Behavior policies are often formulated as continuous generative models, whose iterative denoising processes are expressive but difficult to interpret and prone to producing implausible actions. We propose the Large Discrete Policy (LDiP), a fully discrete behavior modeling framework that selects actions from a large vocabulary of physically plausible candidates. Rather than perturbing actions, LDiP improves expressivity through stochastic iterative scoring: it progressively re-scores and prunes candidates with score-space stochasticity, enabling fine-grained ranking and exploration among plausible actions while preserving an explicit decision process. Across end-to-end planning, closed-loop driving, robotic manipulation, and vision-language-action settings, LDiP consistently outperforms strong discrete and continuous baselines in autonomous driving, and exceeds or matches continuous generative policies in robotic manipulation. These results show that discrete policies, when equipped with effective scoring mechanisms, offer an expressive, plausible, and interpretable alternative for behavior modeling. Project website: https://zhenxinli.net/LargeDiscretePolicy/.
Figures & tables
Figure 1: Paradigms for Behavior Modeling Policies. (a) Iterative denoising policies generate actions through stochastic iterative refinement, offering strong expressivity but remaining an implicit and less interpretable generation process. (b) One-shot discrete policies explicitly select from a fixed action vocabulary, but are limited by single-pass scoring. (c) Our approach combines the strengths of both paradigms by performing stochastic iterative scoring over a discrete action vocabulary, enabling expressive, plausible, and interpretable behavior generation.
Figure 2: The Model Architecture of LDiP. LDiP first tokenizes a fixed action vocabulary into action tokens, which attend to visual observations and optional language instructions in a Transformer decoder. The model then scores all candidates with an MLP, stochastically prunes the vocabulary, and iteratively re-scores the remaining candidates until a single action is selected.
Table 1: Performance on the Navtest v2 Benchmark, End-to-end Planning Models.
Method
VLM
Behavior Modeling
NC ↑
DAC ↑
TTC ↑
C ↑
EP ↑
PDMS ↑
Human
–
–
100
100
100
99.9
87.5
94.8
AutoVLA Zhou et al. (2025)
Qwen2.5-VL-3B Bai et al. (2025b)
Token Generation
98.4
95.6
98.0
99.9
81.9
89.1
ReCogDrive Li et al. (2025d)
InternVL3-8B Zhu et al. (2025)
Diffusion
98.2
97.8
95.2
99.8
83.5
89.6
DriveVLA-W0 Li et al. (2025c)
Emu3-8B Wang et al. (2024)
Discrete
98.7
99.1
95.3
99.3
83.3
90.2
AdaThinkDrive Luo et al. (2025)
InternVL3-8B Zhu et al. (2025)
Token Generation
98.4
97.8
95.2
100
84.4
90.3
SpanVLA Zhou et al. (2026)
Qwen2.5-VL-3B Bai et al. (2025b)
Flow Matching
99.1
97.1
95.2
100
86.3
90.3
Table 2: Performance on the Navtest v1 Benchmark, Vision-Language-Action Models.
Method
Easy
Medium
Hard
Extreme
Overall
RC ↑
HD-Score ↑
RC ↑
HD-Score ↑
RC ↑
HD-Score ↑
RC ↑
HD-Score ↑
RC ↑
HD-Score ↑
VAD* ( Jiang et al., 2023 )
38.7
24.3
27.0
9.9
25.5
10.4
23.0
8.2
27.9
12.3
UniAD* ( Hu et al., 2023 )
58.6
48.7
41.2
29.5
40.4
27.3
26.0
14.3
40.6
28.9
LTF ( Chitta et al., 2022 )
68.4
52.8
40.7
24.6
36.9
19.8
25.5
8.1
41.4
24.8
Diffusion Policy ( Chi et al., 2025 )
72.4
60.8
30.5
15.2
27.4
13.4
28.0
14.9
36.9
23.1
ZTRS ( Li et al., 2025f )
74.8
66.9
46.1
37.9
31.6
21.1
20.0
9.8
42.0
32.9
Table 3: Zero-shot Performance on the HUGSIM Benchmark. UniAD* and VAD* are trained on nuScenes Caesar et al. (2020) , which partially overlap with the evaluation scenarios. Other methods are evaluated with zero-shot transfer. † The controller is tuned for closed-loop driving.
IBC Florence et al. (2021)
LSTM-GMM Mandlekar et al. (2022)
Diffusion Policy Chi et al. (2025)
LDiP (Ours)
Task
DoF
Continuous
Discrete
Lift
6+1
0.73
0.96
1.00
0.99
Can
6+1
0.01
0.88
0.98
0.94
ToolHang
6+1
0.00
0.49
0.47
0.52
PushT
2
0.64
0.54
0.66
0.76
Table 4: Performance on Visual-based Robotic Manipulation . Following Diffusion Policy Chi et al. (2025) , we report averaged success rates over the last 10 checkpoints. We compare against the Transformer-based Diffusion Policy, as both methods adopt a Transformer Decoder for behavior modeling.
Model Variants
NC ↑
DAC ↑
DDC ↑
TLC ↑
EP ↑
TTC ↑
LK ↑
HC ↑
EC ↑
EPDMS ↑
Hydra-MDP- V16384 Li et al. (2024)
98.5
98.7
98.9
99.9
88.5
98.2
97.0
98.3
80.5
86.2
+ Iterative Scoring
97.9
98.3
99.5
99.8
90.6
97.3
98.1
98.1
77.1
86.7
+ Improved Tokenizer & Cross-Attention Decoder
98.4
98.7
99.7
99.8
89.6
97.9
97.4
98.3
78.6
87.1
+ Stochastic Scoring
98.3
98.9
99.7
99.8
91.0
97.9
97.5
98.1
79.1
87.8
Hydra-MDP- V16384 Li et al. (2024)
98.5
98.7
98.9
99.9
88.5
98.2
97.0
98.3
80.5
86.2
+ Noise Injection on Top-8 Actions Yao et al. (2026)
98.6
98.7
99.7
99.9
88.7
98.2
97.0
98.3
80.2
87.2
Table 5: Ablation Study on Key Components.
Table 9
Figure 4: Visualizations on Navtest. The figure shows the selected trajectory , the human trajectory , and the remaining vocabulary at the intermediate and final stages.
Figure 5: Ablation Study on the Width and Depth of LDiP.
Appendix figures & tables3 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 6: Additional Visualizations on Navtest. The figure shows the selected trajectory , the human trajectory , and the remaining vocabulary at the intermediate and final stages.
Figure 7: Additional Visualizations on Robotic Manipulation. The figure shows a full episode of the ToolHang task. We show the key frames with top-8 action chunks from the last scoring stage and the selected action chunk.
Method
Backbone
Params.
Vocab. Size
Iteration Steps
FPS
EPDMS
Diffusion Policy* [ 9 ]
V2-99
115.0M
-
100
4.1
79.1
Hydra-MDP- V16384 [ 31 ]
V2-99
83.0M
16384
1
13.5
86.2
GTRS-Dense [ 34 ]
V2-99
83.0M
8192
1
18.5
84.0
ZTRS [ 33 ]
V2-99
83.4M
8192
1
18.4
85.3
LDiP
V2-99
82.8M
16384
3
12.1
87.8
Appendix
Table 8: Comparisons on Efficiency. We compare the model complexity and runtime efficiency of different policies. The FPS metric is measured on one single NVIDIA A100 GPU with the PyTorch FP32 backend. * The Diffusion Policy utilizes extra networks to encode the Bird’s-Eye-View condition tokens following LTF [ 10 ] , while the DDPM Scheduler [ 17 ] is used for iterative denoising.
Though modern AI models like LLMs predict discrete tokens, today's robotic foundation models represent actions as continuous vectors. In this paper, we challenge this common consensus by asking if continuous action parametrizations are superior to their discrete counterparts. We conduct an extensive comparison of single-step regression and multi-step flow variants of both continuous and discrete policies in both from-scratch single-task and multi-task VLA training, in both simulation and on real hardware. In all regimes, we find that discrete action prediction, even the most naive, uniform-bin quantization, can match or even outperform continuous-action policies in task success rate. Moreover, we find that the challenge to discrete action policies is not action precision, but rather factorization error introduced by product-distribution predictions across time and action dimensions. We show that, when paired with the correct interventions (iterative computation through discrete flows, or distribution sharpening through classifier-free guidance), discrete flow policies can turn this weakness into a strength, enabling more responsive action changes during a predicted action chunk. Lastly, we show that attempts to explicitly inject geometric information into discrete policies, e.g. through corruption processes that emulate continuous flow matching, do not yield consistent improvements. Taken together, our findings question existing assumptions that robotic action prediction requires distinct design decisions compared to other AI domains, and motivate the possibility of discrete action prediction as a compelling alternative to today's continuous action parametrizations. Project page: https://iscoyizj.github.io/discrete-action-website/
Zeji Yi, Soham Dasgupta, Xinyang Zhang +5
Carnegie Mellon University · Amazon FAR (Frontier AI & Robotics)
Autonomous driving requires reasoning about how ego actions shape future world evolution, rather than merely mapping observations to actions. However, most end-to-end methods rely on direct state-to-action imitation, while existing world models often remain weakly aligned with downstream policy generation. We introduce Discrete-WAM, a unified discrete vision-action world-policy framework that represents visual observations, future states, high-level decisions, and ego actions within a shared token space. Built on this discrete alignment, Discrete-WAM jointly trains world modeling, world-policy modeling, and policy modeling through multi-task and multi-stage pretraining, allowing action-conditioned future prediction to directly support policy generation. For downstream planning, Discrete-WAM further decomposes policy generation into hierarchical decision prediction and parallel action-token editing, where the decision token provides a high-level planning skeleton and confidence-based scheduling refines dense future actions efficiently. Experiments on large-scale autonomous-driving benchmarks show that Discrete-WAM achieves strong planning performance while supporting controllable future generation, counterfactual evaluation, surprise-based world-model analysis, and efficient parallel policy decoding. These results suggest that discrete representation alignment, unified world-policy training, and hierarchical token editing provide a promising design paradigm for physical AI.
End-to-end multi-modal planning has been widely adopted to model the uncertainty of driving behavior, typically by scoring candidate trajectories and selecting the optimal one. Existing approaches generally fall into two categories: scoring a large static trajectory vocabulary, or scoring a small set of dynamically generated proposals. While static vocabularies often suffer from coarse discretization of the action space, dynamic proposals provide finer-grained precision and have shown stronger empirical performance on existing benchmarks. However, it remains unclear whether dynamic generation is fundamentally necessary, or whether static vocabularies can already achieve comparable performance when they are sufficiently dense to cover the action space. In this work, we start with a systematic scaling study of Hydra-MDP, a representative scoring-based method, revealing that performance consistently improves as trajectory anchors become denser, without exhibiting saturation before computational constraints are reached. Motivated by this observation, we propose SparseDriveV2 to push the performance boundary of scoring-based planning through two complementary innovations: (1) a scalable vocabulary representation with a factorized structure that decomposes trajectories into geometric paths and velocity profiles, enabling combinatorial coverage of the action space, and (2) a scalable scoring strategy with coarse factorized scoring over paths and velocity profiles followed by fine-grained scoring on a small set of composed trajectories. By combining these two techniques, SparseDriveV2 achieves 92.0 PDMS and 90.1 EPDMS on NAVSIM, with 89.15 Driving Score and 70.00 Success Rate on Bench2Drive with a lightweight ResNet-34 as backbone. Code and model are released at https://github.com/swc-17/SparseDriveV2.
Wenchao Sun, Xuewu Lin, Keyu Chen +4
Tsinghua University, Beijing, China · Horizon Continental Technology, Beijing, China · Horizon, Beijing, China