Compose Your Policies! Improving Diffusion-based or Flow-based Robot Policies via Test-time Distribution-level Composition
Authors: Jiahang Cao
Yize Huang
Hanzhong Guo
Qiang Zhang
Rui Zhang
Weijian Mai
Mu Nan
Jiaxu Wang
Hao Cheng
Jingkai SUN
Gang Han
Wen Zhao
Yijie Guo
Qihao Zheng
Xiao Li
Chunfeng Song
Ping Luo
Andrew Luo
Venue: ICLR 2026 Poster (2026)
Keywords: Diffusion Policies
Policy Composition
Training-free
Primary area: applications to robotics, autonomy, planning
TL;DR: We present General Policy Composition, a training-free method that enhances performance by combining the distributional scores of multiple pre-trained policies via a convex combination and test-time search.

Abstract: Diffusion-based models for robotic control, including vision-language-action (VLA) and vision-action (VA) policies, have demonstrated significant capabilities. Yet their advancement is constrained by the high cost of acquiring large-scale interaction datasets. This work introduces an alternative paradigm for enhancing policy performance ***without additional model training***. Perhaps surprisingly, we demonstrate that the composed policies can exceed the performance of either parent policy. Our contribution is threefold. First, we establish a theoretical foundation showing that the convex composition of distributional scores from multiple diffusion models can yield a superior one-step functional objective compared to any individual score. A Grönwall-type bound is then used to show that this single-step improvement propagates through entire generation trajectories, leading to systemic performance gains. Second, motivated by these results, we propose General Policy Composition (GPC), a training-free method that enhances performance by combining the distributional scores of multiple pre-trained policies via a convex combination and test-time search. GPC is versatile, allowing for the plug-and-play composition of heterogeneous policies, including VA and VLA models, as well as those based on diffusion or flow-matching, irrespective of their input visual modalities. Third, we provide extensive empirical validation. Experiments on Robomimic, PushT, and RoboTwin benchmarks, alongside real-world robotic evaluations, confirm that GPC consistently improves performance and adaptability across a diverse set of tasks. Further analysis of alternative composition operators and weighting strategies offers insights into the mechanisms underlying the success of GPC. These results establish GPC as a simple yet effective method for improving control performance by leveraging existing policies.

Published as a conference paper at ICLR 2026
COMPOSE YOUR POLICIES! IMPROVING DIFFUSION- BASED OR FLOW-BASED ROBOT POLICIES VIA TEST- TIME DISTRIBUTION-LEVEI COMPOSITION
Jiahang Cao 12,3*
Yize Huang! 1.
Hanzhong Guo!
Rui Zhang'
Mu Nan
Weijian Mai
Jiaxu Wang Hao Cheng
Jingkai Sun
Gang Han
Wen Zhao?
Qiang Zhang
Yijie Guo Qihao Zheng
Chunfeng Song?
Xiao Li
Ping Luo'
Andrew F. Luo
'The University of Hong Kong "Beijing Innovation Center of Humanoid Roboties
SShangaai AI Lab *Shanghai Jiaotong University
"hhe Hong Kong University of Science and Technology
ABSTRACT
Diffusion-baselt models for robotic control, including (VLA) and vision-action (VA) policies, have demonstrated significant capabili- ties. Yet their advancement is constrained by the high cost of acquiring large-scale interaction datasets. This work introduces an alternative paradigm for enhancing policy performance without additional model training. Perhaps surprisingly, we demonstrate that the composed policies can exceed the performance of either par- ent policy. Our contribution is threefold. First, we establish theoretical foun- dation showing that the convex composition of distributional scores from multi- ple diffusion models can yield a superior one-step functional objective compared to any individual score. A Grönwall-type bound is then used to show that this single-step improvement propagates through entire generation trajectories, lead- ing to systemic performance gains. Second, motivated by these results, pro- pose General Policy Composition (GPC), a training-free free method that enhances performance by combining the distributional scores of multiple pre-trained poli- cies via a convex combination and test-time search. GPC is versatile, allowing composition of heterogeneous policies, including VA and VLA models, as well as those based on diffusion or flow-matching, irrespective of their input visual modalities. Third, we provide extensive empirical validation. Experiments on Robomimic, PushTT, and RoboTTwin benchmarks, alongside real- world robotic evaluations, confirm that GPC consistently improves performance and adaptability across a diverse set of tasks. Further analysis of alternative com- position operators and weighting strategies offers insights into the mechanisms underlying the success of GPC. These results establish GPC as simple yet effec- tive method for improving control performance by leveraging existing policies. Our project page is in https: /aaeeaaaelll github. 1o/GPC-SSSSS Sitte.
for the plug-and-ple
INTRODUCTION
Diffusion Policies (DPs) (Chi et al., 2023; Ho et al., 2020; Song et al., 2020a) have emerged as pow- erful method for policy parameterization in robot learning, enabling the representation of complex, multi-modal action distributions a key advantage for policies conditioning on digh-dimensional inputs like vision and language in domains from manipulation (Ze et al., 2024b: Zhu et al., 2024; Liu et al., 2024a) to navigation (Sridhar et al., 2024; Zhang et al., 2024a). Despite this progress, the advancement of diffusion- and flow-baser policies is fundamentally constrained by scaling chal- lenges related to both model capacity and data availability. Performance can plateau due to the intrinsic representational limits of given model, yet scaling up the model architecture also requires
$ Equal contribution jiahang8connect .hu.hk Corresponding author a ku.

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Rulominic
112%
Place Fries
1.0
Fuller X
Object
Pre-trained Distribution of Policy A
Distriuttion-on Composition
RoboTwil
CEC
Failane
Composed Distribution
13
12
Pizusible Area
Implassible Arre
0.4
Pre-triined Distribution of Policy
Success Cases
Failare Crarss
Burger
Weight Searching
(a)
(b)
(c)
Figure 1: Illustration of General Policy Composition. (a) Distributions from pre-trained state-
of-the-art diffusion- flow- fowebased policies can be composed to construct stronger policy without additional training, with a test-time search over composition weights picking the best parent-policy mix; score composition corresponds the product of probabilistic density functions (PDFs), steer- ing sampling toward consensus regions. (b) GPC can yield consistent gains across diverse set of tasks. (c) We find the optimal weight when composing two models can vary depending on the task.
the collection of costly interaction datasets fully capture the potential performance benefit (Black et al., 2024). Conventional post-training strategies offer limited solutions; supervised fine-tuning requires expensive data collection (Ouyang al., 2022), while reinforcement learning introduces the complexity of reward engincering and extensive online interaction (Hu et al., 2025).
To overcome these limitations, this work introduces an alternative paradigm: creating stronger poli- cies by composing existing, pre-trained models. While prior work has explored static model compo- sition (Du & Kaelbling, 2024; Wang al., 2024c), we find that the optimal weighting is not universal but is instead highly task dependent, even for fixed set of parent policies. Drawing inspiration from compositional generative modeling. we first establish a theoretical foundation showing that a convex combination of distributional scores can yield provably superior objective for policy improvement. This principle underpins our proposed method of General Policy Composition (GPC, Fig. 1). GPC is training-free framework that, at inference time, combines the distributional scores of multiple pre-trained policies via convex combination and test-time search. This approach flexibly integrates heterogeneous models spanning diffusion- and flow-based architectures, VA and VLA modalities, and diverse sensory inputs to form a more capable policy, all without modifying the base models. Crucially, demonstrate that the resulting composed policy exceed the performance of any of its individual parent policies.
We validate GPC through extensive experiments in both simulation and real-world environments, demonstrating consistent outperformance against single-policy baselines. Our analysis extends to alternative composition operators (c.g., logical AND/OR) and various weighting configurations, of- fering broader insights into why and when composition is effective. Our contributions are summa- rized as follows: (i) We establish a theoretical foundation for robot policy composition, proving that the convex combination of distributional scores can yield an improved functional objective and that this advantage propagates to the system level. (ii) We propose General Policy Composition (GPC), flexible, training-free framework that combines pre-trained policies across different modalities and architectures into a more expressive policy. (iii) We conduct extensive evaluations in simulation and the real world, demonstrating the consistent performance gains of GPC while analyzing key design choices to guide future research in policy composition.
RELATED WORK
Composable Generative Models. Composability refers to the ability to combine multiple compo- nents or distributions into a unified representation while preserving the properties of the individual elements. (i) Visual Generation: Energy-based models (EBMs) (Hinton, 2002; Du & Mordatch, 2019; Grathwohl et al., 2020) support compositionality by summing energies, allowing factor-level combinations. Du et al. (2020) unified perspectives of compositionality for visual generation. Liu et al. (2021) further improved EBMs for scene generation by factorizing relational structures. Skreta al. (2024) introduced the superposition of diffusion models by using ită estimation. (ii) Language
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Policies with difforent visuol modaliiies
Diffusion-basod
ST t, ci Score A
Lower Error
Denoise
DP
DP3 MDT
ccomp(1 (7, f, c)
DP with Modality
Composed Score- Action-
MA Florence DP RDT
Ter-ame
ner
To Score
Exocution
Flow-busod Policies
are
DP with Modality
O Composed Score Action
Scmmp (7r 4
Demoise
Flow Policy
Hurt
solt,,t Score
Surceess
UA
Florence FP mi
RDT with Modality B
Lower Error
Pre-trained State-of-the-art
Policies with different backbones
Juc Testtine Scarchig for
Policies Pool
Overview of our proposed General Policy Composition. Combining distributional scores from pre-trained diffusion-based or flow-based policies on different conditions (e-g.. visual modalities and network backbones), GPC can generate expressive and adaptable action trajectories through convex score combination without additional training.
Figure 2:
Generation: Du et al. (2023b) combined outputs using mulli--gen debate for robust language gen- eration. Lifshitz et al. (2025) proposed multi-agent verification at test-time for improvement.
Diffusion Models in Robot Learning. Due their flexibility and representational power, diffu- sion models (Ho et al., 2020; Song et al., 2020a; Nichol & Dhariwal, 2021) offer novel way to represent policies. The concept of Diffusion Policy (Chi al., 2023) first proposed to model action spaces using diffusion, significantly enhancing expressiveness. Since then, numerous ad- vancements have been made: multimodal DP such MDT (Reuss et al., 2024), trajectory extraction approaches like AWE (Shi et al., 2023). DP3 (Ze et al., 2024b) utilizes point cloud representations achieve sfae-offtheearr performance, and VI.A models, e-g., Octo (Team et al., 2024), mo (Black et al., 2024) and RDT (Liu et al., 2024a). In this work, our GPC can be adopted to various general diffusion-basse (e.g., DP, DP3, MDT, and RDT) or flow-based policies (e.g., flow policy and тo), demonstrating great flexibility (Detailed in App. G).
Compositional Diffusion Models in Robotics. Recent work has explored the use of composi- tional diffusion models in robotics. Janner et al. (2022) applied compositionality to diffusion- planning. Yang et al. (2023b) tackled continuous constraint satisfaction in robotic planning, and Luo al. (2024) improved motion planning by learning potential fields. In addition, Policy Com- position (PoCo) (Wang et al., 2024c) does constraint- task-based, and input modality-bant composition; however, does not explore the weights between policies. Moreover, has been validated in widely adopted simulation environments and provides limited analysis of the underlying composition mechanisms. In contrast, our proposed GPC framework offers broader generality by enabling composition across both VA and VLA models, regardless of input visual modality, and we also deliver deeper insights into the task-dependent weight searching for policy composition.
PRELIMINARIES
Diffusion models (Sohl-Dickstein et al., 2015) are based generative process that iteratively denoises a random noise distribution to generate samples. The following equation describes the update rule for the diffusion process based Langevin dynamics (Song al., 2020b):
(1) where so(T,, !) denotes the learned score function, 04,, Bt, 7r are coefficients determined by the noise schedule and the choice of solver. Different sampling methods, such as DDPM (Ho et al., 2020),
T(-1 44 Te 8 se(Tr. 77 1 7~ (0,
DDIM (Song et al., 2020a), or ODE/SDE-based solvers (Song et al., 2020b), can be recovered by specifying these coefficients accordingly.
Closely related to diffusion models are energy-based models (Hinton, 2002; Du & Mordatch, 2019), which define probability distributions through learnable energy functions. The connection arises because the gradient of the energy function in EBMs plays role analogous to the score function in diffusion models. Further progress made with compositional EBMs (Du et al., 2020), where multiple energy functions be combined by summing their contributions.
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4 THEORETICAL ANALYSIS OF CONVEX SCORE COMPOSITION
We first provide mathematical justification for why convex score composition can improve policy performance. Our analysis shows that (i) at the functional level, convex combinations of scores from pre-trained policies can yield lower score error, and (ii) at the system level, sampling error is bounded by score error through the stability of the sampling dynamics. These results establish con- score composition principled foundation for policy improvement, which directly motivates our proposed General Policy Composition framework (in Sec. 5).
4.1 FUNCTIONAL-LEVER IMPROVEMENT
We begin with the question of whether combining score estimators can yield better approximations to the true score s* The following result shows that there exists a convex combination of two estimators whose error is greater than that of the better individual estimator, and strictly smaller unless their errors are perfectly aligned.
Proposition 4.1 (Single-step improvement via convex combination). Let two score estimators s + b2 12, with deterministic biases b, and random zero-mean
be = 5* b1 + +7 and noise TΙ that plays the role of the diffusion component in the time-reversed stochastic dynamics (e.g., reverse-time ODE). For any convex weight u [O, 1). define E(w) wE1 (1 w) Then the mean-squaree error (ww) = E[E((w - s*12 a convex quadratic in w. Its minimizer w" satisfies
Q(w")= < min (Q()),
with strict inequality in most non-triviad cases.
See proof in App. B. Intuitively, each estimator deviates from the true score in a different way. A convex combination can cancel out these errors, achieving better score estimator. Unless the two models make identical errors, the true score 5* lies closer to some interior point, ensuring that weighted average achieves smaller error. This establishes that convex score composition can reduce estimation error at each step.
4.2 SYSTEM-LEVER STABILITY
While Prop. 4.1 shows improvement the functional level, it remains understand how score errors propagate into trajectory sampling. The following proposition establishes a stability guarantee: the terminal error is controlled by the cumulative score error.
Proposition 4.2 (Score-to so-re- stability). Let x* denote the oracle trajectory derived from the true score s* and xz(t) denote the approximate trajectory derived from estimator 3, both starting from the same initial condition. They satisfy
(1) = F(1, xxxx**() (1), (1, (()))
is(()) = xr ((1,
where F represents the underlying dynamics that map the score into the state update. Suppose F' is Lipschitz in (x,s) 8) with constants Lz(1), Lt(,), and is Lipschitz in x with constant A(t)- Assume the score error admits a uniform bound k(t) (i.e., | s*1l ll x(t)). Define L(t)
La (f) + (t)))(t)) Then for all >0. O,
(T) x (T) & (Se (f" L()) L,(1)²
1/2
1/2
L(
k(t)2
See proof in App. C. This result shows that the sampling dynamics stable: the terminal error grows at most exponentially with the Lipschitz constants, and is directly bounded by the integrated score emror. Thus, reducing score error each step translates to reducing the overall trajectory enror.
4.3 IMPLICATIONS FOR POLICY COMPOSITION
Combining Prop. 4.1 and Prop. 4.2 yields direct implication composed policies.
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Corollary 4.1 (Convex score combination tightens the sampling error bound), Let ((3) denote the upper bound on the expected sampling error derived in Proposition 4.2 (specifically Eq. 21). If a convex combination Scomp
w$1 + (1 w)88 satisfies
E
Scomp
11
min
5; dt,
then the corresponding theoretical error bound is strictly reduced:
B(5comp)
min B(s;).
See proof in App. D. Once funetional-level improvement is established by obtaining an optimal w* (Prop. 4.1), stability ensures this advantage propagates along the trajectory (Prop. 4.2), making convex score composition provably superior to relying on individual scores.
This theoretical analysis provides clear justification for convex score composition: it can improve accuracy at each functional step and propagate this advantage through stable sampling dynamics. leading to system-level gains. These results directly motivate GPC, which leverages convex score combination to build stronger policies from pre- pre-trained components. While the theory guarantees the existence of optimal weights, finding them analytically intractable; hence, in practice employ test-time searching to identify effective weighting strategies, as explored in Sec. 6.
OUR METHOD: GENERAL POLICY COMPOSITION
Building on the mathematical foundation in See, we now present our method, General Policy Composition, as illustrated in Fig. 2. The key idea is to leverage convex score composition to combine multiple pre-trained policies into a stronger and more expressive one. We first revisit the mathematical formulation of compositional diffusion models in Sec. 5.1, which provides a basis for composing policies conditioned on different factors. We then introduce our method in Sec. 5.2, where GPC convexly combines the scores of diffusion flow-based policies across modalities, chitectures, or VA/VLA settings. Finally, we extend this framework in Sec. 5.3 to include alternative composition operators, offering broader view of policy composition beyond convex averaging.
5.1 COMPOSITIONAL DIFFUSION MODELS
The key idea of the compositional diffusion model (CDM) is to model the distribution of a trajectory conditioned multiple concepts 6. similar to the compositional EBMs. Mathematically under an independence assumption, we can express the joint probability of the trajectory based on the set of concepts (ci,...,Cy, Cn3 in Eq. 2, and further reformulate the conditional terms by parameterizing p(a/T))o m(rles) as follows: p(7)
p(T|C),.... Ca) p(T Cl... = p(T) I p(c/7), 1-1
xc p(T) II (p((lcs)) i-1 p(T)
(p(T(c:) p(T)
with p(c/
(3)
where p(c/lT) can be interpreted as an implicit classifier (Ho & Salimans, 2022) and a serves as a weighting factor that modulates the influence of each concept on the overall trajectory distribution.
Then, the score function of the composed distribution can be derived directly from Eq. 3:
V, log p(r|ci....... c.,) V, logp(T) Σ a log V, log logp(r)).
(4)
Using the relationship between the score function of the distribution and noise (Bao et al., 2022), i.e., c0(Tr, t) = -o, V, p(T), we can express the update rule for CDM with the parameterization!
(,,, eo(Tr, 1)
Σ
wi wa(eo(Tes,, eo co !))
(5)
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DP ong
DP
GPC (ours)
Alg. 1: General Policy Composition Sampling
Input: Pre-trained policies Ti, m2 weights wi, W2
Failure X
Suceess
Sucress
(i.e. 1 w1). policies' conditions Ct, C2
1: for w1 = 0.0, ......,,0,.. 0.9; 1.0 : iess time searching
2: Initialize noise trajectory TN ~ ~O 1) per action
for t N ...... denoising steps
Success
X
$1 (T,, (,c)
82 - (T, C2) #t soooe estimation
6:
8comp - 1/ * 81 + # score composition
7:
T--1 Cte 3c Scomp + %
Return: Action trajectory 70
Figure 3: Visualization results of different diffu- sion policies and the composed policy with GPC. Our proposed GPC can successful even when one part of the DP fails. and shows better performance when both parts of the DP work.
Evaluate SR store in reward pools R(ws)
Return: Optimal weights wf - arg maX4r R(ws)
GPC Sampling, Policies are combined via test-time score composition into stronger policy.
Algorithm 1:
(T( where co Tr, 1, ct) (el)/e/(T.. !) represents the noise estimation at time step for trajectory 7; conditioned on the individual concept e; without condition. The weights w, modulate the influence of each concept on the overall noise estimate. This formulation represents a generalization of the classifier- free guidance (CFG) (Ho & Salimans, 2022) technique commonly used in generative models.
5.2 GENERAL POLICY COMPOSITION
Based on the previous foundation, we can now apply the CDM to diffusion policy for robotic tasks. The joint probability distribution of the trajectory conditioned on different modes c (e.g., different visual modality input or different model architecture) can be expressed as follows:
p(T (T, C.) o p(r (ei (p(r(c2) p(Tlc,))
While one could in principle apply CFG sampling as in Eq. 5, our theoretical analysis in Sec. 4 shows that convex combinations scores can provide a better functional objective and propagate stability through sampling dynamics. Motivated by this result, we construct our compositional policy by directly combining the score functions from multiple conditional diffusion policies via convex com- bination. This formulation not only inherits the stability guaranteess established in theory but also enables flexible integration of diverse conditional information.
Formally, let Scomp (Te, c) denotes the composed score, the update rule of GPC is defined as:
(o.soTT.tt,c with Σ w,= =
S comp (T, t.
where se(T,, c;) denotes the score estimate conditioned on concepts C; (e.g., visual modality or policy architecture), and w; represents the weight of convex combination assigned to each concept, ensuring a balanced contribution from all source distributions in the final trajectory estimate.
This convex combination ensures that the composite score remains within the feasible convex hull of individual policies, preventing divergence toward extreme or unstable behaviors. Intuitively, the GPC formulation balances information from different conditions, yielding more stable and coher- ent generative trajectory (e.g., Fig. 3). GPC sampling process is shown Alg.
5.3 GPC WITH SUPERPOSITION
Apart from using the score convex combination, our GPC framework naturally connects to the prin- ciple of superposition (Skreta al., 2024), which encompasses: (i) Logical OR corresponds to sam- pling from mixture of distributions, which is implemented by weighting with the softmax function at each sampling time: w!- = softmax (T log (T(c;) + E), where w; determines the relative contribution of each policy's score in sampling time f, T and 1 are constants; (ii) Logical AND enforces agreement among policies, corresponding to the intersection of their distributions. This is achieved by solving linear system to compute the weights such that d log Po(T(c,) d log pı (T(c,), ensuring consistency across different policies during sampling. In this work, we leverage these for- mulations to instantiate GPC with logical OR and AND operators as the application in Sec. 6.5.

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Table I: Experiment results on Robomimic and PushT. The table shows the success rate f. Our
GPC yields noticeable average improvement compared with the base policies.
Robomimic Lift
PushT PushT
Method
Generative Mode
Type
Can
Square
Average
Base Policies
Dillusion Policy (DP)
Diflusion
VA
34.50
98.50
2.00
21.75
39.19
Mamba Policy (MP)
Diffusion
VA
5.00
98.50
3.00
12.06
29.64
Flow Policy (FP)
Flow Matching
VA
95.00
13.00
77.50
54.25
59.94
Florence Policy-D
Diflusion
VLA
61.50
97.00
46.50
40.00
61.25
Florence Policy-F
Flow Matching
VIA
89.00
98.50
88,50
39.38
78.84
a0
Flow Matching
VLA
96.50
99.00
92.50
57.69
86.42
Composed Poticies via Convex Score Combination
DP+MP
Diffusion
VA & VA
34,50
99.50
8.00
23.63
41.41
+2.22%
Florence-Poliee Police---olc----DD
Diffusion
VLA VA
62.50
100,00
61.50
43.06
66.76 +5.51%
Horence-Policyy Policy-D-MMP
Diflusion
VLA
63.00
100,00
54.50
40.88
64.60 +3.35%
Plosence-oliic-FFFF
Flow Marching
VLA & VA
98.50
98.50
92.50
56.06
86, 39 47.55%
50+FP
Flow Matching
VLA & VA
99.50
100,00
94.00
62.25
88.94 +2.52%
Table 2: Experiment results on ToboTTin with 6 diverse bimanual manipulation tasks. GPC achieves an obvious increase with up to 7% improvement on the success rate.
Method
Model Type
Hanging
Open Lapop
Burgst Frics
RoboT'vin 2.0 Put Object Cabinct
Bools There
Tur Switch
Bosc Phlicies
DR 12
VA
0.10
0.24
0.49
0.56
0.52
0.38
0.46
RDT
VLA
0.13
0.69
0.46
0.32
0.47
0.30
0.40
Composed Policies Comerr
Combrnation
DP + DC
023
0.78
0.71
0.00-55
RUT + DP=s
VLA & VA
018
0.80
0.57
0.59
0.66
0.38
47%
VLA
0344
EXPERIMENT
We conduct experiments to investigate three key questions: (i) How does GPC perform in simulation and real-world experiments? (ii) How do different weight configurations influence the performance of GPC across various scenarios? (iii) How can the advantages of the composed DP be explained?
6.1 EXPERIMENT SETTINGS
Environment Settings. We evaluate on Robomimic (Mandlekar et al., 2022), which includes three manipulation tasks (Can, Lift, Square), PushT (Florence et al., 2021), and RoboTTwin (Mu et al., 2025), a suite of dual-arm collaborative tasks where we select representative ones from versions 1.0 and 2.0 (Chen et al., 2025). We further perform four real-world experiments: Place Bottles, Hang Mug, Close Table, and Punch Holes, with the setups in Fig. 6. More details are in App. I.
Baselines. For Robomimic and PushT, we compare against three VA models: DP (Chi al., 2023), Mamba Policy (MP) (Cao et al., 2025b), Flow Policy (FP, the flow matching version of DP), and three VLA models: Florence-basse and a revised TO (Black et al., 2024) built upon Florence VLM (Xiao et al., 2024). For RoboTwin, we adopt two VA models: DP, DP3 (Ze et al., 2024b), and VLA model RDT (Liu et al., 2024a).
MDT (Reuss al., 2024). Florence-based Flow-based MDT,
Training and Testing Details. Since GPC is training-free, we directly use pre-trained policies trained based on their original settings (more details are in App. I). Each setting evaluated over 200 rollouts (100 for RoboTwin), and report the average success rate (SR). For composition, we employ our GCP and search over weighting coefficients from 0.0 1.0 steps of 0.1.
Optimized weight searching (Optional). Although GPC in principle allows arbitrary convex weights, our framework naturally suggests that the policy with the stronger score should receive a larger weight. This intuition is empirically validated by our findings in Sec. 6.3. Therefore, in prac- tical use, once the relative strengths of the base policies are known, one can directly bias the stronger policy have weight > ~0.5, instead of exhaustively searching the entire interval 10.1. 0.9]. This simple heuristic both respects the underlying score-composition principle and significantly reduces the searching time.
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Table Experiment results of our method under different composition configurations. These
results highlight GPC's versatility and the importance of weight tuning across policies.
Weight Scheduling GPC
Divg
put
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Empty Cup Place
0.42
0.62
0.70
0.86
0.84
0.84
0.76
0.68
0.61
+24%
Both Puliciess Perform Well
Dual Bottles Pick (Hard)
0.49
0.64
0.69
0.71
0.56
0.61
0.65
0.63
0.56
0.58
+7%
Shoe Place
0.37
0.36
0.47
0.52
0.56
0.59
0.60
0.59
0.59
0.53
0.41
+23%
Both Policies
Dual Shoes
0.08
0.14
Perform Bud
Pick Apple Messy
0.05
0.26
0.25
0.13
0.08
0.08
0.06
0.08
+0%
Policy > Policy B
Dual Bottles Pick (Eaes)
0.77
0.36
0.52
0.64
0.70
0.75
0.82
0.81
0.80
0.85
0.80
+8%
Follry e Policy
Block Hamuner Bear
0.00
0.76
0.61
0.3
0.18
0.15
0.12
0.07
0.00
0.00
0.00
+0%
v:
set (l.1.... (.3)
weight Diee walk corresponding to pouse cstimation
30, CDr + o0g 4or,. When ang equals to 0.0 and L.O, GPC degenerates into pipps and Dr respectively.
RoboTwin
Robomimic Can
DPpd
DP
0y-05 5
Florence Flow
w, 93.3333
DP
50-0.00
58-0
DP pu
My
My 0.
GPC
5Ph0.44
5Re0.71
$6:0086
(a) Sample Distibution under Different Modality
(b) Sample Distribution under Different Models
Figure 4: Visual analysis of GPC under different compositions. GPC gen- eralizes (a) modalities and (b) architectures, with appropriate weighting yielding accurate distributions with better SR than individual policies.
Figure 5: Sample distribu- tion through execution time. GPC yiclds more coherent distributions than basclines.
6.2 MAIN RESULTS: GPC ACROSS ARCHITECTURES
MODALITIES
Simulation Results. Our results demonstrate that GPC is broadly applicable across both diffusion- and flow-based policies, and works under a range of general settings: (i) Same input modality, different architectures. GPC successfully composes policies trained the same modality but with different network architectures. For instance, in Tab. 1, combining two VA policies (DP+MP) yields noticeable average improvement of +2.22% VLA model (Florence-D+DPP achieves a larger increase of +5.51%. (fi) Different modalities, similar architectures. GPC also supports the integration of heterogeneous modalities. In Tab. combining RGB-based and point cloud-basee based DPs (DP img DDP improves the average SR from 0.46/0.66 65 to 0.70 (+5%), confirming that convex score composition can exploit complementary information even within the same sensory domain. (iii) Different modalities, different architectures. GPC enables flexible integration across modalities and architectures. For example, combining VLA model with VA policy (RDT+DPpaa) pea) produces consistent improvements, raising the average SR to +7% compared to DP ped. and surprisingly. +32% compared to RDT itself.
the base policies, while combining VA and
Real-world Results. In real-world evaluations (in Tab. 5), GPC shows consistently stronger perfor- mance than single-policy baselines. For instance, in the Clean Table task it achieves 14/20 successes, surpassing base policies. Similarly, delivered gains in Place Bottles (13/20 7/20 and 1 11/20).
Overall, to answer question one, across diverse tasks and benchmarks, GPC consistently improves performance, with an average increase of up +7.55% on Robomimic & PushT, +7% on RoboTwin, and +1 +10% in real-world tasks. These results validate that convex score composition provides a robust and general principle for composing policies, regardless of model type input modality.
6.3 INFLUENCE OF WEIGHT CONFIGURATIONS ON GPC PERFORMANCE
To analyze the second question, we evaluate GPC performance across multiple tasks under different weight configurations in Tab. 3. Several findings summarized:
Q Finding 1:
When both policies have moderate accuracy (e.g., >30%), GPC often achieves higher accuracy under appropriate weight configurations compared to hase policies. For in-
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Table 4: Results GPC with superposition, highlighting performance increase by strong compositional operators.
Table 5: Real-world experiment results, demonstrating the effectivenesss of GPC.
Robomimic
PushT PushT
Methed
Place Berfies
Clea Talle
Punch Hales
Method
Can
Lift
Square
Average
18:30
220
Base Policies
GPC (ours)
13/20
7/20
14:1
9/00
Diflusion Policy (DP)
34.50
98.50
2,00
21.75
Mamba Policy (MP)
5.00
98.50
3.00
12.06
29.64
Florence Policy-D
61.50
97.00
46.50
40.00
61,25
Composed Policies via Logical AND Composiioon
GPC
DP-MP
84.00
99.50
48.00)
28.
64.92
+35.73%
Florence- Horence-Polie--DDe Policy-DDDI
90.50
90.00
36.31
20 +17.95%
Florence- Kouence-Policy-DAr Policy-DMMP
83.00
100,00
90.00
37.38
77.60
+16.35%
5
Composed Policies via Logicu! OR Composition
DP-MP
82,50
99,50
44.00
29.13
63.78
+24.89%
Florence Po
83.50
100.00
89.00
37.87
77.59
+16.34%
Horence-Poliicy-n
86.50
100.00
86.50
38.44
77.86 -6.66
Figure 6: Real-world setup and results.
Table 6: Comparison of training/finetuning time vs.
Table 7: Per-action-chunk inference la- tency in RoboMimic. The overhead of GPC is modest and purely computa- tional.
GPC weight search. Teval = NNollout X poer For
RoboMimic, TRoboMimic x 200 5s 0.27 hr. For real-
eval world, Titeal x 20 * 30s = 0.17 hr.
Methoul
Setting
Time cost
Method
Time per chunk (8)
Training from surntch
IM+ demos. GPUs 100 demos, GPU
14d (OpenVLA 7B), S0U (RDT IB) 5h (DP 200M+) 28th IKDT 18)
Finecuning
DP Florence-Poliey GPC (DP + FP-D)
0.09
GPC (full search)
9 weights (w 0.1:3.9)
Teaa (- 2,Shrs)
0.06
GPC (optimized)
weights (Mllawe (.9
42 (> Ihr)
0.13
stance, in the Empty Cup Place task, Dring and DPped achieve 0.42 and 0.62, respectively, while
GPC peaks at 0.86 (+24%) with w1=0.4, surpassing both unimodal DPs. This improvement re- flects the composition of diffusion scores capturing a more generalized distribution that reduces the reliance on specific conditions, consistent with the theoretical advantages of compositional models.
9. Finding 2:
When one policy has significantly lower accuracy, GPC struggles to surpass the highest accuracy of the better-performing base policies. For example, in the Pick Apple Messy task, Dppe achieves 0.26 and DP img achieves only 0.05. GPC peaks at 0.25, falling short of DP pea. This suggests that low-accuracy scores from weaker modalities can significantly impact the joint distribution, diminishing the overall performance of the composed policy.
Q Finding 3: The improvement of GPC is always maximized when the better-performinn base policy holds larger weight in GPC. For instance, in Dual Bottles Pick (Easy), where Dming achieves 0.77, GPC reaches 0.85 with Wi= =0.8, leveraging the stronger DP effectively. This high- lights the necessity of assigning higher weights to the better-performing distribution maximize the effectiveness of GPC, leading the composed policy toward consensus.
These findings highlight GPC's versatility in leveraging the strengths of different conditions and the importance of appropriately tuming weights to each policy's 's performance.
6.4
TIME AND COMPUTATIONAL EFFICIENCY OF GPC
GPC introduces two main sources of extra cost compared using a single base policy: (i) additional weight search evaluations (Snell et al., 2024), and (ii) increased inference cost per action chunk.
Weight search as repeated evaluations. During weight search, we fix candidate weight configu- ration, run N rollouts to estimate the SR, and then move to the next configuration. Thus, the total search cost T search NNsarrhh Tevals Teval = NNvoloour Terr rollout- As shown in Tab. 6, sweeping w from 0.1 to 0.9 leads to Nsearch = 9 and about 2.5 hours. With our optimized searching method, we can restrict the search to Wstrong [0.6, 0.9], reducing to Nety = 4 (~ 1 hour). Compared to days of training from scratch hours of finetuning, this makes GPC a highly efficient alternative.
Inference-time time overhead. During rollout, GPC incurs extra compute from querying multiple base policies per action chunk. Tab. 7 reports the measured inference latency in RoboMimic: the GPC composition increases latency from 0.09 s to 0.13 s per chunk, which is modest in practice. This overhead is purely computational and can be further reduced with stronger hardware, optimized in- ference runtimes, or future engineering improvements (e.g., model compression (Høeg et al., 2024) or distillation (Liu et al., 2026)).

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Published as a conference paper at ICLR 2026
Table 8: GPC can be applied with different action- chunk lengths and infer time steps. Results are in Robomimic.
Table 9: GPC with three base policies on RoboMimic.
Method
Can
Lift
Square
Method
Setting
Success Rate
Flaw Policy
0.13
0.77
DP
DDPM, chunk 8, 5 steps
0.50
Plorene--Poliey-t
0.89
0.98
0.88
Hlorence- Horence-PPlicy-D Policy-D
DDIM, chunk 16, 10 steps
0.53
0.51
0,96
0.92
GPC (hest 2-palicy)
1.00
0.94
GPC (DP-FP-D) DDIM, chunk 16, 10 steps
0.66
GPC (FP-FP-P+-)))
1.00
1.00
0.94
6.5
COMPREHENSIVE ANALYSIS OF GPC EFFECTIVENESS
Analysis on GPC's Superiority via Visualization. For the third question, Fig. illustrates how GPC improves sample distributions under different settings: (i) GPC under different modalities. In Fig. 4(a), Dmgng and DPpea learn distinct distributions. By adjusting the convex weights, GPC adapts smoothly between them. This demonstrates how GPC leverages knowledge from different modali- ties to form a more complete distribution. (ii) GPC under different architectures. In Fig. 4(b), both Florence and FlowP learn broadly similar distributions, yet each exhibits localized biases. Through convex composition, GPC expands coverage and enhances precision. This shows that even when base models learn similar representations, GPC refines their alignment and achieves stronger results. Overall, these visualizations confirm that GPC generalizes across modalities and architectures, with appropriate weighting yielding broader and more accurate distributions than individual policies.
Analysis on Execution-Time Time Sample Distributions. Fig. 5 shows the evolution of execution-time sample distributions. Baselines iig and DP produce scattered or noisy patterns, particularly in later stages, indicating instability and higher variance. In contrast, GPC yields coherent and concen- trated distributions, ensuring greater stability and mitigating error accumulation during execution.
Experiment Results on GPC with Superposition. We further evaluate GPC under superposition settings. As shown in Tab. 4, composing DP and MP with logical AND boosts the SR to 64.92 (+25.73%), while Florence-D D DP under logical OR reaches 77.59 (+16.34%). These results high- light the potential of superposition to amplify policy performance through stronger composition op- erators. However, superposition also has clear limitations. It is not directly applicable flow-based models, and the requirement to recompute weights at every step increases inference cost.
GPC with heterogeneous inference steps and chunk sizes. GPC is also flexible with different inference steps and chunk sizes. For diffusion steps, we simply pick a unified sampler and number of inference steps at test time and run all policies under this common configuration, e.g., the results in Robo'Twin with DP+RDT. For cettion-chunk. mismatch (assume HA 2 HB), we sample shared noise trajectory of length ,. apply policy B only on the first HB steps, and take a convex combi- nation of scores on the overlap while keeping the tail from policy A. Results in Tab. 8 confirm that this heterogeneous-chee chunk composition also yields clear gains.
GPC with multiple base policies. The score-composition rule of GPC directly extends to three or more base policies via a convex combination their scores. Tab. reports results with three policies on RoboMimic. Three-policy GPC either matches improves upon the best two-policy configura- tion, and consistently outperforms the individual base policies. This shows that GPC scales beyond pairwise composition and can effectively leverage diversity across multiple pretrained policies.
7 DISCUSSION
Limitations. Our GPC demonstrates clear effectiveness across wide range of experiments. De- spite this strength, certain limitations remain. First, test-time weight search is restricted by fixed discretization, which may overlook optimal values; future work could explore adaptive or automatic search strategies. Second, we mainly study dual/triple-policy composition, while scaling to more policies increases computation. Addressing this may require feature sharing or compact representa- tions to enable efficient multi-policy integration.
Conclusion. We introduced General Policy Composition, a training-free framework that improves robotic control by combining the distributional scores of pre-trained policies. Our theoretical analy- sis establishes that convex score composition leads to step-wise and trajectory-Ieve improvements, while experiments on diverse benchmarks and real-world setups confirm consistent performance gains. GPC is simple, versatile, and widely applicable, providing a foundation for future research in policy composition means to enhance performance without additional training resources.
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Minjie Zhu, Yichen Zhu, Jinming Li, Junjie Wen, Zhiyuan Xu, Ning Liu, Ran Cheng, Chaomin Shen, Yaxin Peng, Feifei Feng, et al. Scaling diffusion policy in transformer to 1 billion parame- ters for robotic manipulation. arXiv preprint arXiv:2409. 144 411, 2024.
Brianna Zitkovich, Tianhe Yu, Sichun Xu, Peng Xu, Ted Xiao, Fei Xia, Jialin Wu, Paul Wohlhart, Stefan Welker, Ayzaan Wahid, el. Rt-2: Vision-language-action models transfer web knowledge to robotic control. In Conference on Robot Learning (CoRL), pp. 2165-2183, PMLR, 2023.
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APPENDIX
1. Assumptions, Notation, and Preliminary Facts Basic assumptions, notation, and prelimi- naries.
2. Proof of Proposition 4.1 (Single-step Convex Improvement) Formal proof of the single- step convex improvement result.
3. Proof of Proposition 4.2 (Score-to-Sample Stability) Detailed stability analysis of score- to-sample mapping.
4. Proof of Corollary 4.1 (GPC Tightens the Terminal Bound) Proof that GPC improves the overall error bound.
5. Detailed Tools: Norm Derivative, Integrating Factor, and Inequalities Mathematical tools used in the proofs.
6. How Propositions and Corollary Fit Together Logical connections between the main sults.
7. The Flexibility of GPC with Any Prediction Types Extensions of GPC to different pre- diction types.
8. In-Depth Analysis on What Leads to the Success of GPC - Analysis GPC's success,
9. Experiment Details Experimental setup, architectures, and hyperparameters.
10. Additional Experimental Results Extended quantitative comparisons.
11. Visualization on Robot Tasks Visualizations of robot task rollouts.
12. Detailed Literature Review Extended survey of related work.
13. Future Work Open challenges and future research directions.
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A ASSUMPTIONS, NOTATION, AND PRELIMINARY FACTS
Dynamics. Sampling is modeled as an ODE/SDE:
#(1) Fl,, zf1), +(1,z(()))
[0, T], x(0) 14o,
(8)
where x(t) R, the score : [0, 7| x R - R and F: : [0. T| x I2 x R Rd represents the transformed score due to noise schedule, parameterization, or solver.
Oracle realized flow. We compare the oracle trajectory x (t) solving equation 8 with s*, and the realized trajectory (t) solving equation 8 with 8; both share the same initial conditions.
Score error.
(t := 8(t,z) - (t,
Score error bound assumption. assume:
There exists nonnegative function si() such that for all
[t, & x(t).
Regularity assumptions. We assume:
(AI) Lipsehitz of F. (Sohrab, 2003; Thomson et al., 2008) For a.c. t [0, TJ. there exist inte- grable Ly, Lg 2 0 such that, for all 2; s,
[F(t,z, Ft,, < (x(t)] - vl + L.(t) s-rl
(A2) Score regularity. (t,-) and -t..-) are locally Lipschitz on the tube visited by the flows, with (tmm-deppnndent moduli (t), A(t) E L ([o, and at most lincar growth.
Absolute continuity and norm derivative. If [o, 7 Rd is absolutely continuous, then e'(t) exists a.e. e(t) c(O) Sy ('()) dr, and si() [|e(t)] is absolutely continuous with
o'(t) < [|e((t) for a.e. t.
(9)
We give a complete proof $E.
Why Lipschitz is reasonable. For prohability-flow ODEs of score-hased models, F is affine in s (e.g., reverse ODE (Song et al., 2020b): == f(t, - sst x)) so Lt(t) = g()² (known, bounded on finite T"). The dependence x comes via f(t, 2) (often smooth) and through with networks on compact tubes, local Lipschitz holds and yields finite Lipschitz moduli A A*)1, A()) These are standard in stability analyses of neural ODEs and probability-flow ODEs.
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B PROOF OF PROPOSITION 4.1 (SINGLE-STED CONVEX IMPROVEMENT)
Statement restated. Conditioning on (f, ft), suppose we have two estimators
E = s (t, + bl(1, r/as {1, 2],
where s"(t, zz) is the true score, by are deterministic biases, and πл are zero-mean random noises. For w [0, 1]. define the convex combination
E( (ww)= we + (1 E2
(ww) E,]le(w) s* 2t)
(10)
Notation.
This abstraction (equation 10) unifies different modeling paradigms:
When noise is present, the estimator can be viewed as the output a diffusion model, and the residual term 7 plays the role of the diffusion component in the time-reversed stochastic dynamics (e-g., a reverse-time ODE).
When the noise term vanishes (i.e., 7 0), the formulation reduces deterministic transport setting, which is the flow matching case.
The role of π) is analogous to the stochastic noise introduced in the diffusion forward process (e.g., Gaussian perturbations of the clean sample), ensuring that each estimator E; remains random even when (f, xy) is fixed. All expectations in Proposition 4. are therefore taken with respect to the joint distribution of (7/ 12). and the randomness is solely due 12). We write expectations
E. Bm x2, f].
Goal. Show that Q(w) convex quadratic, derive its coefficients, the minimizer w", the mini- mum value, and conditions for improvement over the endpoints w 0, 1.
Decomposition.
Subtracting 5* st, zt), we write
E(w) 5 = u(w) + v(w),
where
uww) wd1 (1 w)b2. v(w) wi + -w)
Hence
Q(w) = Bllu(w) + r(w)12
= |lu(w)]| + 2 B(((()), + B| Blow))
(II)
Since B[n]] 0, the cross term vanishes, leaving
Q(w)= ||u(w)] +
Bias contribution. Expanding [u(w)] gives
[u[ww]] = ||62 + w(b; - b2)l = |62 + 2w<b2, b1 b2) + w216 62ll?
Noise contribution. Expanding E||b(( [)] gives
[ wT) + 2)12l1 2 E
m 2 + (1 w) 12 2wx(1 w) B(1,, m2)-
Quadratic form. Combining the two contributions, ((w) is quadratic function
Q(w) = Awz + Bw + C,
where
A ||1 bell + El|n1l + El 21E (1E m2),
B 2(b bj - b2) 2E m2 2 2 2E 1/, 12)
C |lbz|| 2 3
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Convexity. By Cauchy- Schwwar
72), &
E m 2 1/2 12
so
A E (
-
1bb
Thus Q(w) is convex, and strictly convex unless both biases and noises coincide. Minimizer.
If A 0, the unique minimizer is
B
E 17 1 E( 72)
(b2. b1
- b2)
w" = 2A
161 62/12 BBmlll 112 + E 1//r2 21 111 21 712
The minimum value is
Q(w)) C- B²
4A
Endpoint comparison.
At w = 0, we have
Q(0) C,
Q(1) A+ A+
The gaps are
Q(0) Q(=))((@))))))))))())))))) 8² 0,
Q(1) - Q(w0)(())))))))) = (2A+B)²
3 0,
1A
with strict inequality unless B 2A B 0.
Special Case I: Unbiased case. If b = b2 = 0, then
A = E ml 2 + EE m2ll - 2 72), B - 2F 12 + 2B, 92),
C E n2
with A > 0 and A 0 unless 7/, 1/2 are perfectly correlated with identical second moments. For A > 0, the unique minimizer is
Elln22 2 E(T1 m72
E
+ E 72 21E( 172)
and the endpoint gaps are
B²
(Ellma 1 E( )72)
Q(0) - Q(w")
0
4A
Elmm + B|| 2 -215(11 n1 712
whenever E(m, 72) * EE 1/212 and
Q(1) - (ww")@ww)))))))))))()) (2A + B)²
(1Ell77 11 1E< 122
4A = Elim 121112|12 2F
m 72)
> 0
whenever * El|m 12. Thus Q(w") min(Q(0). Q(1) whenever m) 1/2 are not perfectly correlated.
Special Case I:: No-noise (deterministic) case with bias estimators with bias). Then
Assume 1/1 1/2 (deterministic
(w) |[b + (1 ww)b2? 2 llb w(b; b2)11;
[0. 1].
Write Q(w) = 2 + 2,3 + 7 with
a ||b] b2l?
B (b2, b b2); 7 = 16211
If b1 # by then and the unconstrained minimizer is wp = - B/aa, giving
g2
minweR Q(wc) 7 a
Hence the endpoint gaps are
8² Therefore, if 3 E (0, 1) (so the constrained minimizer over [0, 1] equals the unconstrained one), we have
gg2 (b2 bj b2) 2
(a B)2
Q(0)-min Q = a 1b b
Q(1) a
3 0.
a
Q(w") min Q Qin))()).(()).
8 (for Q(1)). If w & (0, 1), the constrained minimizer lies at an endpoint and no strict improvement over both endpoints is possible. If by by, then and (ww) ||b 2 for all w.
with strict inequalities unless 3 = 0 (for ((0)
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Remark strict improvement. Strict improvement requires the unconstrained optimum to lie within (0, 1). If one estimator significantly outperforms the other, the optimal weight lies on the boundary, recovering the best single-estimator performance.
C PROOF OF PROPOSITION 4.2 (SCORE-TO-SAMPLE STABILITY)
Overview before proof. The goal of the score-to-sample stability result is to show how errors in the score estimation translates into deviations of the generated trajectory. Formally, view sam- pling as an ODE of the form i(t) = Fit, <t), s(t, x(t))), where the score s directly drives the dynamics, and F represents the transformed output after scheduler, parameterization, solver. Re- placing the oracle score s* with an estimator perturbs this vector field, and the resulting trajectory deviation be quantified.
The proof proceeds by analyzing the trajectory difference e(I) xz(()) - x² x*()). Its derivative naturally splits into two terms: a Lipschitz growth component proportional ||e(t]].. and forcing component proportional to the score error || - s This reduces the problem to a standard stability inequality for ODEs. Applying Grönwall's ' inequality (Gronwall, 1919; Bellman, 1943) then yields a trajectory-level bound expressed in terms of the integrated score error.
Finally, this stability guarantee connects back Proposition 4.1: since convex composition strictly improves score estimation at the single-step level, the bound implies that the composed policy in- herits a strictly tighter trajectory deviation bound. This prepares the ground for Corollary 4.1. which consolidates the results into trajectory-level performance guarantee for GPC.
Statement restated. Let =x)))((( (4) and xa(() solve
x+(t) (t) Ftt, x (t), s* (t, (gxx(())),,
Ez(t) = F(t..s(t)..(tt.::()))
with the same æe (0). Under (A1)-(A2) with
i(1) Lo(1) L.00)
we have for all e [0;
<ca (T) x (T) & (O)))))))) (0)I dt.
(12)
Taking expectation, applying Schwarz. and Jensen and using the assumption of score error bound, we obtain
([e
T c2S L(r) L,(t)² dt )t)
1/2 (T
1/2
Ira (T) - x (T)
k(0))2 dt
(13)
where x(() nonnegative function <(() such that for all x.
(t, < x(t).
(i.e., Score error bound assumption). Please see the detailed proof follows.
A. ABSOLUTE CONTINUITY AND THE ERROR DIFFERENTIAL INEQUALITY
Let e(t) := (t) - x (t). we have
e'(t) F(t, ((t, F(t, x xt), (t,(t*tt (t, (t))*(t)) for t.
(14)
Insert and subtract two intermediate terms to separate æ and s contributions:
[t)((t)] x Ftt, 8(t, F xs. 8s, s(t,
(15)
+ F (t, 8(1, - F1, 5(,,,,,
(16)
+ Ft, s" (t, F(,, ft, (t,
(17)
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By (AI), the first (15) and second (16) equations are bounded by (ttt) - s(t, x>)] and L.(t)]l((t, s* (t, respectively: the third equation 17 is bounded by Ln(() x=1 (t) Using the z-Lipschitzness of from (A2).
|| ms) s(t, x & A(t) (e(()))-
Therefore,
[t)( < (t)(t) + (t)A((t)) [e(t)] (a(t)
(18)
E(1)
B. FROM [|c((t) TO (t) Let 6(1) = |e(()] By equation absolutely continuous and t'(t) < le((t)l for a.e.
Combining with equation 18 gives the scalar differential inequality o'(t) L(t) o(t) L.(t) (t, x (t)) for a.c.
<(0) 0.
(19)
C. GRÖNWALL (INTEGRATING FACTOR) AND THE PATHWISE BOUND
Define A(t) :- S0 i(T) dr and g(t) = AA1) Then a.e.
g'(1) = A(9) (1) ((()(()) & e (L,
Integrate from to T; since (00) = 0 (same initial conditions) we have g = 0:
{" A(t) Lt(() |1,11, (1)) dt.
T()) & jo
Multiply by eAT))
((T) g(T))(TT ('
di.
Since A(T) A(I) S/. i(7) dr, the bound
((T) |ee()) S"" exp (esp(S. ((r)dr)
(1,(, (1) di
(20)
follows, which is exactly equation 12.
D. EXPECTATION AND READABLE UPPER BOUND
We first take expectations of the pathwise bound equation 20:
B e(())
E
St dr di L,(t) (s(t, dt
Notation.
The expectation E|. 1 taken over the randomness of the initial conditions. This already provides a valid (and tight) expected bound. In the following we present slightly looser but cleaner form by applying classical inequalities, which easier to read and to apply in practice.
By Tonelli's ' theorem (non-negative integrand) (Fubini, 1907; Tonelli, 1909):
(T i(r) dr (t) EJA, (t, (t))] dt.
e
Apply Cauchy-Schwarz (Cauchy, 1821) in T]]
T W(I) EI, (t)) ( T
W(t) at) (2r)))(2 ( (R))A,(t, at) 1/2
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where
W(t) = elt d(r) Lg(t).
Use Jensen (Jensen, 1906) (E8 (1) E|J,,|
? to obtain
[ A (t, (t))))
E A. x (t))1²
Readable expected bound.
Combining the above yields
(
1/2
"[" [IAA,(, dt
1/2
(T)e(T)) &
e 25 L(r) L,(t) dt
(21)
Assumption on score error. Using the Assumption of score error bound, which guarantees [A,(4 & x(t) for all x, then
dr L.(t)2dl d (S. k(()?
1/2
1/2
(Te(T)I &
This is exactly the equation 13 and the result of Proposition 4.2.
D PROOF OF COROLLARY 4.1 (GPC TIGHTENS THE TERMINAL BOUND)
Statement restated. Let B()) denote the upper bound on expected sampling error derived in Proposition 4.2. If convex combination Scomp WS1 + (1 w)82 satisfies
S
E| Scomp
s*1]
min
E st
s* 112
then the corresponding theoretical error bound is strictly reduced:
B ((soop))
min B(s:).
Proof.
From Proposition 4.2, the expected trajectory error for any estimator å is bounded by:
1/2
(J" Blls - 8* 2t
1/2
- xx = & B(3) =
25 dr Lo(1)) dt
1/2
where (o dr 2t dt
0 a system-dependent constant independent of the score
estimator. The bound function B(.) is strictly increasing with respect to the integrated mean-squared score error (MSE). Since the premise states that the integrated MSE the composite score Scomp is strictly smaller than that of the individual estimators 8;, it follows immediately that:
B Scomp) min B( (8))).
Thus, convex score composition strictly tightens the theoretical guarantee on the trajectory simula- tion error.
E DETAILED TOOLS: NORM DERIVATIVE, INTEGRATING FACTOR, AND INEQUALITIES
E. NORM DERIVATIVE INEQUALITY
Let e [0.T] Rd be absolutely continuous. Define @(t) = ||e(t)]]. We show & is absolutely continuous and d'()) [1)] for a.e. t.
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Absolute continuity. Since e(t) e(0) + So c((r) dr with el L', and the norm is I-Lipschitz, Φ is absolutely continuous.
Difference--uotieet proof. Fix point where e' exists. Then
(L h) o()) ||e[+ h)l - [e(()]
|e(l + h) e(O)
h
h
h
Taking h gives (t) [e'(t)). This holds for a.c.
Chain-rule proof (when e(() * 0). For s(x) |-||| Vg(x) = x/||0]| when x. t6 O. Then
e(t) Te(t) (T()) d())
/ (1) = (Vgle(0)),
||'((1))
At points with e(t) = 0, use the differenccequotient argument above.
E.2 INTEGRATING FACTOR
Starting from (t) & a(t))(t) + b(t) with x(0) = 0 and a, b E L', define A(t) So a(r) dr and
s()) (())(()) Then
a(t)((t) g((t) e- ((0( -d(t)))))((()) E ((aa(((t).
Integrate:
T g(T) < b(t dt Φ(T) ((0 dt.
Since A(T) A(t) & Sg a, looser bound is (TT) ele Sh b(1)dt. dt.
E.3 TONELLI, CAUCHY-SCHIWARR, AND JENSEN
Given nonnegative integrand H (w,, t) on Ω x [o, 77, Tonelli implies
H(w, () di S"
T
E
B[H ()) dl.
For functions f.g e (3(, TT), 50 fg < llfflz løllz. For random variable Z, Jensen yields ( & Z ?
F HOw PROPOSITIONS AND COROLLARY FIT TOGETHER
Prop. 4.1 guarantees the existence of a convex weight (often interior) that lowers the score MSE under mild, testable conditions (heterogeneous models reduce cross-correlation and diversify bi- ases). Prop. 4.2 translates any reduction in (time-intgrrated) score MSE into reduction of non- asymptotic terminal error bound. Cor. 4.1 merely combines the two: once the functional-level inequality is strict, the certified sampling bound tightens accordingly.
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G THE FLEXIBILITY OF GPC WITH ANY PREDICTION TYPES
A key strength of General Policy Composition (GPC) is its flexibility and independence from the specific parameterization used train the underlying diffusion flow-matching policies. The fun- damental principle GPC is the composition of the underlying score functions the data dis- tributions, sG(T,, t) V,, log (Tt).. Common parameterizations, such noise prediction, data prediction, and v-prediction, are all mathematically inter-convertible and represent this same under- lying score function. This ensures that GPC can seamlessly compose policies trained with different prediction objectives without requiring extra training.
Let's formalize the relationship between these parameterizations. The diffusion forward process defines noisy trajectory at time & from an initial trajectory To and Gaussian noise sample (O, [) as:
ToTo + dcC,
(22)
where O₁ and ag schedule-dependenn coefficients.
Score Prediction (s-prediction). This parameterization directly models the score function. The score is related to the noise by the following identity (Song al., 2020b):
s(T,, t) 7, log (Te)
(23)
oi
Composing scores is the core of GPC. Any other parameterization can be converted to a score before composition.
Noise Prediction (e-prediction). This is the most common parameterization, used in the original DDPM (Ho et al., 2020). The model c is trained to predict the noise A model trained on noise prediction can be converted to score prediction model:
so so t) c
(24)
Since the relationship is linear, composing predicted noises with weights w, is equivalent com- posing the scores with the same weights.
Data Prediction (ropprediction) This parameterization trains the model (ro) to predict the original clean data from the noisy input 7.. The predicted noise can be recovered from the predicted data using the forward process definition:
To ar((T))(T(.1)
c0 Te, 1)
(25)
dz
This allows data- cata-prediction policy to be converted to the score noise representation for compo- sition.
Velocity Prediction (v-prediction). Introduced by (Salimans & Ho, 2022), v-prediction offers improved numerical stability. The target, v, is defined as v = aşé - deTu- A model vo(T,, t) is trained to predict this target. We can recover the noise from v-prediction model's output using:
c0(T,,t) t) (T,) t) oeT.
(26)
From there, the equivalent score can be calculated.
Implications for GPC. The interchangeability of these parameterizations is what makes GPC "solver-agnostic." Suppose want to compose two policies, कi and π2. If m was trained us- ing noise prediction (outputting <)) and T2 was trained using v-prediction (outputting vă), we can perform composition by first converting their outputs to common representation.
For example, we can convert both to the score representation:
(T,, 1) = <),T)) t)
(27)
(T,, = avvi TT. t) TeTe
(28)
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Then, perform the convex composition in the space:
Scomp
w1sg s + wysă.
(29)
This composed score Scomp can then be used in any standard ODE/SDE solver step to generate the next state T
Alternatively, and often more direct in practice, one can convert all outputs to the noise (6) represen- tation before composition, which yields equivalent result due to the linear relationship between score and noise. This flexibility allows GPC to serve as universal, plug-and-play module for combining a wide variety of pre-trained diffusion-based flow-based policies, regardless of their specific training objective or parameterization.
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H IN-DEPTH ANALYSIS ON WHAT LEADS TO THE SUCCESS OF GPC
Intuitively, GPC can be viewed as forming a product-of-experts distribution: the composed score is convex combination of individual scores, corresponding (re-weighted) product of their proba- bility densities. A higher weight on one policy simply means its density contributes more strongly to the final target distribution, concentrating probability mass on trajectories that both experts consider likely.
H.1 THEORETICAL PERSPECTIVE: WIYY CONVEX SCORE COMPOSITION CAN BE BETTER THAN INDIVIDUAL POLICIES
Based on Prop. 4.1, we show that each diffusion timestep there exists convex weight w such that the composed score has a smaller error with respect to the ideal score s" than any individual policy. Prop. 4.2 extends this from single step to the entire denoising trajectory: if at each step the composed score is closer to s*, then the error along the whole trajectory accumulates more favorably, leading a trajectory distribution closer the ideal one. In other words, once per- step improvement in score quality is established, the stability of the generative process allows this advantage to propagate along the full trajectory, making convex score composition provably superior to relying on single policy.
H.2 EMPIRICAL PERSPECTIVE: WHAT DRIVES LARGER GAINS FOR SOME COMBINATIONS
At a high level, we view GPC as a way to aggregate the "good knowledge" learned by different base policies into single, higher-likelihood target distribution, that sampling from the composed score produces higher-quality trajectories than sampling from any individual policy alone. In practice, what counts as "good knowledge" is shaped by several factors:
Complementary modalities provide richer information. When GPC combines policies trained on different modalities (e.g., RGB point cloud), the composed score effectively leverages comple- mentary views of the scene: RGB captures appearance, texture, and color cues, while point clouds provide precise 3D geometry and depth structure. This multimodal fusion reduces perceptual ambi- guity compared to using either modality alone, and can be viewed as increasing the "informational good example of this,
richness" available to the composed policy. The DP+DP3 combination and the visualizations of their sample distributions in Fig. 5(a) support this interpretation.
Diverse architectures capture different inductive biases. Even when policies share the same in- put modality, different architectures can encode different inductive biases and error patterns. For instance, # is DiT-based, whereas Flow Policy uses a U-Net-style backbone. They may model sim- ilar underlying action distributions but emphasize different structures in the data. GPC can exploit this diversity by aggregating their strengths while averaging out idiosyncratic weaknesses, which we reflected in improved performance and the qualitative analysis in Fig. 5(b).
Task-specific strengths shape composition benefits. Task choice also matters: in some tasks, one base policy may be significantly weaker. In such cases, naive averaging (or unbalanced weight) can let the weaker policy drag down the overall performance. Our analysis in Sec. 6.3 (Finding 3) shows that GPC performs best when the #better-performing base policy receives larger weight*, which is especially important when task difficulty or mismatch affects one policy more than the other. Thus, task-specific policy strengths and the ability adjust weights are key factors behind the observed gains.
Weight selection matters in the composed distribution. Our theory guarantees the existence of an optimal weight w*, but in practice GPC still requires choosing concrete weights. These weights control how much each base distribution contributes to the final composed distribution and therefore directly influence how much probability mass is placed on high-quality trajectories. This is why we performed extensive weight-sweep studies: to show how different weights affect performance, and to provide empirical guidance weight selection for real deployments. We view designing better, possibly adaptive, strategies to approximate * as an important direction for future work.
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The Robomimic benchmark (Mandlekar et al., 2022) includes three manipulation tasks: Can, Lift, and Square. We train all baselines with batch size 1024 for 1000 epochs. Training uses DDIM sampling with the scaled linear beta scheduler and prediction with epsilon. Diffusion steps are set 100 during training and 10 inference. Each model is trained with observation horizon = 2 and chunk size = 16. Evaluation is performed across 20 parallel environments, each running 10 episodes, giving total of 200 rollouts. The original code of Robomimic is from https: We reproduce the basclines based on Published as a conference paper at ICLR 2026
1 EXPERIMENT DETAILS
1.1 ROBOMIMIC
//github. com Btl./RISEE--T wtt.-nnntttttteeooiiiiiiiio...i. the codes from https: /ttpttgttthhttt
1.2 PUSHT
The PushT benchmark (Florence et al., 2021) involves planar pushing in a 2D workspace. Here, training uses batch size 256 and runs for 500 epochs, with all other parameters kept identical to Robomimic, Evaluation follows the same protocol of 200 rollouts. The original code of Robomimic is from https://gitthht com/real-staaford /di wwwffffusooooooooooooooooooo licy and https:// github. gittabb..ccm/ggoogeeereeeeecc/ /ib.. We reproduce the baselines based on the codes from http://oooboiiieemmmnneeeestttt.
1.3 ROBOTWIN
RoboTwin (Mu et al., 2025) is dual-arm manipulation benchmark that combines real-world teleoperated demonstrations with high-fidelity synthetic data, offering a standardized platform for studying large-scale manipulation learning. The extended RoboTwin 2.0 (Chen al., 2025) release covers more than 50 tasks, supporting diverse and complex scenarios. Baselines reproduced based on the codes from https: //github com/ honm/Robowwinn-ie fortffomm RcboTwin/tzee
1.0 0 and https: : //tpttutbb.////////// com/ wtt.ccoo/////eeeeceo Rwwoowwn Paltnn-olooommm RoboTwin/tree/mne mmain. The success rate of each task is determined with 100 rollouts.
For our experiments, we evaluate curated subset of tasks:
Empty Cup Place, Dual Bottles Pick (Hard), Dual Bottles Pick (Easy), Shoe Place, Dual Shoes Place, Pick Apple Messy, Block Hammer Beat.
RoboTwin 1.0:
RoboTwin 2.0: Hanging Mug, Open Laptop, Place Burger Fries, Put Object Cabinet, Stack Bowls, Three Turn Switch.
The DPing and DP ped correspond to the diffusion policy based on RGB images (i.e., DP (Chi et al., 2023)) and point cloud (i.e., DP3 (Ze et al., 2024b)), respectively. In RoboTwin 1.0, we reproduce the DPing and DPpar (without using point cloud color) with random seed O. Since the diffusion scores from different policies are composed at each denoising step (Alg. 1), we unify the training settings of both DP ped and DPing. In particular, they are trained with DDPM with 100 training and inference steps. In RoboTwin 2.0 experiments, we train DPs with the same settings RDT to ensure compatibility so that our GPC can be applied consistently. For example, RDT employs sample prediction, we align our diffusion models accordingly by training both DPang and DP under the same prediction setting.
Task Prompt in Twin.win. Here we present the detailed text description and its corresponding text prompt for VLAs. For example, for the Place Burger task, the task description and schema are:
Full description:
"Use dual arm to pick the hamburg and frenchfries and put them onto
the tray."
Schema: "A denotes the hamburg, denotes the tray, denotes the frenchfries"
During training, the VLA receives diverse paraphrased prompts for this task, such as:
"Use both arms move A and to B.*
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Figure 7: Illustration of Experimental Setup.
R
GPC
DPimg
DP ped
Figure 8: Tracking Results of Real-world Experiment in Place Bottles.
"Lift A and C, placing them neatly on B
At test time, unseen paraphrases with the same schema, e.g..:
"Pick A and C, then place them on B."
"Grab A and C together, setting them B."
1.4 REAL-WORLD EXPERIMENTS
We choose DP and DP ped as our base policies for real-world experiments. For DPings we use an Intel RealSense D435 RGB camera at 640 x 480 resolution (primary view and wrist view) to get the RGB images. For pP we use an Intel RealSense L515 depth camera at 640 480, where we obtain point clouds by using depth images together with camera intrinsics. The robot platform is Piper, operated in master-slave teleoperation setup. The illustration of the real-world experimental setup is shown in Fig. 7. Our GPC achieves superior performance compared with the base policies,
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presenting better trajectories in Fig. 8. Training follows official configurations: DP pod is trained for 600 epochs with batch size 256 (official code), while Dimg is trained for 20k steps with batch size 64 (Lerobot (Cadene et al., 2024) diffusion implementation).
1.5 NOTATION GPC FLEXIBILITY
Notably, the prediction types in diffusion models are not strictly restricted to single formulation (e.g., e-prediction, To prediction, or v-prediction), but can be freely combined within our framework. When heterogeneous prediction types are adopted simultaneouslyy, the denoising process requires proper alignment ensure consistency. We provide detailed guidance in Sec. on how reconcile different prediction types in GPC from a theoretical perspective, further demonstrating the flexibilityy of our proposed method.
ADDITIONAL EXPERIMENTAL RESULTS
In this section, we provide the complete set of experimental results to complement the main text. These results include all weight configurations for convex composition, well the out- comes under logical AND and OR operators.
Robomimic and PushT. We report detailed results on the Robomimic (Can, Lift, Square) and PushT tasks. In addition to the average performance reported in the main paper, we include (i) the full tables for convex score combination, logical AND, and logical OR composition (ii) the breakdown of performance under different convex weights w for each task: Can (Tab. 11 & Fig. 9), Square (Tab. 13 & Fig. 10), Lift (Tab.
Tab. 10, and
Fig. 11) and PushT (Tab. 14 & Fig. 12). These results illustrate how GPC adapts across weighting configurations and provide insight into the trade-offs between modalities and model backbones.
RoboTwin. We also provide the complete results RoboTwin 2.0 across all tasks. In particular, we include full tables comparing base policies and their compositions (e.g.. DPing + DPped. RDT + pepa)) with all tested weight settings: Open Labtop (Tab. 15), Place Burger (Tab. 16 Fig. 21), Put Object Cabinet (Tab. 17 & Fig. 24), Hanging Mug (Tab. 18 & Fig. 23), Stack Bowls Three (Tab. 19 & Fig. 14) and Turn Switch (Tab. 20 & Fig. 20). These detailed numbers confirm the robustness of GPC across diverse manipulation tasks and further validate the findings in Sec. 6.
Real-world Experiments. We further report complete results for the four real-world tasks: Place Bottles (Tab. 21 & Fig. 27), Hang Mug (Tab. 22 & Fig. 26), Clean Table (Tab. 23 & Fig. 25), and Punch Holes (Tab. 24 & Fig. 28). Similar to the simulation benchmarks, we provide full compar- isons between base policies and their GPC compositions under all tested weight settings. These results consistently show that GPC achieves higher success rates than individual policies, thereby confirming its effectiveness in practical robotic scenarios.
Summary. Together, these extended results give a comprehensive view of GPC's empirical be- havior across different operators and weightings. They serve reference for understanding not only the average improvements but also the sensitivity of performance to the choice of weights and composition strategies.
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Table 10: Experiments on Robomimic and PushTT with GPC under convex score combination,
Logical AND and Logical OR.
Robomimic Lift
PushT PushTT
Method
Generative Mode
Model Type
Can
Square
Average
Base Policies
Diffusion Policy (DP)
Diffusion
VA
34.50
98.50
2.00
21.75
39.19
Mamba Policy (MP)
Flow Matching
VA
5.00
98.50
3.00
12.06
29.64
Policy (FP)
Diffusion
VA
95.00
13.00
77.50
Florence Policy-D
Diffusion
VIA
61.50
97.00
46.50
40.00
61.25
Florence Policy-F
Flow Matching
VLA
89.00
98.50
88.50
39.38
78.84
m
Flow Matching
VLA
96.50
99.00
92.50
57.69
86.42
Composed Policies via Convex Score Combination
DP+MP
Diffusion
VA & VA
34.50
99.50
8.00
23.63
41.41
+2.22
HTorence-Policy-DAe
Diffusion
VIA VA
62.50
100.00
61.50
43.06
66.76 +5.51
Moorence-Policy D+MP
Policy-D+MP
Diffusion
VLA & VA 63.00
100.00
54.50
40.88
64.60 43.35
Florence-Policy-FFH
Flow Matching
VLA
98.50
98.50
92.50
56.06
86.39 +7.55
#0+FP
Flow Matching
VLA & VA
99.50
100.00
94.00
62.25
88.94 +2.52
Composed Policies via Logical AND Composition
DP+MP
Diffusion
VA VA
84.00
99.50
48.00
28.18
64.92
+25.73
Florence-Police -DDD
Pireene--Poliy-Deee
Diffusion
VLA VA
90.50
100.00
90.00
36.31
79.20 +17.95
Flarence-Polic--DAMM
Diffusion
VLA & VA
83.00
100.00
90.00
37.38
77.60
+16.35
Composed Policies via Logical Composition
DP+MP
Diffusion
VA & VA
82.50
99.50
44.00
29.13
63.78
+24.59
Florence-Police Pricce-Policy-DDDe
Diffusion
VLA & VA
83.50
100.00
89.00
37.87
77.59
+16.34
Florence- Paiee-Poolly--ee -DMMP
Diffusion
86.50
100.00
86.50
38.44
77.86
+16.61
Table 11: Experiments on Robomimic Can with GPC under different weighting.
Can
Method
Generative Mode
Model Type
0.1
0.2
0.3
0.4
0.5
0.6
Policy
Plorence DIT DP
Diffusion
VIA & VA
34.50
34.50
42.50
48.00
56.00
62.50
60.50
63.50
58.00
62.50
61.50
Plorence DIT e Mambal
Diffusion
VLA & VA
5.00
11.50
21.50
30.50
39.00
44.50
47.50
46.50
56.50
63.00
61.50
Plarence Plow-Fleww
Matching
VIA &
96.00
50
x0+FlowP
Flow Masching
VLA & VA
95.00
96.00
99.00
98.00
97.50
98.50
99.50
98.00
96.00
96.00
96.50
Table 12: Experiments on Robomimic Lift with GPC under different weighting.
Method
Generative Mode
Model Type
L.ft
0.5
DP-Mamba Policy
Diffusion
VA & VA
95.50
99.00
99.50
96.50
99.00
98.30
98.50
98.50
98.55)
95.50
98.50
99.00
100.00
99.50
99.50
99.50
97.00
Florence DIT MamiuP
Diffusion
VIA VA
98.50
100.00
99.50
99.00
99.50
99.00
99.00
97.50
98.50
97.00
97.00
Florence Flow-FloxP
Flow Masching
VLA VA
13.00
10.50
12:50
23.50
55.00
81.50
93.00
98.00
100.00
98.50
98.50
30sHlowP
Flw Masching
100.00
100.00
99.50
99.00
Table 13: Experiments on Robomimic Square with GPC under different weighting.
Method
Generntive Mode
Model Type
Square
0.1
0.2
0.3
0.1
0.5
0.6
0.7
MarMan Policy
Diffusion
VA
3.00
3.50
Placence DIT DP
Diffusion
VLA & VA
2.00
12.50
20.00
34.00
44.00
49.00
61.50
57.00
59.50
54.50
46.50
Flocence DIE + Mambal
Diffusion
VLA & VA
3,00
8.00
8.50
17.00
22.00
34.00
45.00
45.50
50.00
54.50
46.50
Plorence Flow Flowp
Masching
VLA &
79.00
85.00
92.00
92.00
92.00
91.00
88.00 00
88.50
92.50
88.50
n0+FlowP
Flow Masching
VLA & VA
77.50
80.50
$4.50
94.00
93.50
94.00
93.50
92.00
90.50
93.50
92.50
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Table 14: Experiments on Push T with GPC under different weighting.
Push
Generative
Type
60
0.1
0.2
0.3
0144
D.5
01.6
0.7
0.8
0.9
1.0
MarMar Policy
18.87
19:88
Florence DIT DP
Diffusion
VLA & VA
21.35
26.75
29.38
32.75
36,06
39.69
41.13
43.06
40.50
40.56
40.00
Floence DIT + Mambal
Dillusion
VLA & VA
12.06
22.88
25.81
30.62
33.94
37.00
38.44
40.50
40.75
40.88
40.00
Flow-FlowP
Masching
47.38
x0+FlowP
Flow Matching
VLA & VA
54.25 54.31
56.81
56.37
53.31
57.69
59.12
61 50
62.25
61.50
57.69
Table 15: Experiments on RoboTwin Open Laptop with GPC under different weighting.
RoboT
Open Laptop
Generative
Type
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
DP+DP3
Diffusion
VA & VA
0.74
0.74
RDT
Diffusion
VA
0.77
RDT DP3
Diffusion
VLA VA
0.93
0.92
0.92
0.91
0.92
0.91
0.86
0.77
0.67
0.69
Table 16: Experiments RoboTwin Place Burger Fries with GPC under different weighting.
Robo Place Burger Fries
Method
Generative Mode
Model Type
0.0
0.1
0.2
0,3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
DP+DP3
Diffusion
VA & VA
0.72
0.73
0.78
0.74
0.72
0.65
0.68
0.64
0.66
0.54
0.49
RDT
Diffusion
VLA VA
0.45
0.46
RDT DP3
Diffusion
VLA VA
0.79
0.46
Table 17: Experiments RwboTwin Put Object Cabinet with GPC under different weighting.
Twin: Put Object Cabinet
Method
Generative Mode
Model Type
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
DP+DP3
Diffusion
VA & VA
0.71
0.80
0.82
0.73
0.66
0.73
0.63
0.67
0.67
0.55
0.56
RDT
Diffusion
VLA VA
0.32
0.32
RDT DP3
Diffusion
VLA VA
0.71
0.71
0.46
0.40
Table 18: Experiments on RoboTwin Hanging Mug with GPC under different weighting.
RoboTwin: Hanging Mug
Method
Generative Mode
Model Type
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
DP+DP3
Diffusion
VA & VA
0.21
0.23
0.20
0.22
0.18
0.17
0.16
0.11
0.15
0.11
0.10
RDT DP
Diffusion
VLA VA
0.10
0.09
0.15
0.11
0.18
0.18
0.15
0.14
0.12
0.13
RDT DP3
Diffusion
VLA
0.30
0.22
0.13
Table 19: Experiments RoboTwin Stack Bowls Three with GPC under different weighting.
RoboTwin: Stack Bowls Three
Method
Generative Mode
Model Type
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
DP+DP3
Diffusion
VA & VA
0.64
0.70
0.66
0.71
0.60
0.53
0.63
0.56
0.59
0.49
0.52
RIYT + DP
Diffusion
VLA VA
0.52
0.65
0.66
0.57
0.66
0.59
0.58
0.50
0.40
0.32
0.47
RDT DP3
Diffusion
VLA VA
0.64
0.55
0.59
0.48
0.42
0.47
Table 20: Experiments on Robo Turn Switch with GPC under different weighting.
RoboTwin:
Turn Switch
Method
Generative Mode
Model Type
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
DP+DP3
Diffusion
VA & VA
0.71
0.68
0.60
0.63
0.67
0.56
0.50
0.45
0.41
0.42
0.38
RDT DP
Diffusion
VLA & VA
0.38
0.28
0.31
0.28
0.36
0.37
0.34
0.30
0.38
0.35
0.30
RIYT DP3
Diffusion
VIAA VA
0.71
0.52
0.54
0.48
0.51
0.59
0.51
0.43
0.42
0.45
0.30
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Table 21: Experiments on Real-world Place Bottle with GPC under different weighting.
weal-:orld: Place Bottle
Method
Generative Mode
Model Type
0.0
0.2
0.4
0.6
0.8
1.0
DP+DP3
Diffusion
VA & VA
11/20
13/20
11/20
12/20
10/20
7/20
Table Experiments on Real-world Hang Mug with GPC under different weighting.
Real-world: Hang Mug
Method
Generative Mode
Model Type
0.0
0.2
0.4
0.6
0.8
DP+DP3
Diffusion
VA & VA
6/20
7/20
5/20
7/20
6/20
5/20
Table 23: Experiments Real-world Clean Table with GPC under different weighting.
Roal-world: Clean Table
Method
Generative Mode
Model Type
0.0
0.2
0.4
0.6
0.8
1.0
DP+DP3
Diffusion
VA & VA
7/20
7/20
14/20
10/20
12/20
12/20
Table 24: Experiments on Real-world Punch Holes with GPC under different weighting.
Real-world: Punch Holes
Method
Generative Mode
Model Type
0.0
0.2
0.4
0.6
0.8
1.0
DP+DP3
Diffusion
VA & VA
6/20
6/20
5/20
7/20
9/20
7/20
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K
VISUALIZATION ON ROBOT TASKS
Figure 9: Illustration of Robomimic Can.
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conference ceaference_papeeee paper a at ICLR (CLR24 2020 0
as a
Figure 10, Illustraation olustration of of R comnimiie Square. .
S 11: I o Robomimic Lift.. Lift. L.ft.
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41
Figure 12: Illustration of PushT.
HEEP
Figure 13: Illustration of RoboTwin 1.0 Blocks Stack (Hard).
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Figure 14: Illustration of RoboTwwi 1.0 Bowl Stack.
Figure 15: Illustration of RoboTTin 1.0 Dual Bottle Pick Hard.
Figure 16: Illustration of RoboTwin 1.0 Dual Shoes Place.
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Figure 17: Illustration of RoboTwwin 1.0 Empty Cup Place.
Figure 18: Illustration of RoboTTwin 1.0 Pick Apple Messy.
Figure 19: Illustration of RoboTwin 1.0 Put Bottles Dustbin.
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Figure 20: Illustration of RoboTwin 2.0 Turn Switch.
Figure 21: Illustration of RoboTwin 2.0 Place Burger Fries.
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Figure 22: Illustration of RoboT Twin 2.0 Open Laptop.
Figure 23: Illustration of RoboTTwi 2.0 Hanging Mug.
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Figure 24: Illustration of Tobo 2.0 Put Object Cabinet.
Figure 25: Illustration of Real-world Experiment Clean Table.
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Figure 26: Illustration of Real-world Experiment Hang Mug.
Figure 27: Illustration of Real-world Experiment Place Bottles
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Figure 28: Illustration of Real-world Experiment Punch Holes.
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L DETAILED LITERATURE REVIEW
Owing to space constraints in the main text, we expand the related work section with detailed literature review. This appendix aims to provide a more comprehensive overview of prior work, highlighting additional studies and applications that could not be discussed in detail in the main body of the paper. All these works have made significant contributions to the robotics community.
L.1 COMPOSITIONAL GENERATIVE MODELING
Compositional generative modeling has recently emerged as a compelling alternative monolithic large-scale models, emphasizing the idea that complex data distributions can be captured more ef- fectively by composing simpler factors. Instead of relying on single, over-parameterized model, researchers argue that distributions can be factorized and modeled in a modular fashion, thereby re- ducing data requirements and improving interpretability (Koller & Friedman, 2009; Murphy, 2022). This line of work draws inspiration from probabilistic graphical models and energy- -aagyy formula- tions, but has been extended to modern deep generative architectures.
A key motivation for compositional modeling is data efficiency. By factorizing distributions into manageable components, one can achieve accurate modeling even under limited training data. For instance, Janner et al. (2022) and Ajay et al. (2022) showed that trajectory generation benefits from decomposing the sequence into components, leading to faster training and improved generalization. In natural language processing, Du et al. (2023b) demonstrated that reasoning can be improved by combining multiple large language models, effectively composing factors across models a "multi-agen framework. Similarly, Liu et al. (Liu et al., 2021) introduced composable diffusion for text-to-image generation, where local sentence-level factors combine to synthesize complex global scenes.
Beyond efficiency, compositionality provides a natural mechanism for generalization to novel tasks and distributions. In decision-making and planning, Ajay al. (2023) proposed hierarchical foun- dation models that integrate language, video, and action policies, enabling flexible recombination for zero-shot planning (Wang et al., 2025c). In robotic manipulation, Yang et al. (2023b) and Mishra et al. (2023) showed that object rearrangement tasks can be solved by composing local constraint factors, while Wang al. (2024c) extended this idea to heterogeneous policy composition (Wang et al., 2024b; Wang, 2025). For visual domains, Du et al. (2023a) and Zhang et al. (2023) devel- oped methods to assemble image collages via factorized regional conditionals, while Yang et al. (2023a) demonstrated that video style transfer can be achieved by composing pretrained prior with a lightweight style model.
Another strand of work investigates how compositional structure can be discovered automatically. Du et al. (2021) and Su et al. (2024) showed that autoencoders trained with product-of-expeett likelihoods naturally uncover object-level factors, which can later be recombined to generate hybrid scenes. In dynamical systems, Comas et al. (2023) inferred relational potentials between particles, enabling recombination of discovered interaction rules. Similarly, Liu al. (2023) found that com- positional components learned on ImageNet correspond to semantic classes, making it possible to synthesize images of unseen multi-class combinations.
At the methodological level, based models (EBMs) provide a natural framework for compo- sition, since energies are additive by construction (Hinton, 2002: Du & Mordatch, 2019; Grathwohl et al., 2021). This perspective has been adapted to diffusion models, where each time step de- fines an implicit EBM and compositions are realized by combining energies across models (Song & Ermon, 2019; Ho et al., 2020; Du et al., 2023a). Extensions to discrete domains employ Metropolis- Hastings with learned proposals (Lii et al., 2022; Verkuil et al., 2022), while Garipov et al. (2023) demonstrated how constraint energies can "sculpt" generative trajectories at inference time.
Despite these advances, challenges remain. Current approaches often assume a fixed structure of composition, limiting adaptability. Efforts by Wiedemer et al. (2023), Lachapelle et al. (2023), Misino et al. (2022), and Sehgal et al. (2023) highlight the need for robust theoretical frameworks that explain compositional generalization and offer methods to automatically infer appropriate fac- torization structures. Addressing these open problems will be crucial for compositional models to scale and integrate seamlessly into real-world generative systems.
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L.2 DIFFUSION MODELS IN ROBOT LEARNING
Diffusion models have become a central paradigm for robot learning, offering probabilistic frame- work for efficient trajectory generation and planning. Building on the recent surveys (Barreiros et al., 2025; Shao et al., 2025: Zhong et al., 2025; Xiang et al., 2025; Firoozi et al., 2025; Song
et al., 2025; Sapkota et al., 2025; Wong et al., 2025: Wolf et al., 2025; An et al., 2025; Zhang
et al., 2025a; Adilkhanov et al., 2025; Lin et al., 2024b; Ma et al., 2024b; Zheng et al., 2025; Liu
et al., 2025b; Urain et al., 2024), we group diffusion-based robot policies into two categories (Song et al., 2025): (i) small-size diffusion- based policies, which integrate CNN or Transformer back- bones with diffusion heads and are trained on task-specifir datasets for efficient visuomotor control, and (ii) large-scale diffusion policies, which couple diffusion modules with pre-trained foundation models or large robot datasets to achieve broader semantic grounding and cross-embodiment gener- alization. Together, these developments demonstrate how diffusion can serve both as a lightweight control primitive in specialized tasks and as scalable component in foundation-style robot policies, bridging the gap between low-level stochastic control and high-level semantic reasoning.
Small-size WNW/Transformer-baseed diffusion policies. A growing body of visuomotor research couples compact CNN or Transformer encoders with diffusion heads, showing that stochastic de- noising can serve as an effective control primitive across diverse manipulation settings. Within this line, several works directly map observations to actions using diffusion: Diffusion Policy (Chi et al., 2023) established the basic recipe for action diffusion with both CNN and Transformer backbones, and DP3 (Ze et al., 2024b) extends the paradigm to point-cloud inputs to strengthen 3D spatial generalization. iDP3 (Ze al., 2024a) extends DP3 for humanoid robots to learn from noisy hu- man data. Mamba Policy (Cao et al., 2025b) improves DP3 by introducing a linear-complexity architecture Mamba (Gu & Dao, 2024; Dao & Gu, 2024). DP (Lu et al., 2025) explicitly in- corporates hierarchical structures to strengthen the integration between visual features and action generation. MCDP (Cao et al., 2025a) integrates DP and DP3 via compositional diffusion to achieve enhanced performances. Temporal architectures tailored for planning appear in Motion Planning Diffusion (Carvalho et al., 2023), while design ablations highlight effective Diffusion- Transformer components (DiT-Block Policy (Dasari et al., 2025)) and introduce ireention-based conditioning for guided control (MTDP (Wang et al., 2025a)). Dexterous grasp synthesis is treated by DexDiffuser (Weng al., 2024). which progressively denoises grasp configurations for multi- fingered hands. Moving beyond pooled embeddings, 3D Diffuser Actor (Ke et al., 2025) conditions on tokenized 3D scene representations, and R&D (Vosylius et al., 2024) presents a unified im- age-action formulation using ViT encoders. For long-horizon or structured problems, ALOHA Un- leashed (Zhao et al., 2025) trains a Transformer with a diffusion loss for bi-manual skills; Chained- Diffuser (Xian & Gkanatsios, 2023) first predicts end-effector keyposes and then connects them with feasible trajectories; and HDP (Ma et al., 2024a) injects kinematics-awee aware priors to improve phys- ical realism. Category-level robustness is pursued by Sr-Diffusion (Yang et al., 2025) via visual foundation priors for spatial semantics and by C3DM (Saxena et al., 2023) through constrained- context conditioning with fixation step to resist distractors. Diffusion has also been adopted as a behavior prior for planning: Diffuser (Janner et al., 2022) frames sampling-ber beasengg-bsedd planning as probabilistic behavior synthesis, while DTP (Fan et al., 2025) adds 2D trajectory guidance in two-stage pipeline. Language- and object-centric formulations include StructDiffusion (Liu et al., 2022), which fuses object-centric Transformers with diffusion under language goals, and PlayFu- sion (Chen et al., 2023), which uses discrete bottlenecks to acquire language-annotated skills. From the data side, ROSIE (Yu al., 2023) exploits state-of-the-ar text-to-image diffusion for aggressive augmentation, and Ha et al. (2023) broadens language conditioning across tasks. Finally, capac- ity can be increased without full monolithic scaling through expert routing: GSC (Mishra et al., 2023) probabilistically chains learned skills with classifier-based guidance to satisfy constraints, and DBC (Chen et al., 2024) stabilizes learning by casting behavioral cloning of expert state-action pairs as diffusion- based modeling.
Beyond the core diffusion-based frameworks, a number of extensions have been proposed to im- prove efficiency, generalization, and adaptability in visuomotor policy learning. Streaming Diffusion Policy (Hoeg et al., 2024) accelerates policy synthesis by producing partially denoised trajectories where each action may retain different noise level, while Bidirectional Decoding (BID) (Liu et al., 2024b) enables test-time inference through a combination of action chunking and closed-loop adap- tation. Crossway Diffusion (Li et al., 2024b) introduces a specialized state decoder together with
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an auxiliary self-supervised learning objective to reinforce policy robustness, and Equivariant Dif- fusion Policy ( (Wang et al., 2024a) exploits domain symmetries to achieve higher sample efficiency and better generalization in the denoising process. Complementary empirical work by Lin et al. (2024a) investigates data scaling effects in imitation learning at scale. Other approaches extend the representational capacity of policies, such as Imagination Policy (Huang al., 2025a), which gen- crates point cloud predictions of target states before converting them into executable actions, and Consistency Policy (Prasad et al., 2024), which distills faster visuomotor policies through a consis- tency regularization process. For fine-tuning, DPPO (Ren et al., 2024) provides unified framework that integrates policy gradient techniques with diffusion policies in continuous control domains. Ex- tensions to tactile-rich scenarios include the Reactive Diffusion Policy (Xue et al., 2025), which combines slow-fast visual-tactile imitation learning for contact-rich manipulation.
Several recent efforts also integrate reasoning and sequence modeling into the diffusion paradigm. The Unified Video Action Model (Li al., 2025) jointly optimizes video prediction and action in- ference for accurate and efficient trajectory generation, while Chain-of-Action (CoA) (Zhang al., 2025b) explicitly reasons backward from task goals, producing coherent trajectories through an action-level chain-of-thought mechanism. Beyond diffusion, flow matching has emerged as strong alternative: ManiFlow (Yan et al., 2025) combines flow matching with consistency training to syn- thesize dexterous actions in just one or two steps; Flow Matching Policy Gradients (McAllister et al., 2025) embed flow matching directly into policy gradient algorithms for reinforcement learning; and VITA evolves latent visual states into latent actions under flow matching framework: Steering Your Diffusion Policy (Wagenmaker et al., 2025) adapts behavior-cloning policies by performing reinforcement learning over the latent noise space, offering a flexible way to guide policy behavior without retraining from scratch. In addition to these extensions, recent works also explore safety and dynamics- aware guidance. DynaGuide (Du & Song, 2025) introduces a steering mechanism for diffusion policies by incorporating feedback from an external dynamics model directly into the denoising process, enabling more physically consistent action generation. Latent Policy Barrier (LPB) (Sun & Song, 2025), inspired by control barrier functions, formulates expert latent embed- dings as implicit safety boundaries that distinguish in-distribution states from out-of--istribun ones, thereby enhancing robustness in visuomotor policy learning.
Together, these results indicate that lightweight diffusion policies augmented by stronger scene en- coders, subgoal scaffolding, data augmentation, MoB-style (Jiang al., 2024) routing are com- petitive and lata-efficient when embodiment and task distributions are relatively constrained.
Large-size LLM-based diffusion policies. At larger scales, diffusion modules integrated with pre-trained vision-language-mmode (VLM) or LLM backbones or trained atop broad cross- embodiment corpora, marrying semantic understanding with probabilistic action generation. Meth- ods leveraging general data pre-training use foundation models to inject world knowledge and linguistic structure: MDT (Reuss et al., 2024) builds on CLIP (Radford et al., 2021) and Voltron (Karamcheti et al., 2023) for long-horizon manipulation with sparse language, enriching instructions via GPT-4 (Achiam et al., 2023); Ha et al. (2023) employs LLMs for high-level plan synthesis and success inference while delegating low-level control to diffusion policies; ROSIE (Yu et al., 2023) uses LLM-authored prompts to drive text-to-image diffusion for targeted data augmen- tation; and TLA (Wen et al., 2025a) freezes multimodal backbone and applies parameter- efficient tuning (~5% trainable) to produce actions efficiently. Compositional planning stacks fur- ther tighten the loop between language and diffusion: HiP (Ajay et al., 2023) composes expert mod- els LLMs for task planning, video diffusion for trajectory proposals, and an inverse model for action mapping, while Plan Diffuser (Sharan et al., 2024) autoregressively emits textual subgoals with an LLM and translates them into visual subgoals via diffusion for downstream control. In parallel, robot data pre-training focuses on large, heterogeneous robot datasets to strengthen embodiment transfer. Octo (Team et al., 2024) aggregates 25 datasets from Open X- X-Embodiment 'O'Neill et al., 2024) and trains Transformer with a diffusion head to map observation/task tokens to action tokens across embodiments; biffusion-VLA (Wen et al., 2025b) pre-trains on Open X-Embodiment and DROID (Khazatsky et al., 2024) and adapts to tasks via LoRA (Hu et al., 2022); ChatVLA (Zhou et al., 2025) co-trains robot and reasoning data with staged alignment and MoE routing re- duce task interference; RDT-1P 1B (Liu et al., 2024a) specializes in fine- mne-graindd (including biman- ual) skills by standardizing unified action space over heterogeneous robots; and LAPA (Ye et al., 2024) systematically studies cross emboddmem pre-training using Bridge (Walke et al., 2023) and Open X-Fmmbdiimen (eile al., 2024). no (Black et al., 2024) couples pre-trained
VLA
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vision language backbone with flow-matching action expert for precise, smooth manipulation; Based on ko, To.5 (Intelligence et al., 2025) uses co-training on heterogeneous tasks to enable broad generalization; Pertsch et al. (2025) and Driess et al. (2025) focused on accelerating the VLAs based on empirical studies; Enerverse (Huang et al., 2025b) and Video Prediction Policy (Hu et al., 2024) use diffusion models for learning visual representations to improve scene understanding and subsequently enhance policy performance; HybridVLA (Liu et al., 2025a) unifies both the continu- ous nature of diffusion-based actions and the contextual reasoning of autoregression within a single LLM; GROOT N1 (Bjorck et al., 2025) is dual-system (Figure, 2024; Cui et al., 2025) VLA for generalist humanoid robots, achieving state-of-the thr- performances across multiple robot embodi- ments; Galaxea GO (Jiang et al., 2025) also adpots the dual-sytem, coupling VLM for multimodal planning and VLA for low-level robot control; Agibot GO-1 (Bu et al., 2025) is a generalist policy that leverages latent action representations to maximize data utilization; Gemini Robotics family (Team et al., 2025) achieves generalized abilities in diverse tasks, including robot control, object detection, pointing, trajectory, and grasp prediction. In addition to using the diffusion policy as the action head, there are many excellent works that employ flow matching (Lipman et al., 2023; Liu, 2022) for action prediction: GraspVLA integrates autoregressive perception tasks and flow matching-basee
action generation into a unified Chain-of-Thought process; GR-3 (Cheang et al., 2025) excels in understanding complex instructions with abstract concepts, generalizes effectively to novel objects and environments: WALL-OSS (Zhai et al.. 2025) presents a coupled architecture, unifying instruction reasoning, subgoal decomposition, and fine- ane-grained action synthesis.
Overall, these large-scale policies suggest convergent recipe in which language models structure objectives and subgoals, diffusion processes synthesize trajectories and actions, and pre-training (on general or robot-centric corpora) supplies the semantic and embodiment priors required for robust generalization.
L.3
MODELS IN ROBOT LEARNING
While diffusion bbated approaches have recently attracted significant attention, wide range of non- diffusion architectures continue to play a pivotal role in robot learning. These models typically leverage sequence modeling, spatial reasoning, and large-scale VLA systems to build versatile ma- nipulation and navigation capabilities. Unlike diffusion policies, which rely on iterative denois- ing, non-diffusion frameworks often emphasize direct policy learning through MLP transform- ers (Vaswani et al., 2017), hierarchical control, or data scaling strategies. In what follows, we summarize representative advances in manipulation and navigation, highlighting how non-diffusion models complement and extend the landscape of robot learning.
Manipulation. A major thread in non non-diffusion visuomotor learning frames control as sequence modeling. ACT (Zhao et al., 2023) introduces a conditional encoder mecoder Transformer that pre- dicts action sequences rather than single steps, attenuating compounding error over long horizons. Building on this idea, MT-ACT (Bharadhwaj et al., 2024) augments training with task semantics to learn universal multi-task manipulator, while CogACT (Li et al., 2024a) couples a VLA backbone so that manguage-guided cognition and low-level motor control are optimized in concert. Chunking Causal Transformer (Zhang et al., 2025c) retains the ACT-style autoregressive policy but segments trajectories into chunks, improving stability and sample efficiency for long sequences. Beyond pure sequence decoding, several works enrich spatial grounding and 3D control: Act3D (Gervet & Xiao, 2023) is a language-conditioned Transformer for 6-DoF manipulation that outputs continuous- resolution 3D action maps via adaptive 3D computation; ICRT (Fu et al., 2024) performs genuine in-context learning on a physical robot, leveraging a handful of contextual trajectories to execute unseen tasks without additional training; and Spatial Policy (Liu al., 2025c) explicitly models scene geometry so that visual predictions align with executable end-effector motions. A comple- mentary line scales VLA systems with data and hierarchy: RT-1 (Brohan et al., 2023) demonstrates that Transformers trained on large, diverse robot datasets yield strong generalists; RT-2 (Zitkovich et al., 2023) transfers web-derived llngunee knowledge into control; RT-X (O'Neill et al., 2024) shows that pretraining on large-scale OXE data can set new performance bars, underscoring the value of data scale; and RT-H (Belkhale et al., 2024) inserts a language-motion layer that bridges high-level instructions and low-level actions through an explicit hierarchy. Practical systemization and modality breadth are advanced by Beyond Sight (Jones et al., 2025) (Octo-style finetuning to adapt generalist visuomotor policies to heterogeneous sensors), Open VLA (Kim et al., 2025) (fully
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released training/testing recipes), and RoboVLM (Li et al., 2024c) (a design study distilling the most consequential choices in VLA pipelines). Finally, emerging embodied models lift perception and coordination to 3D and dexterous settings: 3D-VLA (Zhen et al., 2024) links 3D perception, reasoning, and action via a generative world model; Bi-VLA (Gbaghe et al., 2024) targets coordi- nated bimanual manipulation; LEO (Huang et al., 2024) acts multimodal generalist capable of perceiving, grounding, reasoning, planning, and acting in 3D environments: SpatialBot (Cai et al., 2025) strengthens spatial understanding by fusing RGB with depth; Lift3D (Jia al., 2024) elevates 2D foundation features into robust 3D manipulation representations; and RoboDual (Bu et al., 2024) unifies generalist breadth with specialist precision in synergistic dual-policy framework.
Further advances focus on constraint- driven representations for manipulation. Relational Keypoint Constraints (ReKep) (Huang et al., 2025c) define visually grounded constraints as Python functions that map sets of 3D keypoints in the scene to numerical costs, providing flexible interface for encoding task-specific relations. VosPoser (Huang et al., 2023) leverages large language models to extract affordances and constraints from natural language, composing 3D value maps in the obser- vation space that guide robotic interactions in structured manner.
Together, these works illustrate that non-diffusion architectures, particularly sequence models and VLA systems, achieve strong manipulation generalization through long- monghorizon decoding, explicit spatial grounding, data scaling, and modular hierarchy.
Navigation. For locomotion and navigation, non-diffusion approaches similarly exploit hierar- chy, distillation, and language grounding. Cheng al. (2024b) develop extreme legged parkour by first training a teacher with reinforcement learning and then distilling its competence into student policy that runs purely on onboard depth, enabling agile behaviors in the wild. Mobility VLA (Chi- ang et al., 2024) adopts a hierarchical design: long-context VL.Ms provide scene understanding and commonsense reasoning at the high level, while robust low-level navigator follows a topo- logical graph to execute the plan. NaVid (Zhang et al., 2024b) turns streaming RGB video and natural-language instruction into sequence of textual action directives that a robot can carry out, emphasizing language-ass asatioo for purely visual inputs. NaVILA (Cheng et al., 2024a) extends this idea to legged visual- language language-navigation (VLN) with two levels of control: a finetuned VLM outputs mid-level language actions (e.g.. "turn right 30"), and learned visual locomotion controller faithfully executes those commands. These systems highlight a recurring pattern in non-diffusion navigation: decompose high-level intent into compact linguistic subgoals, pair them with robust low-level policies for accurate robot control.
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M FUTURE WORK
This work opens several avenues for future exploration. On the methodological side, a key direction to move beyond fixed test-time weight discretization. More adaptive weighting strategies could be developed, such as reinforcement learning or gradient-based meta-optimization, to automatically adjust convex weights across tasks and environments. Another natural extension is scale from dual-policy to multi multi-policy composition. Since naively increasing the number of composed policies incurs a high computational cost, future work may explore feature sharing mechanisms or compact latent representations to enable efficient integration. Finally, the design of stronger composition operators remains an open challenge. Our initial results with superdiffusion highlight its potential, but more efficient variants, well as extensions that integrate with flw-based models, could further amplify policy performance.
At a broader level, the principle of policy composition can potentially extend beyond diffusion-based policies. The same compositional framework could be applied to diverse policy classes and archi- tectures, enabling modular integration of heterogeneous skills. Moreover, while experiments focus on robotic VA and VIAA in manipulation tasks, we anticipate a broader impact in related (VLN) tasks, such
domains. For instance, lision-anguaae-naaigaatt the-art methods TrackVLA (Wang et al., 2025b) and LOVON (Peng et al., 2025), may also benefit from compositional strategies to enhance generalization and robustness. Exploring these directions would further validate GPC as a general paradigm for leveraging pre-trained models in complex sequential decision- maniingnmmainggggg domains.
successful state-of-
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Reviews:
[{"review_id": "lqTuAbzaMT", "reviewer": "Reviewer_BM4P", "summary": "The paper proposes General Policy Composition (GPC), a training-free method that improves robotic policies by composing distributional scores from multiple pre-trained diffusion/flow policies at test time. GPC performs a test-time weight search over convex coefficients of two score estimators, then samples trajectories using the composed score. Experiments on a simulated manipulation benchmark and on multiple real-robot tasks show consistent improvements over individual policies.", "questions": "- Have the authors tried to combine 3 or more policies? Curious if it can further improve the performance.\n- Is there any way to combine different policy classes, such as a flow policy and a diffusion policy with this framework?\n\nI’d be happy to reconsider my score once these points are addressed.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The method provides a unified framework for combining diffusion and flow models trained on different modalities, with a flexibility to support multiple prediction types (noise, score, velocity, etc.).\n\n- The actual algorithm is pretty simple and clear without requiring any additional training. \n- Experimental results on Robomimic, PushT, RoboTwin, and four real-robot tasks show consistent gains over each individual policy.", "weaknesses": "- My primary concern is the cost of test-time weight search. It involves querying each diffusion/flow policy several times and will likely add considerable inference overhead. How much additional time does this require in simulation and in real-world experiments? I recommend the authors include an analysis regarding this.\n\n- Implementation details for each policy are missing. What is the revised pi0? What are the model architectures and training setups for the diffusion and flow policies? I recommend the authors include these details.\n\n- If I understand correctly, another limitation is that policies being combined must use the same action-chunk length and the same number of diffusion steps. This requirement substantially limits GPC’s applicability to open-source generalist VLAs, which are often trained with different settings.", "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": "4L8ttc4cow", "reviewer": "Reviewer_vsK6", "summary": "This work presents General Policy Composition (GPC), a training-free framework designed to enhance the performance of robotic control policies, particularly those based on diffusion or flow-matching models, by combining existing pre-trained policies. GPC addresses the high cost and data requirements typically associated with scaling up or fine-tuning control policies. The core mechanism involves composing the distributional scores of two policies during inference, via a convex combination, utilizing a test-time search to identify optimal weighting coefficients. There is a theoretical foundation to show that a convex combination of scores yields a provably superior one-step functional objective compared to individual scores, and this improvement propagates throughout the entire generation trajectory.\n\nEmpirical validation across simulation benchmarks (Robomimic, PushT, RoboTwin) and real-world tasks shows that GPC improves performance, achieving average success rate increases of up to +7.55% in sim and +10% in real-world tasks compared to single-policy baselines. The author's analysis suggests that GPC generates more coherent and concentrated distributions throughout execution, contributing to stability. Although effective, the framework is currently limited by reliance on a fixed discretization for test-time weight search and potential computational increases when scaling beyond dual-policy composition.", "questions": "1. How would you address giant compute overheads for running a VA/VLA model while trying to meet the real-time requirements of running policies on a real robot?\n1. Fig 1: Explain the desired task here in the caption. Preferably give the task prompt or description that is input to the policies.\n1. Line 361 (100-200 rollouts for evals): I’m trying to understand how often this test-time compute is calculated during rollout. What’s the obs horizon over which these trajs are created? Is it one DP inference call per episode?\n1. Sec 6.2 and table 1: What is the reason for some combinations to exhibit a higher performance increase? Please give your analyses and hypotheses, if any. How much of this improvement would you attribute to causes such as choice of task, choice of underlying models, choice of modalitiies for each model, randomness during evals, and any other cause you would like to highlight.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. Simple, effective, and theoretically-motivated idea that is reminiscent of other techniques in ML that use multiple models to get the best outcome (e.g. MoE, boosting).\n1. Idea of utilizing test-time search is sound; it would help the authors to add references talking about the per-compute-unit performance benefits of using test-time compute vs. train-time compute. (e.g. arxiv.org/pdf/2408.03314).\n1. The proposed GPC framework enables composition across both VA and VLA models.", "weaknesses": "1. Potentially very large inference time due to weight search. Already, robotics policies struggle with inference that is not fast enough to keep up with physics.\n1. No major comparison of how much test-time compute is used against the compute used for the base policies that were composed.\n1. No discussion about a potential increased test-time inference latency.", "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": "UOXEZkkxli", "reviewer": "Reviewer_mnxH", "summary": "This paper introduced a training-free method for boosting diffusion-based policies performance via test-time policy composition. Theoretical analysis is provided to support the claim that convex combination of different policy distribution can improve functional objective. The proposed General Policy Composition (GPC) has been validated on various simulation benchmarks and real-world robot system.", "questions": "1. GPC has an implicit assumption that two base policies should have different behavior distributions, how to make sure this is the case in practice?\n2. How much extra inference cost is required for GPC?\n3. In case of VA+VLA, how to guarantee the VA modality correctly follow the language instruction of VLA? If VA's modality is opposite to the language instruction, will GPC in fact harm the final performance?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The idea of training-free test-time policy improvement with policy composition is novel and interesting\n2. The theoretical proof provides good mathematical foundation for the proposed method (I have not thoroughly read the proof in the Appendix, may require extra verification)\n3. Detailed analysis and ablations are conducted in both simulation and real-world experiments.\n4. The paper is well-written in general and easy to follow.", "weaknesses": "1. Based on the results, it appears that the proposed method yields a noticeable performance improvement only when both base policies perform well. As noted in Section 6.3, if either policy performs poorly to begin with, the proposed method tends to struggle and may even degrade overall performance.\n2. The performance of GPC is highly sensitive to weight tuning, which limits its practical generalizability.\n3. GPC’s effectiveness relies on the diversity of modalities offered by the base policies; however, there is no guarantee that such diversity exists, nor is there any further analysis on how varying modalities influence the final performance.", "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": "MyKOtTnKTJ", "reviewer": "Reviewer_d2UQ", "summary": "This paper propose a policy composition methods in imporving the policy performance in the inference time without any data collection or training. This paper conducts comprehensive experimentis in several benchmarks and real world experiments with various base policies, together with detailed theoretical analysis.", "questions": "No questions", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper proposed a novel framework in composing different policies during inference time without collecting more data or training.\n\n2. The proposed method can handle different policies, datasets, and modalities for a task under the same environments.\n\n3. This paper conducts comprehensive experiments and theortical analysis accross several benchmarks and tasks with various different policies.", "weaknesses": "1. Combining different policies and modalities will increase the computation cost during inference time.\n\n2. The output actions should be the same. But in general, for different kinds of policies like DP, VLA, and flow-based policy might be good at using different length of action chunkings. It might be a limitation.\n\n3. The ideas, results, and analysis are interesting, but not quite sure this method is pratical or not... To compose them and get performance, I need to train different policies for a same task, and even collect different data with different modalities. With the same cost of time, collecting more data can also increase the preformance.", "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)