Primary-Fine Decoupling for Action Generation in Robotic Imitation
Authors: Xiaohan Lei
Min Wang
Wengang Zhou
Xingyu Lu
Houqiang Li
Venue: ICLR 2026 Poster (2026)
Keywords: dexterous manipulation
multi-modal policy
MeanFlow
action decoupling
robot imitation learning
Primary area: applications to robotics, autonomy, planning

Abstract: Multi-modal distribution in robotic manipulation action sequences poses critical challenges for imitation learning. 
To this end, existing approaches often model the action space as either a discrete set of tokens or a continuous, latent-variable distribution.
However, both approaches present trade-offs: some methods discretize actions into tokens and therefore lose fine-grained action variations, while others generate continuous actions in a single stage tend to produce unstable mode transitions.
To address these limitations, we propose Primary-Fine Decoupling for Action Generation (PF-DAG), a two-stage framework that decouples coarse action consistency from fine-grained variations. First, we compress action chunks into a small set of discrete modes, enabling a lightweight policy to select consistent coarse modes and avoid mode bouncing. Second, a mode conditioned MeanFlow policy is learned to generate high-fidelity continuous actions.
Theoretically, we prove PF-DAG’s two-stage design achieves a strictly lower MSE bound than single-stage generative policies. 
Empirically, PF-DAG outperforms state-of-the-art baselines across 56 tasks from Adroit, DexArt, and MetaWorld benchmarks. It further generalizes to real-world tactile dexterous manipulation tasks. Our work demonstrates that explicit mode-level decoupling enables both robust multi-modal modeling and reactive closed-loop control for robotic manipulation.

Published as a conference paper at ICLR 2026
PRIMARY-FINE DECOUPLING FOR ACTION GENERA- TION IN ROBOTIC IMITATION
Xiaohan Lei', Min Wang? Wengang Zhou'.2t, Xingyu Lu', Houqiang Li
MMo Key Laboratory of Brain-inspires Intelligent Perception and Cognition. University of Science and Technology of China Institute of Artificial Intelligence, Hefei Comprehensive National Science Center
{leixh, luxingyco10)email wttaaallatt........mmmmmm......a www.sstcc.... eettc.edu.com en wangmin@iate ustc. edu. cn, {zhwg, Lihq]@uster edu.cn
Project Page: fttps::/xxaccannee
ABSTRACT
Multi-modal distribution in robotic manipulation action sequences poses critical challenges for imitation learning. To this end, existing approaches often model the action space as either discrete of tokens or continuous, latent-variable dis- tribution. However, both approaches present trade-offs: some methods discretize actions into tokens and therefore lose fine-grained action variations, while oth- ers generate continuous actions in single stage tend to produce unstable mode transitions. To address these limitations, we propose Primary-Fine Decoupling for Action Generation (PF-DAG), two-stage framework that decouples coarse action consistency from fine-grained variations. First, we compress action chunks into small set of discrete modes, enabling a lightweight policy to select consis- tent coarse modes and avoid mode bouncing. Second, a mode conditioned Mean- Flow policy is learned generate high-fidelity continuous actions. Theoretically, we prove PF-DAG's two-stage design achieves a strictly lower MSE bound than single-stage generative policies. Empirically, PF-DAG outperforms state-of-the- art baselines across 56 tasks from Adroit, Art, and Meta World benchmarks. It further generalizes real-world tactile dexterous manipulation tasks. Our work demonstrates that explicit mode-level decoupling enables both robust multi-modal modeling and reactive closed-loop control for robotic manipulation.
INTRODUCTION
In robotic manipulation, capturing multi-modal distributions in action sequences is essential for learning robust and reliable imitation policies (Florence et al., 2022; Chi et al., 2023). Offline expert trajectories often admit multiple valid actions for the same or similar observations: for example, when an obstacle lies in front of the end-effector, demonstrators may steer either left or right. This richness of valid behaviors complicates learning from offline data and thus motivates the develop- ment of various imitation learning approaches to tackle this challenge.
Among these imitation learning approaches, Behavioral Cloning (BC) treats policy learning pervised regression a = (()) and therefore commonly collapses multiple valid actions into a single mean (Levine et al., 2016; Torabi al., 2018), visualized in Figure (a). Action discretiza- tion represents multiple modes by predicting categorical bins (Brohan et al., 2022; Zitkovich et al., 2023; Kim al., 2024), but coarse discretization introduces reconstruction error and temporal dis- continuities (Shafiullah et al., 2022), failing to match the smoothness of human demonstrations (see Figure (b)). Generative latent-variable methods instead model < 2) so that sampling differ- ent z yields different plausible actions (Zhao et al., 2023; Chi et al., 2023). However, independent per-step resampling tends to produce random switches among modes (Chen et al., 2025) (see
"Corresponding authors: Min Wang (wangmin @ wst..ss...du.cn) and Wengang Zhou watng@ustc.cdu.c)

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Published as a conference paper at ICLR 2026
Human Demonstrations
Learned Policy
Mode Collasse
Temporal Discontinuttos
Mode Bouncing
Consistont & Fine-Gralned
Obstacle
(e) Behavioral Cloning
(b) Discrete Policy
(c) Generative Policy
(d) Ours
Figure 1: A 2D example illustrating multi-modal expert demonstrations and trajectories predicted by different imitation policies. Behavioral cloning predictions collapse into a single mean. Discrete
Policy succeeds but introduces temporal discontinuities. Generative Policy bounces between mode and Our work predicts consistent and fine-grained trajectory.
Figure (c)). Such erratic transitions directly lead to trajectory discontinuities and end-effector pose instability, while further undermining the overall task execution accuracy.
We observe that many manipulation tasks naturally decompose actions into a small set of discrete, interpretable primary modes (coarse prototypes such as "lift-and-fold" or "lift-and-rootae"" together with continuous, within- mode variations that adjust details like grasp offsets and minor trajectory tweaks. Intuitively, primary modes capture coarse, discrete decisions while within-mode residuals encode fine- fine-grained variations. This observation motivates an explicit separation between i) se- lecting a coarse, discrete mode consistently and ii) generating the fine-grained continuous action conditioned on that mode.
Motivated by the above, we propose Primary-Fine Decoupling for Action Generation (PF-DAG), two-stage imitation framework that explicitly separates primary mode selection from continuous action generation. Concretely, PF-DAG first learns a discrete vocabulary of primary modes and a lightweight policy that greedily selects a mode coherently. Then, we introduce mode conditioned MeanFlow policy, which is a one-step continuous decoder to generate high-fidelity actions condi- tioned the selected mode and the current observation. This explicit two-stage decomposition preserves intra-mode variations while reducing mode bouncing by enforcing stable primary choices.
We validate PF-DAG with theoretical and empirical evidence. Among existing methods, single- stage generative policies (Chi et al., 2023; Zhao et al., 2023) are the most direct and competitive end-to-end approach for modeling continuous, multi-modal action distributions, theoretical comparison on this family. Under realistic mode-variance assumptions we show that the two-stage design attains no-higher optimal MSE lower bound than single-stage generative baselines, with a strict improvement whenever the inter-mode variance term is positive. Empirically we test PF-DAG across 56 simulation manipulation tasks (including high-DOF dexterous hands and low-DOF grippers) as well as on real world tactile dexterous manipulation. Results show consistent improvements in accuracy, stability, and sample efficiency compared to diffusion and flow-based baselines, and ablations quantify the contribution of key components. Together, these results suggest that explicitly decoupling coarse discrete decisions from fine-grained continuous generation yields practical and statistical advantages for closed-logy robotic imitation.
we focus
RELATED WORK
2.1 BEHAVIOR CLONING
Behavior cloning (BC) casts policy learning as supervised regression on demonstration data (Wang al., 2017; Torabi et al., 2018; Mandlekar et al., 2021; Hu et al., 2024). In BC, a policy trained to predict the expert's 's action for each observed state, yielding deterministic mapping from states practice (e.g. for pick-and-plas tasks), but
actions. This approach is highly sample-efficien suffers from well-known limitations. In particular, BC policies tend to underfit multi-modal behav- ior (Mandlekar et al., 2021; Shafiullah et al., 2022; Florence al., 2022; Chi al., 2023) and also incur compounding errors at test time (Ross et al., 2011; I; Ke et al., 2021; Tu et al., 2022; Zhao al., 2023). To mitigate these issues, recent work has explored more expressive BC models. Implicit BC and energy-based models learn action-energy landscape per state and solve for actions by optimization (Florence et al., 2022), while mixture-density networks and latent-variable BC attempt to represent multi-modaa distributions explicitly (Jang et al., 2022).
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2.2 DISCRETE POLICY
Discretizing continuous robot actions viewed as tokenization: converting a high-frequency, high- dimensional control signal into a sequence of discrete symbols so that standard sequence-modeling methods can be applied. Framing actions as tokens has two immediate benefits for manipulation imitation. First, next-token prediction over discrete vocabulary represents multi-modal conditional action distributions without collapsing modes into a single mean. Second, sequence models bring powerful context modeling and scalable pretraining recipes from language and vision to control, enabling cross-task and cross-embodiment generalization when token vocabularies are shared or aligned. Recent Sasion-Language-ae Action (VLA) efforts articulate this reframing and its practical advantages for large, generalist robot policies (Zitkovich et al., 2023; O'Neill et al., 2024; Kim al., 2024; Zawalski et al., 2024; Wen et al., 2025; Black et al., 2024; Zheng et al., 2024; Zhen et al., 2024; Cheang et al., 2024; Duan et al., 2024; Zhao et al., 2025).
Existing action tokenizers fall into a few broad families. The simplest and most commonly used approach maps each continuous action dimension at each step to one of a fixed set of bins (Brohan al. 2022; Zitkovich et al., 2023; Kim et al., 2024). Frequency-spage methods like FAST (Pertsch et al., 2025) departs from it and instead compresses action chunks using a time-series transform and lightweight quantization. Others use Vector Quantization (VQ) as latent tokenizers. VQ-based tokenizers learn shared codebook of action atoms and quantize continuous latent representations to nearest codebook entries (Lee et al., 2024; Wang et al., 2025). While effective at capturing multi- modal action distributions, these approaches inherently trade off reconstruction fidelity for discrete simplicity. Our work differs by leveraging tokenization solely for high-level primary mode selection.
2.3 GENERATIVE POLICY
A large class of imitation methods treat policy generation as a stochastic generative problem by introducing latent variables. In this view, policy is written as a To, 2) with sampled from a learned prior. This formulation naturally represents multi-modal conditional action distributions because sampling different z values yields different valid actions for the same observation. Action Chunking with Transformers (ACT) (Zhao et al., 2023) is sequence generator with Conditional Variational Autoencoder (CVAE) as backend. Diffusion Policy (DP) (Chi al., 2023) treat action generation as conditional denoising. Starting from noise, the action is iteratively refined via learned score or denoiser conditioned on observation. More recent normalizing-fool flow policies (Black et al., 2024: Hu et al., 2024; Zhang et al., 2025) provide tractable density estimation and efficient sampling while representing complex, multi-modal action distributions. Although generative policies repre- sent mudti- distributions, they often face mode bouncing (Chen et al., 2025), inference cost (Li et al., 2024), chunk trade-offs (Zhao et al., 2023). Other hierarchical approaches, such as Hierar- chical Diffusion Policy (HDP) (Ma et al., 2024), also use high-level policy guide a low-level generator. However, HDP is designed to rely on explicit, task-specific heuristics like contact-point waypoints to define its hierarchy. In contrast, our PF-DAG learns its primary modes end-to-end directly from action-chunk clusters themselves, offering more general abstraction not tied to pre- defined heuristics. Thus, we propose to combine the strengths of action tokenization with expressive generative decoders that handle the residual continuous variations. Our PF-DAG decouples the pri- mary discrete mode selection from the fine- fine-grained action generation and reduces mode bouncing while preserving continuous variations.
2.4 HIERARCHICAL AND RESIDUAL POLICIES
Our work is also situated within the broader context of hierarchical and residual policies for robot learning (Rana et al., 2023; Cui et al., 2025; Kujanpää et al., 2023; Liang et al., 2024). These ap- proaches commonly decompose the complex control problem into a high-level policy that selects a skill, sub-goal, or context, and a low-level policy that executes control conditioned on the high-level selection (Mete et al., 2024; Feng et al., 2024). For instance, some methods learn residual policies that adapt base controller (Rana et al., 2023), while others focus on discovering discrete skills from demonstration data or language guidance (Chen et al., 2023; Wan et al., 2024; Tanneberg et al., 2021). While PF-DAG shares this general hierarchical structure, its primary motivation and techni- cal design are distinct. Many hierarchical methods focus on long-horizon planning or unsupervised skill discovery. In contrast, PF-DAG is specifically designed to address the problem of mode bounc-
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Pred Action Chunk
PoiniCloud Pt
Observation Feature Extraction
Mode Conditioned
MeanFlat Policy ग
Primary Mode Policy T
Joint
Angles
Mode
Mode Dionttation
Max
Time
Supervise
Action Chunk ((m)
Add
Figgelp Tactile Sensing
Aclin Chunk
Quartized
Joint
Encoder
2 aeoodd
Es
Propriocaption
Figure 2: Overview of our PF-DAG framework. The input observation features are extracted via Observation Feature Extraction and then fed the Primary Mode Policy mi The GT action chunks are compressed into discrete primary modes using VQ-VAE and supervise which are only used in training stage. The Mode Conditioned MeanFlow Policy л2 takes the selected primary mode m and observation features as input, generating high-fidelity continuous actions.
ing inherent in single-stage generative policies when modeling multi-modal action distributions at fine temporal scale.
PF-DAG FORMULATION AND DESIGN
This section first defines the task formulation as closed-loop action-sequence prediction problem, and then presents the three main components of our approach: i) Observation Feature Extraction, ii) compact discrete representation learned with a Vector-Quanizzed VAE (VQ-VAE) (Van Den Oord et al., 2017) and a lightweight Primary Mode Policy that predicts those discrete modes, and iii) mode conditioned one-step continuous decoder based on MeanFlow (Geng al., 2025). Finally, we give theoretical analysis that quantifies why a two-stage, coarse-to-fine decomposition reduces the MSE lower bound compared single-stage generative models.
3.1 CLOSED-LOOP ACTION SEQUENCE PREDICTION
Similar to previous work (Chi et al., 2023; Black et al., 2024), we formulate the manipulation task as closed-loop action sequence prediction. Concretely, at time I, observation is o, = (pe, 8,, f)), where Pa denotes fixed-size point cloud, S; R. denotes robot proprioception. f, E 12x12033 represents tactile sensing data from the hand's fingertips. For the dimension of f,, the first di- mension 5 corresponds to the 5 individual fingertips, the 120 denotes the number of tactile taxels embedded in each fingertip and the last 3 represents the 3-dimensional force vector. The policy predicts an action chunk a, Raxx and executes the first T. S Tp steps before re-planning.
à π (Ot). execute à (0 To 1]. then t + t Te.
(1)
This yields receding- horizon closed-loop control scheme that preserves temporal coherence and allows fast reaction to new observations. Hyperparameters are presented in Appendix.
3.2 OBSERVATION FEATURE EXTRACTION
We first extract the shared observation embedding from input observation o, (pe. St. fz). Fol- lowing a simple PointNet-style (Qi et al., 2017) pipeline, each point's coordinates are lifted by an MLP, and LayerNorm (Ba et al., 2016) is applied inside that per-point MLP. Per-point features are aggregated by symmetric max- max-pooling. The proprioception S; and tactile sensing through respective MLPs and then concatenated with the point-clout embedding. A final projection MLP fuses the concatenated vector into the shared observation embedding.
passed
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3.3 PRIMARY MODE POLICY AND VQ- VAE
Given the shared observation embedding, the framework first selects primary mode. This subsec- tion describes how we learn a compact VAE codebook for action chunks and train a lightweight classifier to predict these primary modes from the observation embedding.
Vector Quantized Variational Autoencoder. Continuous action chunks a are compressed into small discrete set of primary modes E {1...., K} using VQ-VAE. Let the deterministic encoder be Eig : RT + RD and decoder D2 : RDD + RTxx Let the codebook be C = fox E [RD k=1 with codebook size K. We choose K' to be small to capture coarse primary action prototypes and make primary policy easy learn. Given action chunk a, the encoder produces 2, = Ea(a) and we quantize it to the nearest codebook vector:
k' = arg min Iiee cx
2 = C
m. :-:= K.
(2)
We define m as the primary mode. Reconstruction is a (z) We train the VQ- VQ-VAE with the standard commitment and reconstruction terms:
(vo(a) ||a D& (2)1 [|g]EE((a]] z -
(3)
where sgl-] denotes stop-gradien and / is the commitment weight. The primary policy is classifier T (m o) trained to predict the VQ code m from observation o. At test time, we select the discrete mode m for the current chunk by choosing the highest predicted probability from क. Both encoder Eg and decoder D are implemented as compact MLPs.
Primary Mode Policy. The primary policy क (m o) maps the shared observation embedding to a categorical distribution over the K VQ bins. We implement тi as a lightweight MLP classifier. During training Ø1 is optimized with a standard cross-entropy objective that matches the encoder- assigned VQ indices. At test time we use greedy mode selection for reliability. The separation of primary-mode selection as an explicit classifier drastically reduces coarse mode bouncing.
3.4 MODE CONDITIONED MEANFILOW POLICY
After selecting a primary mode m, we recover a high-quality continuous action chunk that respects the selected mode. To balance generation quality and real-time responsíveness, we use one-step generative modeling inspired by MeanFlow (Geng et al., 2025). Instead of multi-step denoising iterations, learned average velocity field predicts the displacement from noise to the desired action in one function evaluation. Let m be the selected discrete mode and á decoder reconstruction of the mode. The role of the one-step generator is to produce a residual Aa conditioned on observation o and mode m, such that the final action chunk is = a (m) + Aa.
D (Cm) be the VQ-
Mode and Observation Conditioned Average Velocity Field. Following McanFlow (Geng al., 2025), we implement the residual as an average velocity field vo T, r; o, m²) where z, denotes a state on the interpolation path between noise sample and the target action, 7 E [0, 1] the in- terpolation start time, and r E (0, 1] is the end time. The MeanFilow field is trained to match the ground-truth average velocity over arbitrary intervals [T. which is written as
v (Z,, T, sg
de
(r - ()
de. av ONa Dr
(4)
dr d2
The dz, is the instantaneous velocity of z, at time r. dr
describes how the average veloeity dr captures how it evolves as the interpolation approaches the target residual. We train Vo with squared-error objective that supervises the predicted average velocity. More detailed derivations of the formulation are provided in Appendix.
av.
responds to perturbations in the residual draft, and 89g
Implementation Details. For backbone modeling use a DiT-style transformer backbone (Pee- bles& & Xie, 2023). Each action chunk is represented as a sequence of tokens. The time-related scalars J and r are expanded via sinusoidal embeddings (Vaswani et al., 2017), which are added to observation embedding, as well as learnable embedding of the discrete mode m. During training, (T,r) is sampled from uniform distribution and Zg is from standard normal distribution.
3.5 THEORETICAL ANALYSIS
With the two-stage architecture defined, we now provide a concise theoretical analysis that explains why this coarse-to-fine decomposition strictly reduces the minimum achievable MSE compared to
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Adroit
DexAm
MetaWorld
Method
Hammer
Door
Pen
Laptop
Fancet
Toiler
Bucket
Medium (6)
Hard (5)
Success
IBC
0.00ge.00
0.00
0.10
g001
0.07
0.16so
0.00gamm
0.11gam
0.00
0.08
BC-H
0.07
0.16
8.09
0.1310.1
0.21
0.10amm.
0.1588.00
0.18
0.15
0.48
0.50
0,25
8.09
0.23310.0
0.58:0.2
0.201aa.0
0.
DP3
1.0020.00
0.62
0.43
0.83
0.82:0.04
0.00
0.45amos
0.33
0.51
HowPolicy
1.000...o
0.58
0.55
0.85
0. 0.42
0.80
0.30
0.47axor
0.3760.47
0.51
PF-DAG (Ours)
1.00:0.00
0.05
0.651
0.90
0.72:0.05
0.8210.02
0.47
0.08
0.72:0.0
0.72
Table I: Quantitative comparison of PF-DAG against state-of-the-art baselines on 18 tasks from three simulation benchmarks.
single-stage generative predictors. Single-stage generative methods produce actions by sampling latent code z ~ (O0, /) and decoding å = π (o, z). Under the squared-error criterion, the best point estimate is the conditional expectation (o) Eg (0, z)]. The resulting expected MSE decomposes into an irreducible data variance term and a model bias:
B |la [))l] E., Var(( o)] + EE, [| o] - [
(5)
When the model unbiased the second term vanishes and the minimum achievable error equals [a[Vaa o)].
In our two-stage scheme the primary stage selects a discrete mode ri(o) and the second stage outputs á(o, m, z) = (2, m, z). For any fixed (o, m), the optimal MSE predictor collapses the stochastic- ity in z to the conditional expectation (* m) = E.g. (T (2, m, 2)]. yielding the irreducible residual Eo.m [Vam(a o, m]] when the model unbiased. By the law of total variance.
Eo,m Var(( o, m)] = E.. Var(a
o)] E. L [armmo (E|a o, ml]]
(6)
which is no greater than E., Var(a o)], and is strictly smaller whenever Varmjo (Eja o, ml) > 0. Intuitively, discretizing into primary modes removes inter-mode variance from the residual error, lowering the MSE bound compared to single-stage latent samplers.
EXPERIMENTS
4.1 SIMULATION EVALUATION
Benchmarks and Datasets. We evaluate our method on manipulation benchmarks that cover broad range of control domains. We use Adroit (Rajeswaran et al., 2017), DexArt (Bao et al., 2023) and MetaWorld (Yu et al., 2020) our simulation benchmarks. 'Thee are implemented on physics engines like MuJoCo (Todorov et al., 2012) and IsaacGym (Makoviychuk et al., 2021). For fair comparison we adopt the same task splits and data collection pipelines as in prior work (Ze et al., 2024): Adroit tasks with high-dimensional Shadow hand and MetaWorld with low-dimensional gripper are trained with 10 expert demos per task, while DexArt with Allegro hand uses 90 expert demos. Demonstrations are collected using scripted policies for MetaWorld tasks, and RL-trained expert agents (Wang et al., 2022; Schulman al., 2017) for Adroit and DexArt. Each experiment is run with three random seeds. For each seed we evaluate the policy for 20 episodes every 200 training epochs and then compute the average of the top-5 highest success rates (Ze et al., 2024). The final metric is the mean and standard deviation across the three seeds.
Experiment Setup. All networks are optimized with AdamW (Loshchilov & Hutter, 2017). We apply a short linear warmup followed by cosine decay for the learning rate. Training proceeds in stages: first we pretrain the VQ-VAE learn compact primary prototypes; then we freeze the codebook and jointly train the Primary Mode Policy πi (cross- (cross-entropy to the VQ indices) and the mode-condition condiionni MeanFlow generator Eg (squared-ern) supervision on sampled (r, r) intervals). At inference we set (T,r) r) 10 for one-step continuous action chunk generation.
Baselines. We compare against the following representative baselines. Implicit Behavioral Cloning (IBC) (Florence et al., 2022) serves as a representative implicit BC method. BC-H (Foster et al., 2024) represents non-generative approaches for mitigating mode instability. Diffusion Policy (DP) (Chi et al., 2023) pioneers the original formulation of image-conditioned diffusion-based poli- cies. While 3D Diffusion Policy (DP3) (Ze et al., 2024) represents a recent advancement in 3D- point-cloud conditioned diffusion-based policies, Flow Policy (FP) (Zhang et al., 2025) falls into the category of normalizing- flow-based policy variants. These baselines provide a spectrum from energy-based model to expressive generative policies.

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BinZ
Bin2
Bin?
Bie?
(a) Mode Collapse
(b) Mode Bouncing
(c) Ours
Figure 3: Visual comparison of failure modes in baselines versus PF-DAG. Mode Collapse outputs
"average" actions, while Mode Bouncing randomly switches between consecutive time steps.
Task Parameters
Success Rate
Task Description
Variations
Demos
Effector
Tactile
Action Dim
Vanilla BC
DP3
(Ours)
Pick Cube
Gripper
0.20
0.60
0.70
Place Baymax
10
Gripper
7
0.40
0.85
0.90
Wipe Table
XHand
7+
0.00
0.55
0.70
Place Toy
XHand
7.4
0.00
0.60
0.80
Table 2: Quantitative comparison of success rates of different methods on real world manipulation
tasks. The table presents key task parameters alongside the performance of each method.
Key Findings. Across Adroit, DexArt and MetaWorld, our method substantially outperforms dif- fusion and other baselines. Table highlights work performance 18 core tasks, while com- prehensive results across all 56 tasks are detailed in Appendix. Beyond that, our two-stage design preserves primary-mode consistency even when action chunks are short, which approaches closed- loop and highly reactive operation. Meanwhile, our primary-mode tiny MLP and the one-step gen- erator together yield fast generation while maintaining high success rates, as discussed in Ablations section. These findings indicate that explicitly decoupling coarse discrete mode selection from con- tinuous intra-mode variation yields both statistical and practical benefits.
4.2 REAL WORLD EVALUATION
Hardware. We evaluate method two single-arm hardware configurations commonly used in manipulation research: a) an UFAC- TORY xArm manipulator equipped with two-finger parallel gripper, and b) xArm paired with ROBOTERA XHand for dexter- ous manipulation. For visual sensing we use third-person Intel RealSense L515 LiDAR camera that provides aligned color and depth frames. For the xArm + gripper setup addi- tionally use low-cost 3D- 3D-printed demonstra- tion arm from GELLO (Wu al., 2024) tele- operation device. For the xArm + XHand setup, human hand motion is captured from Meta Quest 3 headset and retargeted to the XHand. All com- putation runs on a single workstation equipped with an NVIDIA RTX 4090 laptop GPU. The robot and sensors are controlled over a local area network.
Hardware
Manipulated Objects
xArmy?
3D Printed Arm
M
XHand
Gripper
Headsel
Figure 4: Hardware and manipulated objects used in real world experiments.
Teleoperation. We collect demonstrations with two teleoperation pipelines. xArm gripper demon- strations are collected using the GELLO framework (Wu et al., 2024), low-cost and intuitive tele- operation system that allows operators to demonstrate end-effector motions with separate low-cost manipulator. xArm XHand demonstrations are recorded by capturing human hand kinematics via a Meta Quest 3 headset. The recorded wrist 6-DoF pose is mapped to the xArm end-effector via Inverse Kinematics (IK), finger joint values are retargeted to the XHand via AnyTeleop (Qin al., 2023).
https://www.ufactere https://www.rodt

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Ablations
Benchmarks DexArt (4)
PM
MF
Token.
# Modes
Adroit
MetaWorld (11)
Weighted Success
/
VQ- VAE
64
0.77 10.03
0.72 10.04
0.7010.02
0.72
X
VQ-VAE
64
0.02=0.01
0.00
0.0220.01
0.01
X
<
VQ-VAE
64
0.6222.02
0.65220.01
0.51
0.56
VQ-VAL VAE
8
0.72=0.02
D. 00.002
0.55++.00
0.61
VQ-VAE
1024
0.66=0.02
0.68++.08
0.52+0.06
0.58
K meaass
64
0.76_0.05
0.7010.01
0.6910..2
0.70
Table 3:
Ablation study the impact of PR-DAG's key components and hyperparameters. w.
PM denotes whether the primary mode policy is included. w. MF indicates whether the mode- conditioned MeanFlow policy is included. Token. means action tokenization method. # Modes represents the number of discrete primary modes.
Observation and Action Spaces. Visual input the RGB-D stream from the RealSense L515. Frames are backprojected to form colored point cloud. We convert each frame into a fixed-size point cloud by applying Farthest Point Sampling. Proprioceptive observations include the xArm joint angles. When the XHand is integrated, the observation space is extended to include the XHand's joint angles as additional dimensions. For the XHand configuration we additionally log tactile readings from fingertip sensors. All observations normalized using the statistics com- puted on the training split. The policy outputs actions directly in joint space for both setups. We operate in absolute joint position control.
Baselines. We compare our method to two baselines. Vanilla BC processes observations through the same Observation Feature Extraction pipeline used by our method, and a 3-layer MLP is trained to regress actions in standard behavior cloning setup (Levine et al., 2016). DP3 (Ze et al., 2024) is a diffusion- generative policy operating on 3D soant-clou-cconditionn
actions. At inference DP3 employs DDIM (Song et al., 2020) denoising to obtain actions. Both baselines are trained on the identical demonstration sets and evaluated under the same closed-loop control as our method.
Tasks, We evaluate on tasks spanning low-DOF gripper control and high-DOF tactile dexterous manipulation. Low-DOF examples include a Pick Cube task (gripper picks a cube from randomized table locations) and Place Baymax task (place toy "Baymax" from table into a cabinet). High- DOF experiments use a 12-DOF dexterous hand equipped with tactile sensing and include contact- rich tasks such as Wipe Table (multiple possible wiping contact points) and Place Toy Into Bin (multiple candidate toy-boxes yielding multi-modal valid outcomes). For task like Place Baymax we exploit a pretraining to fine-tuning regime. Models pretrained on source task require substantially fewer target-task demonstrations to reach competitive performance.
Result Analysis. Our method consistently outperforms both baselines in success rate across low- DOF and high-DOF/tactile tasks (see Table 2). Qualitatively, Figure 3 visualizes common failure modes of baselines, while policy commits to coherent, single-mode rollouts when appropriate and preserves intra-mode variations elsewhere. Typical failure cases for our method occur at out-of- distribution object placements when tactile sensing is intermittently noisy. These failures rare and amenable to mitigation via modest additional demonstrations or data augmentation.
4.3 ABLATIONS
Primary Mode and MeanFlow Ablation. We ablate the two core components of our pipeline to es- tablish their individual importance. First to remove the Mode-conditioned MeanFlow Policy (MF) so that the system simply uses the Primary Mode Policy (PM)'s predicted VQ code and decodes it via the VQ- VAE reconstruction as the final action. Second is remove the PM so that MF attempts to predict actions without being conditioned on discrete mode. Results are reported in Table 3. Removing MF collapses performance almost completely, showing that a raw VQ reconstruction insufficient as the final action when the number of modes is limited. The quantization error produces large reconstruction distortions that destroy task success. Conversely, removing PM yields a 0.16 absolute drop in success, which demonstrates that explicit primary-mode selection substantially eases the downstream continuous generation problem and prevents coarse-mode bouncing.
Mode Capacity and Tokenization. We study how the number of discrete primary modes K and the choice of tokenization affect the PM learning and final task performance. We vary K E (8, 64, 1024) and compare VQ-VAE with k-means tokenization baseline. Results appear
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Action Chunk Projection
012
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0.71
048
OPS
064
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0.65
044
028
028
0.47
0.48
644
0.69
0.63
0.59
0.58
648
0.48
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24
6.
0.27
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14.6
10.4
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Real-tine Control FPS: 3010
(a) Primary Mode Clustering
(b) Speed-Accuaccy Trrade-off
(c)Action- Length vs, Reactivity
Figure 5: Illustration of critical properties of PF-DAG. (a) Action chunks are projected to 2D via PCA, colored by their assigned primary mode. (b) PF-DAG's one-step MeanFlow decoder achieves FPS comparable to 1-NFE DP3 while maintaining significantly higher success. serves high success even with short chunks by avoiding primary mode bouncing.
(c) PF-DAG pre-
Observation
Mode Probability
Observation
Mode Probability
Observation
Mode Probability
vQ Code Index
vQ Code Index
Code Index
Action
Action
Reference
Disessemble
Figure 6: Visualization of the mode probability distribution predicted by the Primary Mode Policy Ti at three selected frames. The vertical axis of the heatmap represents the mode index.
in Table 3. A small K helps the PM to learn, but it risks underfitting when the task's action-chunk distribution is complex. Large K increases expressivity but makes the PM hard to learn. In our do- mains the trade-off's is modest and K 64 achieves good balance across tasks. Different tokenizers produce similar final success rates, suggesting the approach is robust to discretization methods. Our method mainly needs a reasonable set coarse modes rather than a specific quantizer. To further illustrate mode structure we project action-chunks into 2D (PCA) and color by assigned mode. The visualization shows clear coarse-mode clusters on the action manifold, as visualized Figure (a). We also visualize the policy's 's outputs at different timesteps (see Figure 6). For more detailed qualitative analysis of the primary mode policy's behavior, see Appendix.
Ablation Meanflow. This ablation aims to eval- uate the performance difference between McanFlow and Conditional Flow Matching (CFM) (Lipman et al., 2022), where CFM is tested under different Ordinary Differential Equation (ODE) numerical in- tegration methods. Though CFM theoretically de- fines constant velocity field when mapping from noise to target distribution, the parameterized neural network introduces nonlinearity numerical com- putations. This makes the exploration of diverse ODE integrators non-trivial. For Runge-Kutta inte- gration, adopt the Dormand-Prince 5 method, widely used choice for adaptive-stepsize ODE solving. As shown in Table 4, varying ODE numerical integrators yiclds negligible performance improvements for CFM. In contrast, replacing CFM with MeanFlow results in performance gain.
Variations
ODE Solver
Success
CFM
1-NFE Euler
0.69
CFM
10-NFE Euler 0.69+0.02
CFM
Runge- Kutta 0.68+0.01
Meanflow
1-NFE 0.72+40.02
Table 4: Comparison of success for Mean-
Flow (MF) and Conditional Flow Matching (CFM), varying the ODE solver and NFE.
Speed-Accuracy Trade-off. We examine how the number of function evaluations (NFE) during inference affects both inference speed and success. We compare one-step MeanFlow decoder to DP3 at different NFE settings, plots are in Figure (b). Our one-step generator achieves infer- ence speed comparable DP3 with 1-NFE while delivering substantially higher success. More

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generally, we observe that within the tested range the total NFE has surprisingly small influence on success, which suggests that for these simulated tasks the NFE is not the dominant bottleneck. We hypothesize this limited sensitivity is due to the tasks' tolerance small action perturbations in simulation.
Action-chunk Length and Reactivity. All experiments here conducted real settings de- scribed in the Real World Evaluation section. We sweep action-chunk length and measure success. Shorter chunks make the controller more open-loop reactive and therefore better able respond to unexpected environment changes. However, short chunks also tend to increase trajectory jitter and occasional stoppages. Our method maintains relatively high success even short chunk lengths, showing the two-stage design preserves primary-mode consistency while allowing rapid reactivity. Results appear in Figure (c).
4.4 FAILURE CASES AND LIMITATIONS
While PF-DAG demonstrates strong performance across wide range of manipulation benchmarks, it has two notable limitations. First, because primary-mode selection operates on discretized action chunks, the method exhibits reduced temporal granularity in very high-dynamics, low-latency tasks. Second, the discrete codebook introduces a trade-off between expressivity and learnability. Larger K improves representational capacity but makes ceimay--policy learning harder, while smaller K constrains diversity. We address this in the paper via targeted ablations and validation sweeps. Promising directions to reduce per-task tuning include shared or meta-learned codebooks, end-to- end distillation, and multi-task pretraining to improve generalization and reduce pipeline overhead.
5 CONCLUSION
In this work we present PF-DAG, two-stage imitation learning framework that decouples primary mode selection from fine-grie greiggraied action generation. PF-DAG first uses a VQ- VAE to tokenize action chunks into discrete modes. A lightweight primary policy then trained predict these modes from observations, allowing for stable and consistent coarse mode selection. The framework then employs mode conditioned MeanFlow policy produce high-fidelity continuous actions conditioned on the selected mode, We prove that, under realistic variance assumptions, PF-DAG attains a strictly lower MSE bound than comparable single-stage generative policies. Empirically, PF-DAG outperforms state-of-the of-t baselines on 56 simulated tasks and on real world tactile dexterous manipulation. Future work will extend PF-DAG long- horizon hierarchical control and investigate uncertainty- aware refiners for improved robustness.
6 ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China under Contract 62472141, the Natural Science Foundation of Anhui Province under Contract 2508085Y040, and the Youth Innovation Promotion Association CAS. It was also supported by the GPU cluster built by MCC Lab of Information Science and Technology Institution, USTC and the Supercomputing Center of USTC.
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14


Reviews:
[{"review_id": "Y4qy8FaGS9", "reviewer": "Reviewer_6d45", "summary": "The paper proposes PF-DAG, a two-stage framework that decouples discrete “primary” action modes from continuous, fine-grained residuals. Stage 1 quantizes action chunks with a small VQ-VAE codebook and trains a lightweight classifier pi_1 to select a primary mode from observations. Stage 2 conditions a one-step MeanFlow decoder pi_2 on the selected mode and observations to output high-fidelity continuous actions. A simple variance decomposition argument claims a strictly lower optimal MSE bound than single-stage generative policies. Experiments across 56 tasks (Adroit, DexArt, MetaWorld) and four real-world tasks report higher success and improved speed/stability versus diffusion and flow baselines. The work targets multi-modal action generation and mode-bouncing in closed-loop manipulation and argues significance via better robustness and real-time control.", "questions": "- The authors mentioned the mode bouncing issue, which is also raised in RNR-DP which is cited in the related work in this paper. However it is not served as a baseline. I'm curious whether how it performs in the authors' setting since it tried to tackle similar problem.\n- Would be great if the authors could report stability related metrics (mode-switch rate, jerk, pose variance etc.) to justify the claim.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The writing is good and the paper is easy to follow.\n- The two-stage design that separates coarse mode selection from fine residual generation is clear and practical. The one-step MeanFlow decoder offers compelling speed advantages while maintaining accuracy. \n- Empirical results are broad and consistently favorable across many simulated tasks, and the real-world demos indicate potential practical relevance. The ablations on K and tokenization provide preliminary guidance on design choices.", "weaknesses": "- The greedy mode selection without temporal smoothing can still make mode-bouncing happen and it highly relies on a carefully selected #mode hyperparam\n-  Several design choice (VQ-VAE, MeanFlow) seems only provide marginal improvement based on the ablation studies.\n- Clustering-based coarse-to-fine/mode-selection mechanism has been explored in other robotics domain such as motion forecasting in autonomous driving, the novelty of this paper is somewhat limited.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "3uyWsqKZJP", "reviewer": "Reviewer_4ven", "summary": "This paper introduces a two-stage imitation learning framework PF-DAG for robot manipulation that explicitly separates coarse discrete decisions from fine-grained continuous action generation. The key idea is that many manipulation behaviors can be decomposed into a small number of interpretable primary modes plus within-mode variations. In the first stage, PF-DAG uses a VQ-VAE to encode action chunks into discrete primary modes and trains a lightweight policy to predict these modes from robot observations. In the second stage, a mode-conditioned MeanFlow decoder generates continuous actions conditioned on both the selected mode and the observation, improving action fidelity and stability. Empirically, PF-DAG outperforms behavioral cloning, diffusion, and flow-based baselines across 56 simulated manipulation tasks (Adroit, DexArt, MetaWorld) and transfers successfully to real-world tactile dexterous manipulation.", "questions": "Figure 6 provides an interesting visualization of the mode probability distribution and the corresponding policy behaviors in simulation. Would it be possible for the authors to include videos illustrating this? And if possible, also show the results for K-means side-by-side? Given that Table 3 reports very close performance between VQ-VAE and K-means, I am particularly curious whether the two produce noticeably different qualitative behaviors.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper tackles a key challenge in imitation learning, modeling multi-modal action distributions, with a clear two-stage formulation.\n\nThe Primary-Fine Decoupling design (discrete mode selection + continuous residual generation) is simple yet effective, and leads to more stable, temporally consistent control compared to other diffusion or flow-based baselines.\n\nThe paper is well-supported by both theoretical justification and empirical evidence, including a variance-based MSE bound analysis, as well as comprehensive ablation studies and quantitative experiments. The proposed method shows strong results across diverse benchmarks (Adroit, DexArt, MetaWorld) and have a real-world experiment.", "weaknesses": "While the paper attributes instability to \"mode bouncing\", it does not empirically compare against simpler baselines that include observation or action history. In practice, conditioning on temporal history or predicting waypoints (as done in prior works) can also effectively reduce mode switching. Also, some other related approaches such as \"Behavior Generation with Latent Actions\" (ICML 2024) and \"Hierarchical Diffusion Policy: Manipulation Trajectory Generation via Contact Guidance\" (T-RO) should be discussed or may be compared.\n\nAlthough some real-robot experiments are reported, the hardware evaluation is relatively limited. It lacks more detailed comparisons, visualizations, and failure analyses, making it difficult to assess robustness and reproducibility.\n\nIn Table 3, the performance gap between K-means and VQ-VAE quantization is minimal, raising questions about whether the added complexity of VQ-VAE is necessary or provides substantial benefits beyond a simpler clustering baseline.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Ir25BWq8AA", "reviewer": "Reviewer_YsMa", "summary": "The paper proposes a hierarchical method for imitation learning by firstly decomposing action chunks from demonstrations into discrete high-level coarse skills which are used to condition a residual policy that is trained using MeanFlow, a one-step generative modelling technique, to then produce the final action to be executed on the robot. At the high-level, a Vector Quantized VAE is used to extract a codebook of distinct modes, wherein each discrete mode represents a coarse action. To make up for the errors between a coarse and continuous action arising from a discretization and subsequently to improve the continuous predictions, a second fine-grained policy is used that is conditioned on the predicted high-level skill which adds a residual action to the coarse action.", "questions": "- What are the key contributions that make the paper stand out compared to other hierarchical policy learning approaches? How does this necessarily translate into improved performance gains?\n- Are there any architectural differences between the proposed approach and the baselines? Are the architechtures from the baselines used as is without any modification? Is it the same observation feature extraction followed by the same ($\\pi_2$) network used for the meanflow residual policy without conditioning? If not, then it may not be a fair comparison in my opinion. \n- How is the multisensory information effectively used? Or is it just encoded directly and used to train the policy end-to-end? For example using the high-level to potentially weight the information from the different sensors.\n- The network architechtures for the VQ-VAE and MeanFlow residual network is missing in section A.4. The implementation details (Lines 233-237) do not make this clear either.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 1, "strengths": "The proposed approach shows promising results on a variety of tasks both in simulation and in the real world, not just in terms of accuracy but also in capturing the multimodality effectively. The hierarchical disambiguation helps prevent \"mode bouncing\" which allows for a conditional generation of the fine-grained actions. The use of MeanFlow as compared to Flow Matching also shows a good improvement which adds some novelty. The paper is written well and clear to follow.", "weaknesses": "While the proposed approach shows promise, this approach of hierarchical policy structures for robot learning has been well studied in previous approaches, yet there is no mention or comparison against previous approaches. Only some discussion on Imitation Learning and Action space discretization is presented. There is no comparison against any hierarchical approach, but rather against standard end-to-end visuomotor policy learning approaches like using Diffusion or Flow Matching. Many previous approaches have shown how such a hierarchical structure can be use breakdown policy learning into a high-level skill decomposition module that is then used to condition a low-level policy, even with multisensory inputs or to train a residual policy as the authors propose. The proposed approach is not really a novel idea that is being proposed, but rather a variant of this hierarchical family of approaches that uses a residual policy using MeanFlow, instead of directly conditioning the low-level policy.\n\nSome related works on hierarchical decomposition:\n- Rana, Krishan, et al. \"Residual skill policies: Learning an adaptable skill-based action space for reinforcement learning for robotics.\" Conference on Robot Learning. PMLR, 2023.\n- Cui, Te, et al. \"Hierarchical Autoregressive Modeling With Multi-Scale Refinement for Robot Policy Learning.\" IEEE Robotics and Automation Letters (2025).\n- Chen, Lili, Shikhar Bahl, and Deepak Pathak. \"Playfusion: Skill acquisition via diffusion from language-annotated play.\" Conference on Robot Learning. PMLR, 2023.\n- Mete, Atharva, et al. \"Quest: Self-supervised skill abstractions for learning continuous control.\" Advances in Neural Information Processing Systems 37 (2024): 4062-4089.\n- Wan, Weikang, et al. \"Lotus: Continual imitation learning for robot manipulation through unsupervised skill discovery.\" 2024 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2024.\n- Kujanpää, Kalle, Joni Pajarinen, and Alexander Ilin. \"Hierarchical imitation learning with vector quantized models.\" International Conference on Machine Learning. PMLR, 2023.\n- Zhao, Tianxiang, et al. \"Skill disentanglement for imitation learning from suboptimal demonstrations.\" Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2023.\n- Tanneberg, Daniel, et al. \"Skid raw: Skill discovery from raw trajectories.\" IEEE robotics and automation letters 6.3 (2021): 4696-4703.\n- Ju, Zhaoxun, et al. \"Rethinking mutual information for language conditioned skill discovery on imitation learning.\" Proceedings of the International Conference on Automated Planning and Scheduling. Vol. 34. 2024.\n- Liang, Zhixuan, et al. \"Skilldiffuser: Interpretable hierarchical planning via skill abstractions in diffusion-based task execution.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.\n- Hao, Ce, et al. \"Skill-critic: Refining learned skills for hierarchical reinforcement learning.\" IEEE Robotics and Automation Letters 9.4 (2024): 3625-3632.\n- Feng, Ruoxuan, et al. \"Play to the Score: Stage-Guided Dynamic Multi-Sensory Fusion for Robotic Manipulation.\" Conference on Robot Learning. PMLR, 2025.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "U7dFINMiz3", "reviewer": "Reviewer_u2ZP", "summary": "This paper introduces PF-DAG (Primary-Fine Decoupling for Action Generation), a two-stage imitation learning framework that separates coarse discrete mode selection from fine-grained continuous action generation in robotic manipulation. The method first compresses action chunks into discrete primary modes using a VQ-VAE and predicts these modes through a lightweight classifier π₁ (Sec. 3.3). Conditioned on the selected mode, a one-step MeanFlow policy π₂ produces continuous residual actions (Sec. 3.4). The authors show theoretically (Eq. 6) that this two-stage design achieves a lower optimal MSE bound than single-stage generative models by removing inter-mode variance. Experiments on 56 manipulation tasks across Adroit, DexArt, and MetaWorld (Table 1, Table 5) demonstrate significant improvements over diffusion and flow-based baselines such as DP3 and FlowPolicy. Real-world evaluations on xArm and XHand setups (Table 2) further support PF-DAG’s efficiency and robustness, and ablations (Table 3, Table 7) examine the contributions of each component, the number of discrete modes, and tokenization schemes.", "questions": "please address the concerns above", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper presents a clean, interpretable two-stage structure that maps well onto the inherent hierarchy of manipulation behaviors. The distinction between discrete primary modes (coarse subgoals) and continuous fine variations (residual control) is intuitive and empirically justified by improved temporal stability and reduced “mode bouncing” (Fig. 3, Fig. 5c).\n\n2. PF-DAG is evaluated on 56 simulated and several real-world tasks, with consistent and sizable gains over strong diffusion and flow baselines (Table 1, Table 5). The inclusion of tactile sensing and dexterous-hand setups makes the evaluation unusually comprehensive for imitation learning studies.\n\n3. The ablation studies (Table 3) systematically isolate the contributions of the Primary Mode Policy and MeanFlow decoder, demonstrating clear complementary effects. Additional analyses on the number of discrete modes (Table 7) and solver sensitivity (Table 4) reveal robustness to hyperparameters and architecture choices.\n\n4. The MeanFlow one-step generation (Sec. 3.4) avoids the high computational overhead of multi-step diffusion or normalizing flow inference, achieving inference speeds comparable to 1-NFE diffusion with substantially higher success (Fig. 5b). This efficiency supports PF-DAG’s practicality for real-time control.", "weaknesses": "1. The MSE bound proof in Sec. 3.5 assumes oracle access to correct mode assignments, ignoring errors from the learned π₁. In practice, misclassification reintroduces inter-mode variance, invalidating the “strictly lower bound” claim except in the idealized setting of perfect mode prediction.\n\n2. The VQ-VAE learns discrete modes via unsupervised L₂ reconstruction (Eq. 3), but this can merge semantically distinct actions or distort temporal consistency, particularly in high-DOF settings (DexArt). The resulting quantization bias contradicts the clean variance decomposition used in the theoretical section.\n\n3. The MeanFlow decoder (Eq. 4, 16) predicts deterministic residuals rather than sampling from a conditional distribution, meaning PF-DAG cannot represent intra-mode uncertainty. This weakens the paper’s claim of “multi-modal modeling” within each mode.\n\n4. Although the paper highlights interpretability benefits (Fig. 5a, Fig. 7), these are shown only through qualitative cluster plots. No quantitative metrics (e.g., mode purity, task-level consistency) are provided, making the claim of interpretable sub-behaviors unsupported.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)