample a minibatch of contexts, target trajectories, and prediction CoTs from풟. 3: Normalize target trajectories using the fixed action statistics. 4: Sample flow times 푡 and independent noise 휀∼풩(0, 퐼). 5: Form 푥 푡 =(1− 푡)푥 0 + 푡휀 for each training sample. 6: Encode context 푐 =(푆,퐸, 퐶, 퐻), noisy action 푥 푡 with time 푡, and shifted CoT tokens 푦 <푘 . 7: Run one shared-transformer forward pass with AUGUstus-mode hybrid attention. 8: Read the clean-trajectory prediction ˆ 푥 0 and the token distribution 푝 휃 (푦 푘 | 푦 <푘 , 푐, 푥 푡 ). 9: Compute the joint flow-matching and teacher-forced CoT loss in Eq. (3) and include the auxiliary module losses. 10: Backpropagate both losses jointly through the shared transformer and update 휃. 11: Validate with action-only denoising. 12: end for 13: return The selected cold-start policy 휋 SFT . Algorithm 6 AUGUstus deployment: complete AUGUstus-mode inference Require: Trained policy 휋 휃 ; context 푐 =(푆,퐸, 퐶, 퐻); schedule 1 = 푡 0 >· > 푡 푁 = 0; optional CoT flag. Ensure: Future ego trajectory 푥 out and, only if requested, prediction CoT 푦. 1: Encode the causal context prefix once and cache its states. 2: Draw 푥 ∼풩(0, 퐼) in normalized action space. 3: for 푛 = 0 to 푁− 1 do 4: Evaluate the bidirectional action block against the cached context to obtain ˆ 푥 0 . 5: Apply the deterministic flow step: 푥 ← 푥−(푡 푛 − 푡 푛+1 )(푥− ˆ 푥 0 )/푡 푛 . 6: end for 7: Invert the fixed action normalization to obtain 푥 out . 8: if prediction CoT is requested then 9: Append the denoised action block to the context with zero-time conditioning. 10: Autoregressively decode 푦 푘 ∼ 푝 휃 (·| 푦 <푘 , 푐, 푥) with causal CoT attention. 11: return (푥 out , 푦). 12: else 13: return 푥 out without CoT decoding. 14: end if D.3 Complete Training and Inference Algorithms Algorithms 5 and 6 give the full cold-start and deployment procedures corresponding to the contrasts in Algorithms 1 and 2. Both use the same AUGUstus-mode attention (action before CoT): context is causal, actions are bidirectional, and causal CoT tokens can read context and actions but not vice versa. Training uses noisy ground-truth actions and teacher-forced prediction CoT; deployment uses initial Gaussian noise and deterministic action denoising, with no ground-truth action or CoT required. Action normalization, time conditioning, and auxiliary module losses follow Appendix A and Appendix D.2. D.4 Complete two-stage unified GRPO Algorithm 7 specifies the complete two-stage post-training procedure. The reference is frozen at SFT throughout both stages; the behavior policy is snapshotted before each on-policy rollout batch. Within each context group, initial flow noise is shared, whereas transition exploration noise and CoT sampling distinguish the rollouts. The standard run uses the noise settings in Appendix B.5, the reward and format gates in Appendix D.1, and the optimization settings in Appendix D.2. The same prediction reward is used in both stages. Stage I uses푅 pred + 5 PDMS, whereas Stage I uses푅 pred + 5(푅 endpoint + 푅 safe )with the planning safety gate. 22 Algorithm 7 AUGUstus-GRPO: complete two-stage unified optimization Require: Cold-start policy 휋 SFT ; contexts풟; group size 퐺; denoising schedule; clip and KL weights. Ensure: Two-stage action–CoT policy 휋 ∗ I . 1: Freeze 휋 ref ← 휋 SFT and initialize 휋 휃 ← 휋 SFT . 2: for stage 푠 ∈1, 2 do 3: if 푠 = 2 then 4:Warm-start 휋 휃 ← 휋 ∗ I , the best validation-PDMS Stage-I checkpoint. 5: end if 6: for each on-policy RL iteration do 7:Snapshot the behavior policy 휋 old ← 휋 휃 and sample a context minibatch. 8:for each context 푐 in the minibatch do 9:Draw one initial 푥 1 ∼풩(0, 퐼) shared by the 퐺 rollouts. 10:for 푖 = 1 to 퐺 do 11:Initialize 푥 푖,푡 0 ← 푥 1 . 12:for 푛 = 0 to 푁− 1 do 13:Predict ˆ 푥 old 0 = 푓 old (푥 푖,푡 푛 ,푡 푛 , 푐). 14:Draw kernel noise 푧 and sample 푥 푖,푡 푛+1 ← 푐 푥 푥 푖,푡 푛 + 푐 0 ˆ 푥 old 0 + 휎 푠 푧 via Eq. (8). 15:Record both states, ˆ 푥 old 0 , 푧, and the kernel coefficients for re-scoring. 16:end for 17:Set 푥 푖 ← 푥 푖,0 ; decode action-conditioned CoT 푦 푖 and record its token log probabilities. 18:Compute 푅 pred,푖 with the same prediction scoring and format gate in both stages. 19:if 푠 = 1 then 20:Set 푅 plan,푖 ← PDMS 푖 . 21:else 22:Set 푅 plan,푖 ← 푅 ep,푖 + 푅 safe,푖 and apply the planning safety gate. 23:end if 24:Set 푅 푖 ← 푅 pred,푖 + 5푅 plan,푖 . 25:end for 26:Normalize group rewards into the shared advantages 퐴 푖 using Eq. (4). 27:end for 28:Re-evaluate recorded action states and CoT prefixes under 휋 휃 and the frozen 휋 ref . 29:Evaluate JaT-GRPO ratios directly from ˆ 푥 휃 0 − ˆ 푥 old 0 using Eq. (14). 30:Evaluate the action and CoT ratios and their native KL terms; keep each rollout’s shared 퐴 푖 . 31:Compute the two clipped objectives풥 푎 and풥 푐 . 32:Jointly update 휃 withℒ =−풥 푎 + 훽 푎 KL act + 훼 푐 (−풥 푐 + 훽 푐 KL CoT ). 33:Synchronize the updated policy for the next rollout batch and retain the best validation checkpoint. 34: end for 35: Save the selected stage checkpoint as 휋 ∗ I or 휋 ∗ I . 36: end for 37: return 휋 ∗ I . D.5 Three-stage training trace The SFT checkpoint provides scene grounding and a stable action prior. Stage I uses PDMS to improve progress and establishes the first RL checkpoint. Stage I switches to endpoint and safety shaping to recover within-group variance after PDMS saturates. The qualitative traces in Fig. 13 show the same progression: the predicted path becomes more compliant at Stage I and then adds a larger safety margin at Stage I. Meanwhile, the CoT prediction accuracy improves from 0.75 at SFT to 0.85 after RL, indicating increasingly accurate identification of critical objects and thereby enhancing the model’s action planning capability. 23 SFTRL stage 1RL stage 2 100102030 Lateral (m) 10 0 10 20 30 40 Longitudinal (m) SFT PDMS 0.47 100102030 Lateral (m) RL stage 1 PDMS 0.97 100102030 Lateral (m) RL stage 2 PDMS 0.98 SFTRL stage 1RL stage 2 100102030 Lateral (m) 10 0 10 20 30 40 50 Longitudinal (m) SFT PDMS 0.47 100102030 Lateral (m) RL stage 1 PDMS 0.96 100102030 Lateral (m) RL stage 2 PDMS 0.97 SFTRL stage 1RL stage 2 100102030 Lateral (m) 10 0 10 20 30 Longitudinal (m) SFT PDMS 0.49 100102030 Lateral (m) RL stage 1 PDMS 0.96 100102030 Lateral (m) RL stage 2 PDMS 0.98 Figure 13 Three-stage RL visualization. Each case shows the same scene under SFT, RL Stage I, and RL Stage I. Stage I moves the path toward the desired progress profile; Stage I retains that progress while increasing the safety margin. The displayed case-level PDMS values are illustrative qualitative traces, whereas the aggregate values are in Table 7. D.6 Deployment Complexity Latency. The deployed path is a causal visual prefix followed by one bidirectional eight-token action suffix. The vision encoder remains eager because the multimodal preprocessing contains host synchronization; the prefix and denoising suffix are captured in one CUDA graph. Table 10 reports the steady-state batch-one measurements from the profiling script in fast_inference.md. The eager profile launches about3.7k small kernels and performs roughly 200 pageable host-to-device copies per sample. Graph replay removes this CPU dispatch overhead and reduces the LLM stage from 91.83 to33.19ms (2.77×), while leaving the visual stage unchanged. The action suffix contributes only eight tokens on top of a roughly 2,257-token context. Optional post-hoc CoT is therefore deliberately disabled in the speed-critical configuration: a measured 166-token explanation takes about 4.5 s at batch one, whereas the action-only path is below 100 ms. Scorer Module. Let퐶 vis be the visual encoder cost,퐶 pre (퐿)the prefix cost for퐿context tokens, and퐶 act (푇) 24 Table 10 Measured batch-one latency on one H800. Path or moduleMean (ms) Fraction Vision encoder and M-RoPE40.2054.6% Context prefix, eager46.0434.8% One-step denoising, eager45.7034.6% LLM stage, CUDA-graph replay33.1945.1% End-to-end, eager131.88– End-to-end, CUDA graph73.67 13.6 Hz the eight-token action suffix. Our single-trajectory path is 푇 ours = 퐶 vis + 퐶 pre (퐿)+ 퐶 act (푇), 푇 = 8,(22) and is independent of the number of candidates. A VLA+scorer system that generates푁trajectories and scores them costs approximately 푇 scorer (푁) = 푁 퐶 pre (퐿)+ 퐶 act (푇) + 퐶 vis + 푁퐶 score .(23) Thus,푁=32–64multiplies the expensive VLM pass even if the scorer itself is lightweight. As a result, this VLA+scorer design is difficult to run in real time on vehicle hardware. We therefore generate one trajectory in one network evaluation; the deployed path takes 73.6 ms on an H800 (13.6 Hz) and 83 ms on the real vehicle (12 Hz), while retaining SOTA public-benchmark performance. E Qualitative Results on Public, Private Data, and Driving Test E.1 Public benchmark examples The public examples compare the same scene across ReCogDrive (Xiong et al., 2026), AutoDrive-P 3 Ye et al. (2026b), and AUGUstus. The twelve cases in Fig. 14 and Fig. 15 provides representative qualitative comparisons. E.2 Internal 1,000 km data The internal set contains long-tail interactions and camera conditions not present in NAVSIM. Figures 16 and Figures 17 shows twelve representative cases from the 1,000 km evaluation; the category-level aggregate remains the one reported in Table 4. E.3 Regression and flow-matching baselines Figure 18 and Figure 19 keeps the direct VLM+regression and VLM+flow-matching comparison in one image. Both baselines use the same scene input; the comparison isolates the action parameterization and the shared CoT training rather than a sensor change. 25 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Figure 14 Public-set qualitative comparison (part 1/2). Each panel contrasts ReCogDrive, AutoDrive-P 3 , and AUGUstus on the same public scene. The single AUGUstus trajectory is both collision-free and route compliant in these examples. 26 RecogDriveAutoDrive-P3AUGUstus (Ours) 100102030 Lateral (m) 10 0 10 20 30 Longitudinal (m) RecogDrive PDMS 0.00 NC 0.00 Having collision 100102030 Lateral (m) AutoDrive-P3 PDMS 0.79 EP 0.50 Low progress 100102030 Lateral (m) AUGUstus (Ours) PDMS 1.00 EP 1.00 NC 1.00 Safety and high progress � � � � � � � � � � � � � � � � � � � � � � � � � � RecogDriveAutoDrive-P3AUGUstus (Ours) 100102030 Lateral (m) 10 0 10 20 30 40 Longitudinal (m) RecogDrive PDMS 0.00 NC 0.00 Having collision 100102030 Lateral (m) AutoDrive-P3 PDMS 0.79 EP 0.51 Low progress 100102030 Lateral (m) AUGUstus (Ours) PDMS 1.00 EP 1.00 NC 1.00 Safety and high progress Figure 15 Public-set qualitative comparison (part 2/2). Three additional public scenes comparing ReCogDrive, AutoDrive-P 3 , and AUGUstus under the same visualization protocol. 27 front leftfrontfront right rear leftrearrear right 2010010203040506070 BEV 10 0 10 Ego Agent History trajectory GT trajectory Predict trajectory front leftfrontfront right rear leftrearrear right 605040302010010203040506070 BEV 30 20 10 0 Ego Agent History trajectory GT trajectory Predict trajectory front leftfrontfront right rear leftrearrear right 706050403020100102030405060708090 BEV 40 30 20 10 0 Ego Agent History trajectory GT trajectory Predict trajectory Figure 16 Internal 1,000 km qualitative examples. Representative long-tail interactions and camera conditions from the private evaluation set. 28 front leftfrontfront right rear leftrearrear right 302010010203040 BEV 0 10 Ego Agent History trajectory GT trajectory Predict trajectory front leftfrontfront right rear leftrearrear right 30201001020304050 BEV 0 10 20 Ego Agent History trajectory GT trajectory Predict trajectory front leftfrontfront right rear leftrearrear right 1001020 BEV 0 Ego Agent History trajectory GT trajectory Predict trajectory Figure 17 Internal 1,000 km qualitative examples. Representative long-tail interactions and camera conditions from the private evaluation set. (part 2/2). 29 front leftfrontfront right rear leftrearrear right 2010010203040506070 BEV 10 0 10 Ego Agent History trajectory GT trajectory Ours trajectory FM trajectory RH trajectory front leftfrontfront right rear leftrearrear right 10010203040 BEV 0 10 Ego Agent History trajectory GT trajectory Ours trajectory FM trajectory RH trajectory front leftfrontfront right rear leftrearrear right 201001020304050607080 BEV 10 0 10 Ego Agent History trajectory GT trajectory Ours trajectory FM trajectory RH trajectory Figure 18 Internal qualitative comparison of VLM+regression, VLM+flow matching, and AUGUstus (part 1/2). 30 front leftfrontfront right rear leftrearrear right 20100102030405060708090 BEV 10 0 10 Ego Agent History trajectory GT trajectory Ours trajectory FM trajectory RH trajectory front leftfrontfront right rear leftrearrear right 80706050403020100102030405060708090100110120 BEV 0 10 20 30 40 50 Ego Agent History trajectory GT trajectory Ours trajectory FM trajectory RH trajectory front leftfrontfront right rear leftrearrear right 403020100102030405060708090100110 BEV 30 20 10 0 Ego Agent History trajectory GT trajectory Ours trajectory FM trajectory RH trajectory Figure 19 Internal qualitative comparison of VLM+regression, VLM+flow matching, and AUGUstus (part 2/2). 31 E.4 Real-vehicle visualization The real-vehicle examples use the same action-only deployment path as the latency measurement. The camera mosaic and bird’s-eye trajectory in Fig. 20 show that the one-step output remains smooth in nighttime and multi-camera conditions. front leftfrontfront right rear leftrearrear right 1001020 BEV 0 lateral (m) [left +] Ego Agent History trajectory Predict trajectory front leftfrontfront right rear leftrearrear right 2010010203040506070 BEV 10 0 10 lateral (m) [left +] Ego Agent History trajectory Predict trajectory Figure 20 Real-vehicle qualitative examples. The deployed action-only path runs at 12 Hz on the vehicle. The BEV trajectory is generated directly by the shared model; CoT decoding is omitted from this loop. 32