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Discrete Forcing: Infusing Discrete Guidance into Continuous Denoising for Few-Step Action Experts

Jingbo Wang, Wenxuan Song, Wenhao Yu, Han Zhao, Xi Wang, Jiayi Chen, Donglin Wang, Yan Wang, Haoang Li

arXiv:2609.39526v1cs.RO

TL;DR

Action generation in VLA models must balance compact coarse structure with precise continuous actions, which often need multiple denoising steps. Discrete Forcing predicts discrete tokens before refining continuous actions, using shared layers and specialized branches. It reports improved performance and faster inference than comparable continuous experts, with gains as capacity grows and on real-world manipulation tasks.

  • Problem

    Discrete action tokens compactly encode high-level information but sacrifice precision, whereas continuous actions offer higher precision yet typically require many denoising steps, and actions lack an established coarse-to-fine structure.

    Source: §1 · p. 2

  • Method

    Discrete Forcing first denoises discrete tokens for coarse action structure, then uses them to initialize continuous action denoising within a shared-backbone expert with specialized branches.

    Source: §1 · pp. 2–3

  • Results

    Discrete Forcing improves performance and inference speed over continuous action experts with comparable parameter counts, with consistent gains as capacity grows and real-world gains on high-precision and dynamic manipulation tasks.

    Source: §1 · p. 3, §5 · p. 10

  • Takeaways & Limitations

    Discrete-to-continuous generation is a promising approach to efficient and precise robot action modeling.

    Source: §5 · p. 10

Abstract

from arXiv · show

Efficient action generation in vision-language-action (VLA) models requires capturing both coarse action structure and fine-grained details. Discrete action tokens provide compact structural representations but sacrifice precision, while continuous action tokens offer high precision but often require multiple denoising steps. We introduce Discrete Forcing, a flow-matching framework that combines these representations through an explicit coarse-to-fine generation process. It first predicts discrete action tokens to establish a coarse action structure, then uses them to guide continuous action refinement. The discrete and continuous components share a common diffusion transformer backbone with specialized branches, maintaining a parameter count comparable to a conventional single-branch model while requiring only one forward pass per branch. Extensive evaluations across multiple benchmarks demonstrate improved performance and faster inference over a parameter-matched continuous action expert, with consistent performance gains as model capacity increases. Real-world experiments further demonstrate improvements on high-precision and dynamic manipulation tasks.

1 Introduction

Discrete Forcing models action generation as discrete-to-continuous coarse-to-fine denoising, addressing the tension between compact structural tokens and precise but slower continuous actions. It uses shared DiT layers with specialized branches and reports stronger, faster results than a parameter-matched continuous action expert.

1 Introduction

  • Because actions lack a clearly defined frequency-domain structure, the paper asks whether action generation can follow a coarse-to-fine process observed in other domains.Source: §1 · p. 2
  • Discrete tokens compactly capture high-level action information but sacrifice precision, while continuous action denoising offers higher precision but typically requires many slow denoising steps.Source: §1 · p. 2
  • Discrete Forcing outperforms a conventional continuous action expert and runs faster, with consistent gains as model capacity increases and on high-precision and dynamic manipulation tasks.The reported evidence spans benchmark and real-world experiments.Source: §1 · p. 3
  • Discrete Forcing first denoises discrete tokens to establish coarse action structure, then uses them to initialize continuous denoising for precise details.The discrete prediction serves as a “scratchpad” for continuous refinement.Source: §1 · pp. 2–3
  • Shared DiT layers and specialized branches match a conventional DiT’s parameter count while requiring one forward pass through each branch.The shared layers precede separate discrete and continuous branches.Source: §1 · pp. 2–3

2 Related Work

Prior work explores varied action representations, coarse-to-fine policies, and methods for reducing action-generation cost. Discrete Forcing positions its discrete and continuous stages as two representations of the same trajectory and uses one forward evaluation per stage.

Action Representations in VLA Models

Coarse-to-Fine Action Generation

  • Unlike prior hierarchies that use discrete states as intents, Discrete Forcing treats discrete and continuous predictions as representations of the same trajectory, with the discrete prediction defining the continuous flow’s source distribution.Source: §2 · p. 3

Few-Step and Efficient Action Generation

  • Prior efficiency methods accelerate existing paradigms through parallelization or distillation; Discrete Forcing instead trains discrete-to-continuous generation directly from action demonstrations with one forward evaluation per stage.Source: §2 · p. 3

3 Method

The method frames continuous action generation as flow-based denoising, then combines discrete structure prediction with continuous refinement in a partially shared action expert. Training couples masked discrete recovery to discrete-guided continuous flow and reconstruction, and inference uses one pass per branch.

3.1 Preliminary: Denoising-based Action Generation

  • Continuous action generation starts with a noisy action chunk and observation, predicts the interpolation path’s conditional vector field, then integrates it from τ = 1 to τ = 0.The noise level τ lies in [0, 1].Source: §3.1 · p. 4

3.2 Architecture of Discrete Forcing Head

  • The expert shares its first Ls Transformer layers, then uses separate discrete and continuous layers and heads; each branch runs once without increasing conventional Action DiT parameter count.Discrete inputs use 255 action bins plus a [MASK] token, while continuous inputs are encoded by an MLP.Source: §3.2 · p. 4

3.3 Training

  • Training masks discrete action tokens at a sampled corruption level and trains the discrete branch to recover the original bins at masked positions.The branch predicts categorical distributions over bins; its objective is evaluated at the masked indices.Source: §3.3 · pp. 4–5
  • The continuous branch learns a vector field from a source built from quantized actions and Gaussian noise, with an added reconstruction objective for direct target recovery.The source is interpolated toward the target action; reconstruction is introduced to enable one-step continuous denoising.Source: §3.3 · p. 5

3.4 Inference

  • Inference takes two forward passes: one predicts a discrete action prior, which is dequantized into a continuous source, and one continuous step refines it for robot execution.Table 1 groups methods by iterative generation (NFE > 2) versus fast generation (NFE ≤2).Source: §3.4 · p. 5, Table 1 · p. 6

4 Experiments

Across simulation benchmarks, Discrete Forcing reports higher success than comparison methods; its performance also improves with scale while maintaining inference-efficiency gains. Mechanism analyses, ablations, and real-world trials examine how its discrete-to-continuous design contributes to these results.

4.1 Simulation Experiments

  • 97.6% average success on LIBERO leads fast-generation methods; Discrete Forcing also reaches 59.32% on RoboTwin 2.0 and 56.8% on RoboCasa-GR1.On LIBERO, it exceeds StarVLA by 2.5 percentage points at the same 1.5B parameter scale and two-NFE budget; RoboTwin results use no robot-specific pre-training.Source: §4.1 · p. 6, Table 2 · p. 7

4.2 Analysis of Model Scaling

  • Discrete Forcing improves monotonically across the evaluated 1.0B–5.5B scales; its 1.0B variant is 2.97× faster than the 5.5B baseline while approaching its success rate.The 1.0B variant reaches 47.96% success versus 48.60% for the 5.5B baseline and uses 81.8% fewer parameters.Source: §4.2 · pp. 6–7, Figure 3 · p. 8

4.3 Inference Efficiency

  • Against the 10-step baseline, Discrete Forcing gives 5× faster action generation and over 2× faster end-to-end inference, with higher success rate.All variants use 3.09 GiB peak GPU memory; the 2-step StarVLA baseline is faster than its 10-step version but has an obvious success-rate drop.Source: §4.3 · p. 7, Table 3 · p. 7

4.4 Mechanism of Structural Action Generation

  • DF@1 reaches 0.989 Global Direction Similarity at one NFE and 0.0399 Normalized Trajectory Shape Error, lower than StarVLA across 1–10 NFEs.DF@1 already has trajectory geometry close to ground truth; DF@2 adds local adjustments around that discrete trajectory.Source: §4.4 · pp. 7–8, Figure 4 · p. 9

4.5 Ablation Studies

  • Discrete →Continuous performs best; predicted-source training yields 95.3% versus 95.2% with ground-truth-source training.Using the same representation for both stages, adding explicit branch communication, removing discrete guidance, or removing the one-step objective reduces performance; ground-truth-source training avoids an extra discrete forward pass.Source: §4.5 · p. 8

4.6 Real-World Experiments

  • 74.9% average Task Progress, a 16.4% improvement; Discrete Forcing outperforms both baselines across four real-world tasks.Gains are particularly pronounced on Pick Rotating Light and Grasp Moving Cube, which require tracking moving targets and timely action execution.Source: §4.6 · p. 9

5 Conclusion

The conclusion presents Discrete Forcing as a shared-backbone, discrete-to-continuous action-generation framework with reported gains in benchmark performance, inference speed, scaling, and real-world manipulation.

5 Conclusion

  • Discrete Forcing combines coarse discrete action structure with continuous refinement in one flow-matching action expert, using shared DiT layers and specialized branches.It matches a conventional single-branch DiT's parameter count and requires one forward pass per branch; evaluations report improved performance and faster inference, with gains as capacity grows and on high-precision and dynamic tasks.Source: §5 · pp. 9–10

A Implementation Details

  • Table 5 summarizes LIBERO implementation and training configurations, including architecture, optimization, objective weights, sampling, and evaluation protocol.The supplied passage identifies the table's scope without detailing its configuration values.Source: A Implementation Details · p. 15, Table 5 · p. 15

B Detailed Simulation Experimental Settings

The simulation evaluation covers single-arm, dual-arm, and humanoid manipulation through LIBERO, RoboTwin 2.0, and RoboCasa-GR1.

C RoboTwin 2.0 Task-Level Results

Table 6 provides task-level RoboTwin 2.0 success rates and an average across all task-level rates.

D RoboCasa-GR1 Task-Level Results

This section expands the RoboCasa-GR1 aggregate comparison into per-task success rates and specifies the evaluation coverage.

E Structural Action Analysis Details

The analysis measures predicted action chunks’ global direction and normalized trajectory shape, using offline LIBERO demonstrations to probe action-generation dynamics.

  • Global Direction Similarity is the cosine similarity between predicted and ground-truth net displacement, with higher values indicating better directional agreement.Source: E Structural Action Analysis Details · p. 17
  • Normalized Trajectory Shape Error compares point-wise distances between path-length-normalized predicted and ground-truth trajectories, with lower values indicating better shape preservation.Source: E Structural Action Analysis Details · pp. 17–18
  • The offline analysis samples 200 horizon-8 action chunks across five LIBERO tasks, pools them with equal task weights, and reports means with 95% bootstrap confidence intervals.It uses 2,000 bootstrap resamples.Source: E Structural Action Analysis Details · p. 18

F Extra Ablation Results

The extra ablations identify a strong shared-layer setting and a best tested mixture for the discrete-guided continuous source; the following section includes a real-world setup figure.

F Extra Ablation Results

  • 95.2% is the highest LIBERO-Long success rate, achieved with two shared Action DiT layers.The ablation suggests limited early sharing supports common action-relevant representations, while excessive sharing restricts branch specialization.Source: Table 8 · p. 18, F Extra Ablation Results · p. 18
  • α = 0.3 achieves the best performance among the tested discrete-guided continuous source settings.α controls the contribution of the dequantized discrete action, while 1 − α controls Gaussian noise.Source: Table 9 · p. 18, F Extra Ablation Results · p. 18

G Real-World Experimental Details

G.1 Real-World Tasks

The real-world task set spans repeated precise insertion, size-based bimanual matching, and manipulation of moving targets; progress is measured by milestone completion.

  • Task progress rate is the completion rate of each milestone.Source: §G.1 · p. 19
  • Transfer Tubes requires transferring four tubes into designated rack slots through eight grasp-and-insert milestones.The training dataset contains 200 episodes.Source: §G.1 · p. 19
  • Match Size requires matching four cylinders to corresponding holes and completing eight grasp-and-insert milestones with bimanual insertion.The training dataset contains 200 episodes.Source: §G.1 · p. 19
  • Pick Rotating Light requires locating, grasping, and placing the illuminated module on a continuously rotating turntable.The task has four milestones and a 100-episode training dataset.Source: §G.1 · p. 19
  • Grasp Moving Cube requires intercepting a block pulled leftward by a rope and placing it on a designated plate.The task has three milestones and a 100-episode training dataset.Source: §G.1 · p. 19

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