Geometry-aware Policy Imitation
Authors: Yiming Li
Nael Darwiche
Amirreza Razmjoo
Sichao Liu
Yilun Du
Auke Ijspeert
Sylvain Calinon
Venue: ICLR 2026 Poster (2026)
Keywords: imitation learning; diffusion policy
Primary area: applications to robotics, autonomy, planning
TL;DR: We propose Geometry-Aware Policy Imitation (GPI) for robot imitation learning.

Abstract: We propose a Geometry-Aware Policy Imitation (GPI) approach that rethinks imitation learning by treating demonstrations as geometric curves rather than collections of state–action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: a progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines a controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across low-dimensional robot states and high-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations as separate models and allows efficient composition of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experiments show that GPI achieves higher success rates than diffusion-based policies while running 20× faster, requiring less memory, and remaining robust to perturbations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning.

Published as a conference paper at ICLR 2026
GEOMETRY-AWARE POLICY IMITATION
Yiming Li
Nael Darwiche
Amirreza Razmjoo*t
Sichao Liu
Yilun Du
Auke Ljspeert!
Sylvain Calinon*
Idiap Research Institute
i EPFL
$ Harvard University
ABSTRACT
We propose a Geometry-aware Policy Imitation (GPI) approach that rethinks im- itation learning by treating demonstrations geometric curves rather than col- lections of state-action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across wiw-diensiioal robot states and nigh-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations separate models and allows efficient com- position of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experi- ments show that GPI achieves higher success rates than diffusion-based policies while running 20x faster, requiring less memory, and remaining robust to pertur- bations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning. Project page: https://yiminglii 1998 19t.../iiiubb.o//pjje///CCC
INTRODUCTION
Robots are increasingly expected to perform complex tasks in unstructured environments, rang- ing from dexterous manipulation to interactive collaboration. Imitation learning offers a promising path toward this goal, as it enables robots to acquire policies directly from expert demonstrations without relying on explicit dynamics models or simulation. Existing imitation approaches can be grouped into three families. Explicit policies treat imitation as supervised regression from states to actions (Calinon et al., 2007). They are fast at inference but struggle with multimodality and gener- alization. Implicit policies learn energy functions over state-action pairs (Florence al., 2022), but are hard to train and slow to optimize deployment. Generative policies, such as diffusion flow- matching models (Chi et al., 2023; Lipman et al., 2023), excel at modeling multimodality but remain computationally heavy and brittle under distribution shifts. Despite their differences, all three ap- proaches compress demonstrations into parametric models that must be retrained to incorporate new data and that often discard the geometric structure underlying expert behavior.
We argue that imitation learning can be made more direct, interpretable, and efficient by adopting geometric approach. At its core, imitation means: (i) following the expert's 's direction of motion, while (ii) approaching expert states as closely as possible. Viewed this way, a demonstration is not just a collection of samples but geometric curve in state space, annotated with tangents that indicate expert actions. This perspective motivates our approach, Geometry-Aware Policy Imita- tion (GPI). GPI represents demonstrations as distance fields that can be projected onto the robot's actuated subspace, where control is applied. From these fields naturally emerge two complemen- tary primitives: a progression flow that advances along expert trajectories, and an attraction flow that pulls current states toward them. Superimposing these flows defines a controllable vector field that drives imitation (Li & Calinon, 2025). This approach provides an approximation that reduces deviation while advancing along expert behaviors (Figure 1). In addition, the policy is guided by distance field composition that retrieves flow fields from the most similar demonstrations, promoting coherent behavior and enabling robustness even under unknown dynamies.

---

Published as a conference paper at ICLR 2026
S
S Vd'(o)
[ )dc
(x)
Forward dynamics
Projection
x'
1
Full state space
Actuated state space
State evolution
Miltimodality
Reward
Inference Time
Memory Footprint
DP
Ours
Ours
Ours
15.8%
79 txf
Millseconds
65 Omo
67.0ms
Memory (MB)
355,000B
Reward
60-
300
252,0MB
102
34,0MB
0.6mm
4.7MB
State
Vision-based
State State-based
Vision-based
State-basod
Vision-busod
Evaluations on Push-T benchmark
Figure Overview of Geometry-Awars Policy Imitation (GPI). GPI treats demonstrations as geometric curves that induce distance fields in the full state space. (Top) The state space is projected onto the robot's ac- tuated subspace, where control is applied. The projected distance field gives risc to two complementary flows: aftraction flow from the negative gradient (red arrow) and progression flow from trajectory tangents (yel- low arrow). Together, they define a dynamical system that reduces the distance to demonstrations and advances along them, thus imitating expert behavior. The resulting action tu is executed through the system's 's dynamics, yielding state evolution J [az, u) dt in the full state space. Multiple demonstrations can be composed naturally via Boolean operations on distance fields. Despite unknown system dynamics, the resulting trajectory aligns closely with the most similar demonstration determined by the distance metric. (Bottom) On the PushT benchmark, GPI achieves multimodal imitation with higher reward, runs 20-100x faster than diffusion poli- cies (DDIM with 10 steps), and requires substantially less memory.
A key strength of GPI is its decoupling of imitation into two modular components: (i) metric learn- ing, which defines how states are represented and compared; and (ii) behavior synthesis, which constructs policies directly from distance and flow fields. This separation offers substantial flexibil- ity: low-dimensional states can use Euclidean geodesic distances, while nigh-dimensional obser- vations can rely on latent embeddings from pretrained or task mesc-specific encoders. Policy synthesis itself is non-parametric and lightweight, enabling efficient composition of demonstrations without retraining and supporting multimodality by preserving distinct trajectories as separate flows (Pari et al., 2022). Moreover, because GPI only requires state representation that supports distance computation, rather than directly fitting a full policy function, the learning problem is considerably simpler than in generative models. Lightweight encoders are typically sufficient, which reduces training complexity and enables fast inference at deployment.
We evaluate GPI extensively in both simulation and real robots. In simulation. bench- mark across diverse domains -iraainnnincuuinng planar pushing, 6-DoF manipulation, and dexterous hand wintrol-with state spaces ranging from low-dimensional control vectors raw vision inputs. For visual observations, we study multiple feature representations, from pretrained encoders to self- supervised embeddings. On real hardware, demonstrate GPI on both a Franka arm and the Aloha bimanual system, showing that it scales robustly beyond controlled environments.
In summary, our contributions are:
i) Geometry-Aware Policy Imitation (GPI), which represents demonstrations as geometric curves that induce composable distance fields, providing unified representation for both met- ric reasoning and action synthesis;
A simple and modular formulation, where state representation relies only on a suitable dis- tance metric and action synthesis is realized through compositions of control primitives. Both components are lightweight, flexible, and grounded in well-studied principles; iii) Extensive validation in simulation and on real robots, showing that GPI achieves higher per- formance and enables efficient policy imitation-ove 20x faster than sfate-of-ther the-arr diffusion policies-vv while remaining interpretable and multimodal.
2

---

Published as a conference paper at ICLR 2026
2 GEOMETRY-AWARE POLICY IMITATION
GPI constructs policies directly from demonstrations by representing them as geometric curves in state space. Each demonstration induces distance field that encodes state similarity and gives rise to two complementary control primitives: (i) progression flow that advances along demonstrated motions, and (ii) attraction flow that corrects deviations by pulling states toward the trajectory- Their superposition defines a dynamical system that imitates expert behavior. Local policies derived from individual demonstrations are then composed via distance- weighting, producing a coher- ent global policy that is efficient, interpretable, and robust to perturbations. Figure 1-op illustrates these components schematically.
2.1
METHOD
We are given N expert demonstrations D = = where each (+) is a trajectory consisting of sequence of states and actions
(1) = (<x) ui (3)
(I)
with states zt ( E X. actions u, ( E U, and horizon T:
State and actuated subspace. A state x may include both environment variables (e.g., object poses. images) that are unactuated, and robot variables that are directly actuated by control inputs. We denote by x' = P(x:) the projection of æ onto the actuated subspace X" C X, where P + X" is the projection operator. Each trajectory p(( can then be viewed as a geometric curve in state space, which induces a distance field d(x, r()) measuring the proximity between query state 2, and the demonstration.
Action space. We assume velocity control in the actuated subspace, i.e., u, = ai/. Each demon- stration (+) then defines a curve x whose actions u, are the tangent directions in X'. Velocity control is used here for clarity, but it not a prerequisite: the formulation extends naturally to accelerations or torques, which can be executed through the robot's s kinematics or dynamics models.
Policy as flow field in actuated space. From the distance field d(æ. (()) induced by a demon- stration r(), we derive two complementary flows in the actuated subspace: Progression flow, given by the demonstrated tangent action u and Attraction flow, obtained from the partial derivative of the distance field with respect actuated coordinates, - d(x [()), which corrects deviations by pulling states back toward demonstra- tions. Their superposition defines a policy in the actuated subspace:
* ((i (.(),,)> which advances along the expert trajectory;
Te (x.) X1 (I u (i) <(=,)) (z)) V d(z, r())
where n(x.) = arg min, d(x,, x denotes the nearest demonstrated state, and \1. 2 0 are weights-either constant or distance-dependent chosen so that attraction dominates far from demon- strations, while progression dominates near them. This policy has been shown to yield stable first- order dynamical system that asymptotically converges to the demonstrated trajectory if the state and action variables continuous (Li & Calinon, 2025)'. This can be achieved by representing a discrete trajectory with continuous functions such as splines. Thus, the robot's behavior remains robust, predictable, and safe even under environmental changes or perturbations.
Composition across demonstrations. To obtain a global policy, we compose local flow-based policies across multiple demonstrations. Given the K nearest demonstrations, the global policy is
exp( - dd | [(())
TT..) Σ wa (w. (xx);
wi (2:)
-i=1 exp( 3 d(x [())
where Tı(x)) is the local policy induced by demonstration ((), d(æ, ((0) is the distance from query state v, to the trajectory 1(1,, and 8 > 0 is a temperature parameter controlling the sharpness of selection. This distance-based composition ensures that flows are retrieved from the most relevant demonstrations, yielding coherent behavior even under unknown dynamics. A detailed description of GPI is provided in Algorithm (Appendix B).
See Appendix A for the proof.
3

---

Published as a conference paper at ICLR 2026
Task-sppciff
Pretrained model
x
z
x
Encoder
z
Decoder
x
model
Figure Typical ways obtain latent embedding z raw imputs æ. (i) train task-specific lightweight model to capture task-relevant features; (ii) use a VAE to learn task-agnostic features; or (iii) apply pretrained model to obtain features without additional training.
2.2 CHOICE OF DISTANCE METRIC
central design choice in GPI is the distance metric d(z, T which measures the similarity between a query state and demonstration. The state naturally consists of two complementary parts: the robot-actuated variables (e.g.. joint angles, end-effector pose) and the environment-related variables (e.g., object poses, images). Accordingly, the distance metric can be decomposed into robot feature doob and an environment feature dewe, where the former also shapes the attraction flow in actuated space and the latter only influences demonstration selection and weighting.
Robot distance drub- For joint or end-effector positions æ E IR", Euclidean distance is standard:
dac (z), x22) ||||| 22l12-
(4)
For end-effector orientations represented as quaternions, geodesic distances on 5 respect rotational geometry:
dquat ( x2) = 2 arccos([(()) xz2)))
(5)
These two cases cover the most common representations in joint space and task space for robotics.
Environment distance dewv- This compares lask-relevant but indirectly controllable variables, such as object poses or scene images. For low-dimensional object poses, denv can be computed with Eu- clidean or geodesic distances, reusing the formulations above. For nigh-dimensional observations, it is common to define dewv in a latent space. Let x = (x) denote the latent embedding of æ. Then
denv (x1, x22) denv (21, 22).
where = (x))) and 22 = (x(2)) are latent embeddings produced by parametric model V/ that latent space, and d(-,-) denotes a suitable distance (e.g., Euclidean or cosine). This formulation supports multiple sources of embeddings: (i) task-specific models, where could encode predicted object poses or desired robot actions learned via supervision; (ii) latent variables from variational autoencoders (VAEs) trained with self-supervised objectives (Kingma & Welling, 2013); and (iii) pretrained vision or multimodal encoders such as SAM (Kirillov et al., 2023), DINO (Siméoni et al., 2025), and CLIP (Radford et al., 2021), see Figure 2 for an overview. Classical dimensionality redduction methods, such as principal component analysis (PCA), can also be used to obtain compact latent feature (Hotelling, 1933).
maps raw observations
While both debb and danv contribute to the overall distance metric, their roles differ: dany influences only the similarity ranking across demonstrations, whereas djub additionally shapes the attraction flow in the actuated subspace. This decomposition makes explicit how environmental features guide demonstration selection, while robot features govern the actual corrective control.
2.3 A 2D EXAMPLE
To illustrate GPI, we consider simplified 2D setting where the state consists only of actuated variables x'. This abstraction is common in kinematic planning tasks. where environment dynamics are ignored. In this case, the distance field reduces to the robot-related term, d(æ.)) = d.a (n²))) so that state evolution and policy flows are fully contained the same space. While prior work typically trains diffusion flow-matching models for policy generation in this setting (Jiang al., 2025), GPI instead addresses the problem a fully non-paramctric manner, relying directly on the distance and flow fields.
Figure 3(a) shows two demonstrations forming a Y-shaped pattern: ( (green) and ( (blue) overlap initially and then diverge into separate branches. Temporal progression is indicated by transparency from = 0 to t = 1. Each demonstration induces a Euclidean distance field whose valleys align with its trajectory; composing them yields global distance field (Figure 3b) visualized
4

---

Published as a conference paper at ICLR 2026
(a) Demonstrations
Flow field with action u ē
(b) Energy landscape
(d) Flow field with u A1 2
Figure 3: From demonstrations to policy flows. Demonstrations. (b) Energy from composed distances. (c) Progression-only flow u x may drift off the demonstrations. (d) Adding attraction pulls states toward the demonstrations and along them, ensuring convergence.
λ Aa and
energy landscape with dense corridors along the demos and natural decision boundary the bifurcation. Figures 3(c,d) show the resulting flow fields: each row includes the single-demo flow (left) and the composed flow (both demos), with rollout trajectories overlaid on the energy land- scape (right). Panel (c) depicts the progression flow, which follows the local tangent of the nearest demonstration: Panel (d) augments this with an attraction term that pulls states toward the trajec- tories, ensuring stable convergence. The rollout trajectories (red) show the integrated trajectories two cases. From this perspective, diffusion policies perform well because their denoising steps implicitly induce attraction flow toward demonstrations rather than relying solely on progression.
By representing demonstrations distance and flow fields, policy imitation shifts from fitting parametric model to geometric reasoning grounded in similarity, curvature, and composition, yield- demonstrations enrich the distance field by adding basins of attraction without retraining, and inference reduces to distance evaluations plus weighted averag- ing of expert actions, making it lightweight and parallelizable; measurement from action synthesis keeps the framework modular, allowing task-specific distance metrics and flow compositions; Multimodality- each each demonstration defines its own distance and flow field, preserving distinct behaviors the policy branches smoothly toward the nearest demon- strated mode instead of averaging conflicting actions; Interpretability- which demonstrations influence the current action, while actions remain a linear superposition of demonstrated behaviors and corrective flows, ensuring safe, bounded outputs.
ing several benefits: Efficiency-
similarity
distance metric reveals
EXPERIMENTAL RESULTS
3.1
SIMULATION EXPERIMENTS
We first evaluate GPI on the PushTT benchmark, a widely adopted task which a robot must push a T-shaped object into target configuration (Chi et al., 2023). This environment is particularly suit- able for evaluation: it has well-established baselines for comparison, requires handling inherently multimodal pushing strategies, and involves contact-rich dynamics that cannot be solved by simple kinematic planning.
For state-based inputs, demonstrations consist of the agent position, the object position, and the object orientation. Distances are computed as weighted combination of these components. The actuated subspace corresponds to the agent position, with its first-order derivative (velocity) serving as the action. Note that the original environment specifies actions in position control, which we adapt to velocity control for consistency with our flow-based formulation. Control policies are synthesized from the flow fields induced in the actuated subspace by corresponding demonstrations, and then executed in the environment with unknown interaction dynamics. For vision-based inputs, the state comprises the agent pose and RGB image. Distances computed jointly over the agent pose and an image embedding. To align with the state-based formulation, we train a lightweight -pecific model produce the image embedding the predicted object pose.
5

---

Published as a conference paper at ICLR 2026
Table 1: Performance comparison on Push-T T (state-hased vs. vision-hased).
Push-T (statc-buseed
Push-T (vision-busee)
Mothod
(Avg./Max.) ) score (8)
Training/ / Inference Time
Memory
(rgg/Max.) score (%)
Training Inference Time
Memory
DDPM
82.3/ 86.3
MB
80.9 85.5
2.5b. ms
353
DDIM
81.5 85.1
1.0h/ ms
252 MB
79.1 / K3.1
2.5h/ 67 ms
353
FMP
77.6 80.2
1.0b/ 58 ms
251 MB
75.17 79.3
2.5b
352 MB
83.1 87.88
0.8 h.8h/fo
77.57
2.0b/
GPI (Ours)
85.8 89,0
0h/ 0.6 ms
0.7 MB
83.3/
0,3 3.3 ms
44MB
Experiments were conducted dices C.I and C.2. We report performance using three complementary metries: (i) Average / maxi- reward, evaluated over multiple random seeds and environment variations, following the same protocol as the baselines; (ii) time, including training time and per-step inference time; and (iii) memory foolprint, including memory cost for model parameters and stored demonstrations. We compare GPI against Diffusion Policy (DP) (Chi et al., 2023), Flow Matching Policy (FMP) (Zhang & Gienger, 2024), and Streaming Flow Policy (SFP) (Jiang al., 2025). All baselines are im- plemented using their official public codebases. For DP, we evaluate both a 100-step Denoising Diffusion Probabilistic Model (DDPM) (Ho al., 2020) and 10-step Denoising Diffusion Implicit Model (DDIM) (Song et al., 2021). Following standard practice, DP and FMP predict an H-step action sequence (H = 8), whereas SFP and GPI naturally support reactive planning and operate with one-step horizon (Hl 1). Results are summarized in Table 1. GPI achieves higher success rates across all tasks than these baselines while being substantially more computationally efficient.
NVIDIA RTX 3090 GPU. Further details appear in Appen-
In the state-based setting, inference involves only low-dimensional, paraaaaretticc distance evalua- tions and flow field composition, resulting in a latency of 0.6 ms insnnerlly 100x faster than diffusion- or flow matching based basclines. Although GPI requires storing all demonstrations for distance measurement, the overall memory footprint remains lower than that of training large neural poli- cies? Moreover, the underlying computations are lightweight and naturally parallelizable, further contributing to its efficiency. For aision-based inputs, we employ a ResNet-18 encoder trained solely for feature extraction rather than precise action prediction, which simplifies training and im- proves efficiency. As a result, training completes in only 0.3 hours and inference runs at 3.3 ms per step. Memory requirements are also reduced, since we store only the lightweight encoder and latent embeddings of demonstrations rather than raw images or large policy networks. Additionally, this modular structure allows the visual encoder to be reused across different tasks.
We further conduct series of ablations to high- light the distinctive properties of GPI:
1.0
Robustness. We evaluate GPI's robustness along three complementary dimensions.
088
Reward
Planning horizon: GPI is reactive by default (H = 1), but it can also be extended to receding-horizon scheme by updating the dis- tance every steps. As shown Figure 4, performance remains stable for horizons up to 16, showing GPI can operate either as a purely reactive controller (robust to external distur- bances) or as a receding- planner (with improved temporal consistency).
0.6
6-4
State-based (Avg)
State based (Max)
02
Vision based (Avg)
Viston based (Max)
Dssend
0.
2
16
32
Action Horizon
Figure 4: Robustness to action horizons.
Number of neighbors: In action composition, compare K 3,3,5, 10. As shown in Fig-
ure 5. the curves are nearly overlapping in both relative and absolute state settings, confirming that performance is largely insensitive to the choice of K. In addition, we also ablate the softmax tem- perature 3 used in (3) for composing demonstrations, and the results are reported in Appendix D.4. This highlights the reliability of GPI's local composition mechanism.
State representation: We compare object-centric (relative) and global (absolute) state formulations (Figure 5). Both achieve strong performance, but relative states consistently yield slightly higher
"ee Appendix 1.1 for detailed explanation.

---

Published as a conference paper at ICLR 2026
Relative State
Absolute State
1.0
Reward
Reward
0.4
I=10
0.0
100K
Number of Demonstrations
Number of Demonstrations
Figure 5: Robustness of GPI with respect demonstrations, K (neighbors), and state representations.
scores, especially in data-scarce regimes. This suggests that GPI is robust to representation choices, with relative states offering an advantage when demonstrations are limited.
Distance metrics. We evaluate how the choice of distance metric and the relative weighting between robot and environment components affect performance; detailed ablations and results are reported in Appendix D.3.
Scalability with data sizes. A distinctive advantage of GPI is that, being non-parametric and training-free in the state- base- setting, it enables direct study of how performance scales with the number demonstrations, without the need retraining. To this end, we augment the dataset with up to 160K samples regenerated from the original diffusion policy work and evaluate how perfor- mance evolves as the demonstration set grows. This setting is particularly suitable for GPI, since demonstration density directly influences both the distance query and the selection of actions in the composed policy, As shown in Figure 5, success rates increase consistently as the dataset expands from 1K 20K demonstrations, after which performance begins to saturate. This trend reveals two key insights: (i) larger demonstration sets provide denser coverage of the state space, thereby reduc- ing approximation errors introduced by the chosen distance metric, and (ii) our approach as a practical diagnostic fool-indicating how many demonstrations are sufficient to achieve reliable policy performance before training parametric models. The method also accommodates incremental incorporation of new demonstrations, without the need for full retraining, For a detailed analysis sis of latency and memory scalability as the number of demonstrations and the latent dimension increase, please refer to Appendix D.2.
serve
Stochasticity and multimodality. To in- duce stochasticity and multimodality, we inject Gaussian noise (N o²) into the query state in the actuated space (corresponding to the agent's
1.0
250
0.9
200
Reward
0.8
Diveessi
position). This perturbation alters the effec-
0.7
150
tive distance fields used in composition, thereby modifying the synthesized flow field and in- ducing multimodal behavior. In Figure 6,
0.6
Reward Diversity
compare the average score achieved under dif- ferent noise levels. To quantify diversity, measure the average distance among trajecto- ries generated with different random perturba- tions sampled from the same noise distribution. The results show that larger noise values in- crease trajectory diversity but degrade perfor- mance, whereas smaller noise levels yield more deterministic behavior. Importantly, GPI exhibits multimodal behavior even under low noise (e.g.,
0.4
50
0.3
0.5
0.0
Noise Level
Figure 6: Noise-level ablations for score and diver- sity.
0.2), illustrated in Figure (bottom left). Beyond Gaussian perturbations, stochasticity can also be enhanced by randomly subsampling the set of demonstrations at each inference time. We found that this strategy improve performance in practice, for instance, by helping the robot escape from regions where it would otherwise become stuck.

---

Published as a conference paper at ICLR 2026
Natural composition of control primitives. We interpret progression and attraction two ba- sic control primitives that can naturally combined within the flow field. By varying their rel- ative weights (2), we interpolate between velocity-like (progression-driven) and position-lii like (attraction-drisc) control. As shown in Figure 7, GPI maintains consistently high scores across a wide range of weightings, demonstrating flexibility in composing these primitives test time rather than relying solely on fixed neural network outputs. In this view, progression promoles forward motion and task advancement, while attraction provides goal alignment and stability.
Generalization across tasks. We evaluate GPI on RoboMimic (Lift, Can, Square) (Mandlekar et al., 2021) and Adroit (Door. Pen, Ham- mer, Relocate) benchmarks (Rajeswaran et al.,
Average Reward
0.20
0.37
0.42
0.45
0.55
0.56
0.56
0.40
2018), spanning state spaces of 9-46 dimen- sions and action spaces of 7-30. GPI consis- tently matches or exceeds the performance of Diffusion Policy without requiring any para- metric training (Table 2), demonstrating robust generalization across diverse domains. The snapshots of those tasks shown in Figures and 12 (in Appendix D.5) respectively. Ad- ditionally, we test GPI on 2D Maze task (Chen et al., 2025; Janner et al., 2022) and visual- ization results in shown in Figure 13 in Ap- pendix D.6.
Progression (A,)
0.46
0.57
0.67
0.72
0.74
0.74
0.80 0.60
0.60
0.79
0.76
0.6
1,20 1.00
0.74
0.82
0.84
0.78
0.76
0.84
0.87
0.87
0.85
0.0
0.20
0.40
0.60
0.80
1.00
1.20
Attraction (Az)
Figure 7: Ablations on two control primitives.
Table 2: Task description and performance on Robomimic and Adroit Hand henchmarks.
Robomimic
Adroit Hand
Task Method
Lift
Can
Square
Door
Pen
Hammer
Relocate
State Dim
16
16
39
45
46
39
Description
Action Dim
7
24
30
Demonstrations
300
300
300
5000
5000
5000
5000
DP
1.00
0.94
0.87
1.00
0.89
0.83
0.91
Results
Ours
1.00
0.96
0.82
1.00
0.95
0.88
0.91
Generalization across visual representa-
tions. As discussed in Section 2.1, GPI naturally accommodates multiple choices of latent em- beddings, including task-specific encoders, VAEs, and pretrained models. We evaluate four variants on PUSIT:: (i) ResNet feature (He et al., 2016) pretrained within the Diffusion Policy implemen- tation, with PCA applied for dimensionality reduction; (ii) an unsupervised variational autoencoder (VAE) trained solely on RGB images, serving task-agnostic feature extractor; and (iii) pre- trained Segment Anything (SAM) model (Kirillov et al., 2023) followed by a pose-estimation mod- ule whose predicted object pose Appendices C.3 (ResNet+PCA). C.4 (VAE) and C.5 (SAM). Additionally, we compare our VAE- based encoder to self-supervised Bootstrap Your Own Latent (BYOL) encoder (Grill et al., 2020) for feature extraction, which is also used in VINN (Pari et al., 2022) for non non-parametric policy synthesis.
the embedding- Implementation details provided in
Results in Table show that GPI with the same ResNet features followed by PCA achieves performance compa- rable to Diffusion Policy, which uses the same ResNet features with diffusion head. Interestingly, a lightweight VAE encoder trained only for reconstruction also yields strong performance. With the KL KL regularizer encouraging latents to stay near the prior N (0, I), it produces smooth latent space in which linear interpolations tend to remain on-manifold. This VAE trains in ~ 0.3 hours and runs at ~ 4 ms per inference- inference-comparaaiee comparable to our task-specific vi- sual head (Table 1). In contrast, self-supervised BYOL.
Table 3: Performance of various visual rep- resentations on the pushT task.
Feature Extractor
Avg. Score
Diffusion Policy Task-specific Head
85%
87%
ResNet+PCA VAE
84%
88%
Pretrained SAM
41%
BYOL feature
67%
8

---

Published as a conference paper at ICLR 2026
feature performs worse than the VAE on PUSHT. A plau-
sible explanation is that the VAE's reconstruction objective encourages latent codes to retain and smoothly parameterize scene geometry, which is particularly well matched to GPI's distance fields and flows, whereas BOQI, emphasizes invariance to augmentations and may discard some of this geometric information. Finally, even an off-the-shelf pretrained SAM model within the GPI frame- work achieves a 41% average score without any fine-tuning. This variant underperforms our other encoders, likely due to sensitivity to segmentation quality and the downstream pose estimation mod- ule; we expect that task-specific fine-tuning would improve its performance.
3.2 ROBOT EXPERIMENTS
To further evaluate GPI, we conduct robot experiments on two challenging tasks:
(i) Box flip. The robot must flip a box by exploiting con- tacts among the end-effector, the box, and an aluminum crossbeam, which is challenging due known, highly nonlinear dynam- ics. We collect 121 demonstra- tions on an ALOHA platform (Al-
daco al., 2024). The dataset con- tains over 50, 000 RGB images and action pairs. A lightweight neu-
ral network takes raw RGB im- age as input and predicts an action; this predicted action serves the image embedding. Distances are computed jointly over the robot joint configuration and the action embedding to construct the dis- tance field, from which the flow field is derived for the robot's execution. We observe an infer- time of approximately 7 ms and memory footprint of 140 MB, comprising 139 MB for the feature-extraction model and 1 MB for storing latent features. In 50 flip trials, 39 are successful, corresponding to 78% success rate. A trial is counted as successful if the robot flips the box the target orientation within 500 control steps at Hz. During these experiments, we also introduce occlusions and external disturbances; GPI still reliably completes the flip, indicating robustness to sensing and dynamics perturbations.
Figure Real-robot flipping task. GPI successfully completes the task via multimodal behavior (Top rows) and demonstrates robust- ness to visual disturbances (Bottom).
(ii) Human-robot fruit handover. A human hands fruit to the robot. The robot must exe- cute a smooth, anticipatory interaction while synchronizing its timing with the human and re- maining robust to unpredictable motions and sensing noise. This task is run on a Franka robot.
We collect a single demonstration to align the robot's motion phase with the human hand tra- jectory. At execution time, a pretrained CLIP model (Radford et al., 2021) provides fruit- detection score, which we combine with the de- viation from the demonstrated hand trajectory to define the distance field. This field deter- mines the robot's phase and progression; the robot follows the progression flow until the de- sired phase is reached. yielding synchronized and fluid handovers, We observe 46 successful handovers out of 50 trials, resulting in 92% success rate. A trial is counted as successful the robot correctly recognizes the fruit and anticipates and adapts the human hand mo- tion to complete the delivery. During execution, vary the object shapes and initial positions while still using only a single demonstration, and the policy consistently completes the task, demon- strating robustness and generalization.
Figure 9; Real robot experiment on human-robo inter- action task.

---

Published as a conference paper at ICLR 2026
More details about the robot platform, experimental setup, and training details are illustrated in Appendices C.6 and C.7, respectively. The robot behavior during two tasks is shown in Figures 8, and the attached video.
4 RELATED WORK
Among approaches to acquiring robotic skinlse-rinforrcement learning (Sutton & Barto, 1998) and optimal control (Bertsekas, 1995), imitation learning (IL) (Osa et al., 2018) stands out for not requiring explicit task models or cost functions, making it especially appealing when dynamics hard to model. Even when such models exist, demonstrations can accelerate and improve solutions (Nair et al., 2018; Razmjoo et al., 2021). Early approaches focus on time-dependent dynamical movement primitives, such Dynamic movement primitives (DMP) ([jspeert et al., 2013) and Probabilistic Movement Primitives (ProMP) (Paraschos et al., 2013), or time-independent dynamical systems (Khansari-Zadee Zadeh & Billard, 2011). They provide well-established approaches and efficient frameworks, but are usually limited in capturing complex, multi-modal demonstration patterns. Recent learning- baased approaches, such as Implicit Behavior cloning and Diffusion policy, address this issue and have demonstrated impressive performance across range of tasks (Florence al, 2022; Chi al., 2023; Zhang & Gienger, 2024). However, these methods introduce challenges such as hard to train, slow inference, and need multi-step inference (LeCun al., 2006; Du & Mordatch, 2019; Song & Ermon, 2019; Nijkamp et al., 2020; Zhang & Gienger, 2024). GPI bridges dynamical systems and modern learning by representing demonstrations distance fields- naturally to metric learning for high-level scene representations while inducing flow fields for low-level control. The closest prior, VINN (Pari al., 2022), learns visual representations via self-supervision and retrieves policies with kNN, achieving strong visual imitation. In contrast, GPI supports diverse latent representations and synthesizes policy flows- demonstrating effectiveness on tasks with complex dynamics.
LIMITATION AND CONCLUSION
We present Geometry-aware Policy Imitation (GPI), which treats demonstrations as geometric curves that induce a distance field and policy flows. This perspective yields a simple, flexible, efficient, multimodal, and interpretable policy that composes behaviors and integrates with diverse latent representations. Our approach has a few limitations that are worth exploring in future work:
Choice of distance metric and representation. The metric and visual representation are the key design levers that shape the induced flows. In this work, we rely on simple, manually specified met- rics and off off-the-shelf encoders. Making these components learnable and co-optimizing them with policy synthesis potentiall conditioned on task or context-come out-of-distribution generalization while preserving the geometric structure that makes GPI inter- pretable. Another promising direction is to leverage large models to provide task-relevant robotic features (Intelligence et al., 2025; Barreiros et al., 2025).
further improve robustness and
Scene dy nymiiss and stability. Our current results follow the standard imitation learning paradigm: environment dynamics and unactuated components are treated as unknown, and policies are learned purely from data rather than from a full dynamics model. A natural extension is incorporate known or learned dynamics models into the flow construction and analyze when the resulting closed loop provably stable and robust, for example via Lyapunov contraction certificates with perturbation and model-miisatth bounds. This could provide stronger guarantees in safety-critical settings. Our Lyapunov-style analysis assumes smooth distance field in the actuated subspace, it does not formally extend to discretized or non-smooth demonstrations, even though our time-discretized benchmarks remain empirically robust.
Scalability of demonstrations. GPI stores only latent features and distances are computed in single batched operation, leading to favorable latency and memory scaling in our empirical study. However, the memory footprint still grows linearly with the number of stored states. Future work could reduce this dependence via compact implicit distance parameterizations while preserving ge- ometric fidelity and fast retrieval.
10

---

Published as a conference paper at ICLR 2026
REFERENCES
Jorge Aldaco, Travis Armstrong, Robert Baruch, Jeff Bingham, Sanky Chan, Kenneth Draper, De- bidatta Dwibedi, Chelsea Finn, Pete Florence, Spencer Goodrich, al. Aloha 2: enhanced low-cost hardware for bimanual teleoperation. arXiv preprint arXiv:2405.02292, 2024. 9
Jose Barreiros, Andrew Beaulicu, Aditya Bhat, Rick Cory, Eric Cousineau, Hongkai Dai, Ching- Hsin Fang. Kunimatsu Hashimoto, Muhammad Zubair Irshad, Masha Itkina, et al. A care- examination large behavior models for multitask dexterous manipulation. arXiv preprint arXiv:2507.05331, 2025. 10
Dimitri P. Bertsekas. Dynamic Programming and Optimal Control, Volumes and II. Athena Sci- entific, Belmont, MA, 1st edition, 1995. 10
Sylvain Calinon, Florent Guenter, and Aude Billard. On learning, representing, and generalizing a task in humanoid robot. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cyber- netics), 37(2)2286-298, 2007.
Boyuan Chen, Diego Martí Monsó, Yilun Du, Max Simchowitz, Russ Tedrake, and Vincent Sitz- mann. Diffusion foreing: Next-token prediction meets full-sequence diffusion. Advances in Neural Information Processing Systems, 37:24081-24125, 2025. 8, 22
Cheng Chi, Zhenjia Xu, Siyuan Feng, Eric Cousineau, Yilun Du, Benjamin Burchfiel, Russ Tedrake, and Shuran Song. Diffusion policy: Visuomotor policy learning via action diffusion. The Inter- national Journal of Robotics Research, pp. 02783649241273666 2023. 1, 5, 6, 10
Yilun Du and Igor Mordatch. Implicit generation and generalization in energy-based models. In Advances in Neural Information Processing Systems (NeurIPS), volume 32, 2019. 10
Pete Florence, Corey Lynch, Andy Zeng, Oscar Ramirez, Ayzaan Wahid, Laura Downs, Adrian Wong, Johnny Lee, Igor Mordatch, and Jonathan Tompson. Implicit behavioral cloning. In Conference on robot learning, pp. 158-168. PMLR, 2022. 1, 10
Jean-Bastien Grill, Florian Strub, Florent Altché, Corentin Tallec, Pierre Richemond, Elena Buchatskaya, Carl Doersch, Bernardo Avila Pires, Zhaohan Guo, Mohammad Gheshlaghi Azar, et al. Bootstrap your own latent-a new approach self- self-supervised learning. Advances in neural information processing systems, 33:21271 11212721212844 2020.
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recog- nition. Proceedings of the IEEE conference on computer vision and pattern recognition, pp- 770-778, 2016. 8
Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840-66 6851, 2020.
Harold Hotelling. Analysis of complex of statistical variables into principal components. Journal of Educational Psychology. 24(6) 1933.
Auke Jan ljspeert, Jun Nakanishi, Heiko Hoffmann, Peter Pastor, and Stefan Schaal. Dynamical movement primitives: learning attractor models for motor behaviors. Neural computation, 25(2): 328-373, 2013. 10
Physical Intelligence, Kevin Black, Noah Brown, James Darpinian, Karan Dhabalia, Danny Driess, Adnan Esmail, Michael Equi, Chelsea Finn, Niccolo Fusai, et al. \pi_ (0.5) vision-language- action model with open-world generalization. arXiv preprint arXiv:2504. 150444 2025. 10
Michael Janner, Yilun Du, Joshua Tenenbaum, and Sergey Levine. Planning with diffusion for flexible behavior synthesis. In International Conference on Machine Learning, 2022. 8, 22
Sunshine Jiang, Xiaolin Fang, Nicholas Roy, Tomás Lozano-Pérez, Leslie Pack Kaelbling, and Sid- dharth Ancha. Streaming flow policy: Simplifying diffusion / flow-matching policies by treating action trajectories flow trajectories. arXiv preprint 1rX.v:2505.21881, 2025.

---

Published as a conference paper at ICLR 2026
S Mohammad Yeaassri-Zaaele and Aude Billard. Learning stable nonlinear dynamical systems with Gaussian mixture models. IEEE Transactions on Robotics, 27(5):943-9577 2011.
10
Diederik P Kingma and Max Welling. arXiv:1312.6114, 2013.
Auto-encoding variational
bayes.
arXiv preprint
Alexander Kirillov, Eric Mintun, Nikhila Ravi, Hanzi Mao, Chloe Rolland, Laura Gustafson, Tete Xiao, Spencer Whitehead, Alexander C Berg, Wan-Yen Lo, et al. Segment anything. In 2023 IEEE/CVF International Conference on Computer Vision (ICCV), pp. 3992-4003. IEEE Com- puter Society, 2023. 4,
Yann LeCun, Sumit Chopra, Raia Hadsell, M Ranzato, Fujie Huang, al. A tutorial energy- based learning. Predicting structured data, 1(0), 2006. 10
Y. Li and S. Calinon. From movement primitives to distance fields to dynamical systems. 1EEE Roboties and Automation Letters (RA-L), 2025. 3,3
Yaron Lipman, Ricky TQ Chen, Heli Ben-Hamu, Maximilian Nickel, and Matt Le. Flow matching for generative modeling. In 1 1Ith International Conference Learning Representations, ICLR 2023, 2023.
Ajay Mandlekar, Danfei Xu, Josiah Wong, Soroush Nasiriany, Chen Wang, Rohun Kulkarni, Li Fei- Fei, Silvio Savarese, Yuke Zhu, and Roberto Martin-Martin. What matters in learning from offline human demonstrations for robot manipulation. In Conference on Robot Learning (CoRL), 2021.
Ashvin Nair, Bob McGrew, Marein Andrychowicz, Wojeiech Zaremba, and Abbeel. Overcoming exploration in reinforcement learning with demonstrations. International Conference on Robotics and Automation (ICRA), pp. 6292-6299, 2018. 10
Erik Nijkamp, Mitch Hill, Tian Han, Song-Chun Zhu, and Ying Nian Wu. Learning non-convergent non-persistent short-run MCMC toward anergy-based model. In Advances in Neural Information Processing Systems (NeurIPS), volume 33, pp. 11588-11600, 2020. 10
Takayuki Osa, Fabio Pardo, Gerhard Neumann, J. Andrew Bagnell, Pieter Abbeel, and Jan Peters. An algorithmic perspective on imitation learning. Foundations and Trends in Robotics, 7(1-2): 1-179, 2018. doi: 10. 10.1561/2300000055, 10
Alexandros Paraschos, Christian Daniel, Jan R Peters, and Gerhard Neumann. Probabilistic move- ment primitives. Advances in neural information processing systems, 26, 2013. 10
Jyothish Pari, Nur Muhammad (Mahi) Shafiullah, Sridhar Pandian Arunachalam, and Lerrel Pinto.
The Surprising Effectiveness of Representation Learning for Visual Imitation. In Proceedings of Robotics: Science and Systems, New York City, NY, USA, June 2022. doi: 10.15607/RSS.200 20022. XVIII.010. 2, 10
Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agar- wal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and llya Sutskever. Learning transferable visual models from natural language supervision. In Proceedings of the 38th International Conference Machine Learning, volume 139 of ICML, pp. 8748-8763 2021. 4,9
Aravind Rajeswaran, Vikash Kumar, Abhishek Gupta, Giulia Vezzani, John Schulman, Emanuel Todorov, and Sergey Levine. Learning complex dexterous manipulation with deep reinforcement learning and demonstrations. Robotics: Science and Systems XIV, 2018. 8
A. Razmjoo, T. S. Lembono, and S. Calinon. Optimal control combining emulation and imitation to acquire physical assistance skills. In 20th International Conference on Advanced Robotics (ICAR), pp. 338-343. IEFF, 2021. 10
12

---

Published as a conference paper at ICLR 2026
Oriane Siméoni, Huy V. Vo, Maximilian Seitzer, Federico Baldassarre, Maxime Oquab, Cijo Jose, Vasil Khalidov, Marc Szafraniec, Seungeun Yi, Michaël Ramamonjisoa, Francisco Massa, Daniel Haziza, Luca Wehrstedt, Jianyuan Wang. Timothée Darcet, Théo Moutakanni, Leonel Sentana, Claire Roberts, Andrea Vedaldi, Jamie Tolan, John Brandt, Camille Couprie, Julien Mairal, Hervé Jégou, Patrick Labatut, and Piotr Bojanowski. DINOv3, 2025. URL https::ttp/.c.c........t htt.t:://///ttttt. httppps///axxvorrrrrrrpm
abs/2508 10104.
Jiaminn Song. Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. In Interna- tional Conference on Learning Representations, 2021.
Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. In Advances in Neural Information Processing Systems (NeurIPS), volume 32, 2019. 10
Richard S. Sutton and Andrew G. Barto. Reinforcement Learning: An Introduction. MIT Press,
Cambridge, MA, 1st edition, 1998. 10
Fan Zhang and Michael Gienger. Affordance-based robot manipulation with flow matching. arXiv preprint arXiv:2409.0/088 2024. 10
13

---

Published as a conference paper at ICLR 2026
APPENDIX
A CONVERGENCE OF THE FLOW POLICY
We prove convergence of the policy introduced in Section 2.1, which combines progression and attraction flows to form stable dynamical system in the actuated subspace. For clarity, we rewrite the flow policy (equation 2) as
Φ = - X2 Vd(x),
where d(xx) is the distance to the demonstration, Vd((a) its gradient, át- the tangent velocity at the projection point Te,, and Å1 22 weight progression and attraction.
We analyze stability using the Lyapunov function
((x) = d (x) 2 0,
(8)
which vanishes only on the demonstration. Its time derivative
V(x) = d(x) Vd(x)) a.
(9)
Substituting the dynamics gives
V(x) = d(x) Vd(x) T (Ar - A2 Vd(()))
(10)
To simplify this expression, we use the fact that the projection point æt- is defined as the minimizer of the squared distance
| - xe 2
(11)
At this minimizer, the derivative with respect must vanish:
(at- x)) T d;-
(12)
This condition implies that the displacement vector at.- æc and therefore the gradient Vd((w), is orthogonal to the trajectory tangent .;:::
vd(x) 2.- = 0.
(13)
With this orthogonality property, the Lyapunov derivative reduces to
V(x) = ->>d(())\
0,
(14)
with equality only d(x)) = 0. This shows that the system globally stable and asymptotically converges the demonstrated trajectory in the actuated space.
Assumptions and scope. This analysis is carried out for a continuous-time system in the actu- ated subspace, assuming smooth demonstration trajectory and well-defined, differentiable dis- tance field around it. The result should therefore be interpreted as convergence guarantee for this idealized setting. practice, GPI implemented in discrete time and with time-discretized demonstrations; the same flow construction is used, and we empirically observe stable rollouts in all benchmarks.
14

---

Published as a conference paper at ICLR 2026
B GPI ALGORITHM
Algorithm Geomelry-Aware Policy Imitation
Require: D [T Ji= each [ {(x})) u, ( 1o projection P: encoder V; robot/environ-
ment distances droh, denv; mixing Oryb, Oenv 0; weights (1).,, A2(+); temperature (3; top- Ensure: Control u E X" at query 2%
1: x' + P(x,),
f- (x.)
2: for all E [L....,N] (parallel over demonstrations) do
3: Per-time distances
rob + (droblazz 2t ((())
))+
d(t) f (denv(Zo, ((xx(
4: Combined distance: d()) t- arobd + Qeny denv
5: Nearest time index and scalar distance:
( (x:)) - arg min di")
d(xr, ((0) min de
6: Progression flow: un (1) t u (x.) = x(1)
(x.)
7: Attraction flow: (3)
V vi drabl x x (6)
aet
8: Local policy:
A1(((x= [()))) u + >s(d(z (()) u
9: Top-K K selection by demonstration distance: 1K + indices of the K smallest d(x. [())
- e Bddr,, [(())
Softmax weights over selected demos:
w: wi(xo) t EjErk exp( - 3 d(xx, (()) (k)
11: Global policy: u T(xo)= = Σ
(x(xo) (xxo)
El
12: return u
15

---

Published as a conference paper at ICLR 2026
C IMPLEMENTATION DETAILS
C.I PUSHT TASK WITH STATE-BASER INPUTS
For low-dimensional states, each demonstration is represented
x a Ma Tb. yo, 0o] 12,
where (Ia; Ma) denote the agent position, (In, m/) the block position, and 0, the block orientation. The associated action specifies the target location for a low-level controller:
ut Largett Vtarget),
which we rewrite for velocity control the relative displacement:
(1)
Turget
Taz
Utarget
ya.-
All state variables normalized [0, 1] before computing distances. The distance field d(ær, T()) defined as the weighted sum of three components:
d( ,x!") = Wobj [1 36) (x)-(2;;) (x//) v/b (1) ll2 + Wagt (Z Va) - (ar(²) y. ll2 + wy ang(O,, o(),, (15)
where ang(..) denotes angular distance. Unless otherwise stated, the weights are set Wobj
Wagt w/g = 1.0.
Each demonstration induces a distance field and an associated flow policy. At inference time, the global policy is formed by composing the K nearest demonstration policies, with Å₁ = A2 = 1.0. Evaluation is performed on environment seeds 500-510 using three distinct policy seeds.
We further explore several variants to improve the flexibility of GPI:
Relative vs. absolute state representation. The PushT task involves nonlinear contact dynam- ics, so the choice of state representation is important. In the relative variant, the agent position is expressed in the object's coordinate frame:
Pa R( R(-06) ((ra, Ba) - (It, 16)).
(16)
where R()0,) is the SE(2) rotation matrix aligning the block's 's orientation to the x-axis. The demonstrated action u, is similarly transformed. During execution, the predicted action mapped back to global coordinates via the inverse transformation:
R(0b) û (Ib. Vb).
(17)
Smooth flow fields. When the action horizon is set to 1, the controller is highly reactive and may produce abrupt changes whenever the nearest demonstration switches. To mitigate this, we apply first-order smoothing to the action sequence:
u smooth a ur + (1 - a)) u
smooth
(18)
where a E [0, 1] is a smoothing parameter.
Recent-action suppression. To mitigate oscillatory behavior arising from repeatedly selecting near- identical actions, we maintain a sliding-window memory M of the most recent M actions. During action selection, the candidate u, lies within a tolerance e of any element in M, is suppressed and the next-best candidate from the composed policy is chosen. This mechanism enforces diversity over short horizons, prevents immediate backtracking to previously executed actions, and ensures the policy explores novel trajectories while preserving responsiveness.
Perturbed query states. To evaluate robustness, we perturb the query agent position with additive Gaussian noise:
='= +e, E E~ ~0,
(19)
where x' (Iaa No) the agent substate. The noise variance a² is annealed over time, decaying from 0.1 at the beginning of exccution to 0.001 at later steps. This perturbation injects stochasticity into the query states, which increases variability in the retrieved flows and can induce multimodal behaviors.
Subsampled demonstrations. For efficiency and robustness, instead using all demonstrations, randomly sample subset I sub I at each query. The global policy is then composed over I sub- Empirically, we find that subsampling does not reduce performance; in some cases, the induced stochasticity even helps the agent escape undesirable cycles "stacked" behaviors.
16

---

Published as a conference paper at ICLR 2026
C.2 PUSHT TASK WITH VISION-BASEI INPUTS
In the PushT'' environment, observations consist of an RGB image together with agent positions (Fas Va). Each demonstration state is represented
(2) Ia. Ma. I
Vision encoder. To obtain compact image features, we use an encoder with a ResNet-18 backbone (group normalization) and projection head (MLP with sizes [512, 256, 128, 3J). The encoder is trained with mean squared error (MSE) loss to predict the object position and orientation:
(T) ~ (Zo, No: fa].
LMSE Σ
o pred
Furrge
2
Training is performed for 200 epochs using the Adam optimizer with a learning rate of 0.001.
Distance metric and policy synthesis. After training, each demonstration image is embedded as
2 (I
and for a query state 3g = [Ta. Va. I].
2o =T)).
Distances defined in this learned feature space and policy synthesis then proceeds identically to the state-based inputs.
C.3 PUSHT TASK WITH RESNET- 18 ENCODER AND PCA
We construct a compact observation embedding by reusing the same ResNet-18 encoder from the Diffusion Policy implementation (task-pretrained on PUSHT), At inference, this encoder is frozen and used as fixed feature extractor. We aggregate features over a short temporal win- dow (obs sobs_horizns www.horizonn zon = 2), apply PCA for dimensionality reduction on the image features, and concatenate with the last two agent positions (normalized and reweighted to balance scale). Each demonstration is thus represented in this joint embedding space. At test time, the current observation embedded the same way, and the closest demonstration under cosine similarity is identified. The policy then follows the flow induced by this demonstration, with progression and attraction weights set to A = A2 = 1.0.
Per-timestep features. Given image I and agent position [Ta, Vals extract a 512-D descriptor (T) with the frozen ResNet-18 backbone (final FC removed; BatchNorm - GroupNorm as the diffusion policy).
Temporal windowing and dimensionality reduction. With obs horizon T = 2, we flatten the last T descriptors and apply IncrementalPCA to project them 16 principal components:
PCA (C (T.)) 16
2,
Concatenation with agent positions. To balance image and agent information, we concatenate the PCA emhedding 2t with the normalized agent positions from the last two steps. All embeddings L2-normalized before similarity computations.
Policy selection. At test time, the query embedding is compared to the demonstration database using cosine similarity, and the flow is executed with λ = A2 = 1.0. To prevent degenerate repeats, the selected pair removed from the database the next step.
C.4 PUSHT TASK WITH VAE
We construct compact observation embedding using convolutional variational autoencoder (VAE) trained directly on PUSHT images. At inference, we discard the decoder and use only the encoder to produce latent codes, which are concatenated with scaled agent positions form the fi- nal embedding. The global policy then follows the flow induced by the closest demonstration under cosine similarity, with progression and attraction weights set λ da 1.0.
17

---

Published as a conference paper at ICLR 2026
Per-timestep features. Given image I with pixel values normalized to [0, 1], the VAB encoder outputs Gaussian posterior
#t go(= It), Ze R.
with diagonal covariance. At inference, we use only the posterior mean 14 the latent feature.
Retrieval. At test time, we encode the current observation window to obtain 2t, normalize it, and compute cosine similarity against the stored database features. The demonstration with the highest similarity is selected, and its associated action sequence defines the flow. Cosine similarity achieved slightly higher performance (average return 0.88) compared to Euclidean distance (Rs 0.85).
Training Setup. We train the VAE with a standard Gaussian prior p(z) = -N 7) and a Gaussian reconstruction likelihood p(x z) = A(x(2), 1²1) with fixed r = 2 x 10-1. This choice of т 0.2 both the reconstruction loss and the KL. divergence decreased steadily, whereas using smaller r values led to optimization stalling (neither term decreased). Training was performed for 25 epochs with the Adam optimizer (learning rate 1 x 10 At inference, we discard the decoder and use only the encoder's posterior mean.
balanced the reconstruction and KL terms: with
C.5 PUSHTT TASK WITH SAM-BASED POSE EMBEDDING
We estimate object pose directly from images using a pretrained SAM/SAM2 pipeline (no fine- tuning). From each frame we obtain a binary mask of the T-block, from which we extract its centroid (I6, y/5 and axial orientation 0, (defined modulo T). Combined with the agent position (Ia, Ba), this yields the state
Zt = Tas Na. Tb. yo. 0 E R..
All variables normalized to j0, 1] before distance computations; angular differences the same axial angular distance as in the state-based setup. Distances and policy composition follow the same formulation, with weights Wahj Wagt
wgg 1.0 and flow execution with λ >2 1.0.
Per-timestep pose extraction. Given SAM mask, the centroid is
(wh, yh
centroid(mask).
and the orientation is computed from second-order moments of foreground pixels. Let Pog denote centralized moments; the principal axis corresponding to the largest covariance eigenvalue indicates the clongation direction. We define
O, atan2 1220
μoo + ++),
wrap 8, (-T,, n.. and treat it as axial (modulo x) for angular distance.
Retrieval and policy selection. At test time, we form æ; = [Eas Ya vb. yo, 0o), apply the same normalization above, and compute distances to all stored demonstration states using the state- based metric. We retrieve the nearest neighbors (default = 1) and execute the composed flow with X, 2a2 1.0.
Tracking and prompting details. We use SAM2's video predictor (sam2. wwwheiiatttte hiera.tiny) to track the T-block across frames, re-prompting each step with skeletal outline derived from the most recent pose estimate to stabilize mask propagation. To compensate for small systematic bias in predicted centroids, we apply constant offset correction to (I%, yo). calibrated on seeds 500-700.
Limitations. Performance depends on segmentation quality; occlusions and viewpoint changes can induce drift the estimated pose, which in affects retrieval and control.
C.6 ROBOT-FLIP TASK
Robot teleoperation: We utilized a bimanual robotic system configured with ViperX300s (fol- lower) and WidowX250 (leader), along with RealSense D405 camera from a top-down view. The open-source platform. By using robot teleoperation,
system is built strations, each contains 200 to 1000 timesteps to complete the flip task. The dataset is structured composed
collected 121 demon-
in HDF5 format and includes robot actions and observations, where observations of effort, images, joint angles, and joint velocities. Specifically, we teleoperated the leader robot (WidowX255 to control the follower (ViperX300s) robot for manipulation tasks (flip the box). The
18

---

Published as a conference paper at ICLR 2026
camera records images at 848 x480 resolution with 30 Hz frequency, and then crops them to x20x240 resolution for policy training.
Policy imitation. The policy imitation process is similar to the pushT task with vision- bason inputs. Specifically, we use a vision encoder that takes RGB images as imput and predicts the desired robot action latent embedding using MSE loss. Training is performed for 100 epochs using the Adam optimizer with learning rate of 0.0001. After training, we calculate the latent feature of each demonstrated image feature database. The online inference involves the computation of distance field that includes both distance measurement in this latent space and an additional distance metric for joint position displacement, guiding the flow field and policy composition. Both attraction and progression parameters are set to 1.0 during execution. To ensure the temporal consistency, the task run with horizon=100.
ReaaSense D405
Cameera view
WidoxX250
Viper3300s
Figure 10: ALOHA telcoperation platform.
C.7 HUMAN-ROBOT INTERACTION TASK
We use the openai cecii-iiit--iiiii base patch32 CLIP model for vision-language grounding. Positive and negative text prompts for hand-held object detection are listed below.
Text prompts.
pos__roee jos_prompts
"a photo of hand holding banana",
hand holding an apple",
"a human hand holding an orange",
"a hand helding pear",
"a hand holding strawberry",
hand helding grapes", hand holding piece of fruit",
"a person's s hand holding a fruit",
"close-up of hand holding a fruit",
neg pog_prompts
"an empty hand",
"a hand with nothing in it",
hand holding baseball",
"a hand helding a black ball",
"a hand holding a blue cup",
"a hand helding plastic cup", hand holding adhesive tape", hand holding tape roll",
"a hand holding a screwdriver",
"a hand helding a tool",
"a hand holding non-fruit object",
19

---

Published as a conference paper at ICLR 2026
D ADDITIONAL EXPERIMENTAL RESULTS
D.1 MEMORY COST
The
PUSHT dataset has 25,000 x 7 = 175.000 elements, requiring 175,000 x = 0.67 MB with float 32, consistent with the observed 0.7 MB. For comparison, MLP with layers [7, 512, 256, 128, 1] has 168,449 parameters (R 0.64 MB), which is at a similar scale. However, typical models are far larger than simple MLP; e.g., state-based diffusion policy exceeds 200 MB.
Although GPI's memory grows linearly with the number of demonstrations, this is practical in our setting: robot actions are now-dimensional, and nigh-dimensional observations are stored compact latent features. Inference is lightweight, parallelizable, and can use subsampling or approximate nearest-neight neighbr search to bound latency. As we demonstrated in the paper, GPI achieves orders-of- magnitude gains in efficiency over standard baselines in common imitation-learning settings.
D.2 COMPLEXITY AND SCALABILITY
Complexity of one control step. All demonstrations stored in tensor of shape (NT, D), where N is the number of demonstrations, T is the trajectory length, and D is the state feature dimension. Given the current observation of shape (1, D). compute its distance to all stored states in single batched operation. The complexity of this retrieval step is therefore O ONNTD), implemented in parallel on GPU. Once the top-K neighbors are selected, combining their flows to compute the final control command is O(K)) D), which is negligible for small K compared to the retrieval cost.
Empirical scalability. To make the scaling explicit, we report retrieval latency and memory usage as we vary the number of stored states from 102 to 10 and the feature dimension D from 5 to 512. Latency is measured in milliseconds (ms) on a single GPU, and memory usage is reported in megabytes (MB). We measure the cost of computing Euclidean distances between single query state and all stored features, which is the component that grows with the database size:
Table 4: Retrieval latency and memory usage for a single query as a function of the number of stored states and feature dimension D. Each entry reports latency (ms) memory (MB).
# states
D =
= 32
D = 128
= 512
1 10a
0.039/ / 0.00
0.033 / 0.01
0.034 / 0.05
0.033 / 0.20
1 X 103
0.039 0.02 0.02
0.036 0.12 0.12
0.035 / 0.49
0.039 1.96
1 10a
0.033/0.15
0.037 1.22
0.068 / 4.88
0.217 19.6
1 x 105
0.051 / 1.91
0.221 / 12.2
0.517 / 48.8
1.973 / 196
1 x 106
0.291 19.1
1.920 122
4.891 488
19.26 1955
Even with very large databases (10% states) and high-dimensional features (D = 512), retrieval remains below 20 ms with about GB (approximately 1955 MB) of memory, which is compatible with typical real-time manipulation settings.
D.3 ABLATIONS ON DISTANCE METRICS
In all experiments, the metric used by GPI is constructed from simple and physically motivated components: Euclidean distance for robot states (e.g.. joint angles, end-effector positions), geodesic distance for quaternions, and cosine similarity for latent visual embeddings. These choices follow the geometry and physical meaning of each state component. All state dimensions are normalized before distance computation, which further reduces sensitivity to manual tuning.
To assess sensitivity to the specific form of the metric, we perform an ablation on the PushT task comparing L1 distance, L2 distance, and cosine similarity, both in the original state space and in VAE-based latent space. The average rewards are summarized in Table 5.
In the state space, both L1 and L2 distances perform well, indicating that GPI is not sensitive to the exact choice of norm as long as the metric consistent with the underlying state geometry. In the latent space, cosine similarity performs best, with I.I and 1.2 still competitive, consistent with
20

---

Published as a conference paper at ICLR 2026
Table 5: Average reward for different distance metrics the pushT task.
Metric
State space
Latent space (VAE)
L1 norm distance
88
81
L2 norm distance
86
85
Cosine similarity
88
87
standard practice for feature emheddings. Even when directly using cosine similarity in the state space, performance remains reasonable. Overall, these results indicate that GPI does not rely fragile, hand-tuned metries and works reliably with simple, task-aligned distances.
We also study how the relative weighting between the environment distance denv and the robot dis- tance dmb influences performance on PushT and Robomimic tasks. We define the combined metric
d = Wrob drob + Weny dewy:
(20)
and vary the ratio Wenv Wrob- The results are given in Table Performance clearly degraded when the environment weight is extremely small or large (e.g., Wenn/ Wrob = 0.01 or 100), but remains high over broad intermediate range (approximately Weme Wmb E [0.1, 10)), with the best results typically obtained near equal weighting (around 0.5-1.0). These trends confirm that the metric and
its weighting are important design choices, but also show that GPI remains robust to a wide range of relative weightings between robot and environment distances.
Table 6: Evaluation of robot-environment distance weighting on various benchmarks.
Wenv/ Wrob
0.01
0.1
0.5
1.0
5.0
10.0
100.0
PushT
0.38
0.76
0.83
0.87
0.80
0.80
0.54
Lift
0.68
0.85
0.98
1.00
0.83
0.78
0.52
Can
0.61
0.73
0.88
0.96
0.79
0.58
0.18
Square
0.23
0.55
0.72
0.82
0.63
0.51
0.16
D.4 ABLATION ON COMPOSITION HYPERPARAMETERS
We ablate the softmax temperature 3 used (3) for composing the top-K demonstrations on PushT (taae-based)) As shown in Table 7, performance remains stable over several orders of magnitude of B.
Table Effect of the softmax temperature PushT.
B
10-4
10
10-2
10-1
Avg. Score 85.1 1.2
84.8 + 0.9
85.8 + 1.2
85.6 + 1.4
D.5 ROBOMIMIC AND ADROIT HAND TASKS
21

---

Published as a conference paper at ICLR 2026
Figure 11: Snapshots of experimental results for Lift, Can, and Square tasks on Robomimic environments.
Figure 12: Snapshots of experimental results for Door, Hammer, Pen, and Relocate on Adroit hand tasks.
D.6 2D MAZE
We evaluate our approach on the 2D Maze benchmark, previously used by (Chen et al., 2025; Janner al., 2022). Unlike these methods, our approach training-fred free: at test time select a suffix of single demonstration using simple distance metric and execute it. Concretely, for demonstration i of length H and timestep k; we minimize
D(i, k) = 10 10 - x
1l2 + 5 [x, - xx00 + 0.1 AH k))
where Xy is the initial state, x the k-th state of demonstration i, X, the task goal, and x is the goal state associated with demonstration The final term penalizes long remaining horizons; since 2D Maze demonstrations can include detours, this bias favors suffixes that proceed more directly to the goal. After selecting ((*K*), we execute the suffix (x(*)) } the plan. In doing so, method also recovers the effective task horizon H ke, something most alternative approaches
cannot determine directly. Instead, they must either: (i) assume long horizon and truncate once
22

---

Published as a conference paper at ICLR 2026
the task is completed, (ii) assume short horizon and repeat until completion, or (iii) try multiple horizons and select the smallest successful one.
COS
JS End
Start
Figure 13: Results 2D Maze using method. Without any training, simple distance based criterion achieves 100% success rate across tasks, an average inference time 0.08 seconds.
E REPRODUCIBILITY STATEMENT
We will release code, configuration files, and evaluation scripts upon publication. Key imple- mentation details and protocols are documented the main text and appendix to facilitate reproduc- tion in the interim.
F USE OF LARGE LANGUAGE MODELS (LLMS)
We used LLMs (e.g., ChatGPT and Claude) rephrase and polish the manuscript and to assist with coding tasks. All LLM-generated code was reviewed, edited, and integrated by the authors; the LLM did not design algorithms or produce experimental results.
23


Reviews:
[{"review_id": "WZyNzOyoXq", "reviewer": "Reviewer_zwd9", "summary": "The paper proposes Geometry-Aware Policy Imitation, a method that treats expert demonstrations as geometric curves in state space instead of discrete state–action samples. Each demonstration defines a distance field, from which two flows are derived, a progression flow using demonstrated tangents, and an attraction flow using the negative gradient of the distance field. Their weighted sum forms a vector field that produces control commands. The paper states that this approach separates metric learning (state representation and distance computation) from behavior synthesis (flow combination). It presents a Lyapunov-based argument that the combined flow is stable in the actuated subspace and converges toward the demonstration. Experiments are reported on Push-T, Robomimic, Adroit and two real-robot tasks.", "questions": "- Can the authors provide quantitative results showing how different distance metrics (Euclidean, geodesic, latent cosine) affect performance?\n- Are there measured success rates or task completions for the ALOHA and Franka experiments?\n- How does retrieval latency or memory use change with increasing numbers of demonstrations?\n- How sensitive is the method to discontinuities or non-smooth demonstrations?\n- Can the authors clarify whether diffusion-policy baselines were reimplemented under identical conditions or reused from prior work?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "- Clear and consistent mathematical formulation.\n- Demonstrated efficiency on Push-T. \n- Comprehensive documentation of experimental settings, including both state-based and vision-based inputs.\n- Modular structure allowing different encoders. \n- The text includes explicit ablations on the number of neighbors, action horizon, and noise levels.", "weaknesses": "- The convergence proof covers only smooth, continuous trajectories in the actuated subspace. The paper does not provide analysis for environments with unactuated dynamics or discontinuities.\n- The paper defines multiple possible distance metrics, but no quantitative comparison or sensitivity analysis across metrics is reported.\n- Quantitative comparisons are limited to diffusion-based baselines.\n- The paper gives descriptive outcomes and system specifications but no numerical success or robustness statistics in the real-robots experiments. \n- The method requires storing features for all demonstrations. The text notes linear memory growth but provides no empirical scaling or retrieval-time measurements.\n- Multimodality is illustrated through noise perturbations but not quantified beyond the presented plots.", "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": "26KtGNEAbg", "reviewer": "Reviewer_g86J", "summary": "The paper proposes Geometry-aware Policy Imitation (GPI), which treats each demonstration as a geometric curve and builds a distance field in state space. Two complementary control primitives—(progression along the curve tangents and attraction via the negative distance gradient in the actuated subspace)—are superposed to form a lightweight, non-parametric vector-field policy. Multiple demonstrations are composed by distance-weighted retrieval (top-K with softmax temperature). This decouples metric learning (state representation / distance) from behavior synthesis (flow composition). Experiments on PushT (state + vision), RoboMimic (Lift/Can/Square) and Adroit (Door/Pen/Hammer/Relocate) plus two real-robot tasks (box flip on ALOHA, fruit handover on Franka) show GPI attains equal or higher success than diffusion policies while being 20–100× faster and more memory-efficient; a Lyapunov-style analysis argues convergence of the flow policy.", "questions": "1.Retrieval & scaling. What is the exact complexity of one control step (in terms of demos N, trajectory lengths, and latent dimension)? Do you use approximate NN (e.g., FAISS) or down-sampling; how does latency scale to ~10⁶ states? \n\n2.Adaptive weighting. You set λ₁, λ₂ constant or distance-dependent. Can these be scheduled online (e.g., larger attraction far from demos, or curvature-aware progression) and do you have guidelines for selecting β, K robustly across tasks? \n\n3.Vision robustness. Since denv does not shape attraction, how do you mitigate mis-selection due to perceptual drift (e.g., lighting/occlusion)? Would a small attraction term in latent space (or a learned cross-term) help?\n\n4.Baselines. Could you add comparisons to flow-matching policies and recent “streaming flow” formulations that also interpret action trajectories as flows? This would clarify whether speed/robustness advantages hold beyond diffusion.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1.Clear geometric formulation & interpretability. Turning demonstrations into distance/flow fields yields an intuitive, controllable policy; the roles of attraction vs. progression and the top-K composition are explicit.\n\n2.Efficiency. State-based PushT runs at ~0.6 ms per step vs. ~65 ms for DDIM-10; vision-based uses a light encoder with small memory. No training is needed for state-based settings.\n\n3.Metric learning is flexible: task-specific heads, VAE latents, or pretrained features (ResNet/PCA, CLIP, SAM), and only robot-space distance shapes attraction—vision is used mainly for demo selection.\n\n4.Theoretical sanity check. A concise Lyapunov argument establishes asymptotic convergence in the actuated subspace under the proposed dynamics", "weaknesses": "1.Metric dependence & high-dimensional brittleness. Performance hinges on the chosen distance; SAM underperforms without fine-tuning, and the method relies on learned embeddings for selection while only drob shapes attraction—raising questions under perceptual noise or representation drift.\n\n2.Comparisons and settings. Diffusion baselines are strong but specific (DDPM-100/DDIM-10). It would help to compare against recent flow-matching/streaming-flow policy variants and to ensure action-space/horizon choices align fairly (the method uses H=1 reactive control).\n\n3.Assumption clarity. The convergence proof assumes smooth distance fields and projection to the nearest point on a continuous curve (e.g., splines). Practicalities with discrete demos, non-holonomic constraints, and contact discontinuities are not fully analyzed.", "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": "lXEbsxGx6H", "reviewer": "Reviewer_aXzo", "summary": "This paper proposes Geometry-aware Policy Imitation (GPI), a non-parametric approach to imitation learning that treats demonstrations as geometric curves inducing distance fields in state space. From these fields, GPI derives two control primitives: a progression flow (advancing along trajectories) and an attraction flow (correcting deviations). The method achieves competitive or superior performance compared to diffusion policies while being 20-100× faster and requiring less memory. Experiments span simulation (PushT, RoboMimic, Adroit) and real robots (ALOHA, Franka), demonstrating efficiency, multimodality, and robustness.", "questions": "See weaknesses.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "- The geometric perspective on imitation learning is intuitive and well-motivated. The idea is quite novel and interesting.\n- The policy inference speedup and memory reduction have a significant advantage over Diffusion Policy.\n- The 2D example is illustrative.", "weaknesses": "- The policy rollout success rates is almost the same as Diffusion Policy. The authors may use more complex tasks to show the performance differences.\n- The real robot experiments are limited and do not report success rates.\n- The paper does not compare to VINN (Pari et al. 2022), though cited as the closest prior work.\n- The paper does not explore under what conditions the convergence proof holds when dynamics are unknown/misspecified.\n- The paper does not show performances when demonstrations are suboptimal or contain mistakes.", "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": "6KurJqb4Or", "reviewer": "Reviewer_tvdn", "summary": "This paper proposes Geometry-Aware Policy Imitation (GPI), an imitation learning framework using expert demonstrations as state-space geometric curves. It generates a non-parametric vector field via distance fields, decouples metric learning and policy synthesis, and outperforms diffusion-based policies.", "questions": "see weakness section", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- This paper is overall very clearly written.\n\n- The proposed method is straightforward in implementation yet very effective.\n\n- Real-world experiments are valuable. I appreciate the authors' efforts to conduct real-world validations of their approach", "weaknesses": "**Weakness 1. Analysis of Stability Under Strong Perturbations**\n\nWhile the paper demonstrates robustness to small Gaussian perturbations and unknown dynamics, it lacks evaluation under strong, real-world perturbations (e.g., sudden object collisions, sensor noise bursts, or large deviations from demonstration trajectories). The Lyapunov stability proof in Appendix A assumes continuous state/action spaces and ideal distance field computation, but no experiments test whether GPI maintains convergence when perturbations violate these assumptions. This gap raises doubts about GPI’s practicality for unstructured environments where severe perturbations are common.\n\n\n**Weakness 2 Distance Metric Design and Adaptability**\n\nThe choice of distance metric (decomposed into $\\(d_{rob}\\) $and $\\(d_{env}\\)$) is a critical design lever for GPI, yet the paper relies on hand-tuned weights (e.g., $\\(w_{obj}=w_{agt}=w_{\\theta}=1.0\\$) in PushT) and preselected metric types (Euclidean for positions, geodesic for quaternions) without systematic validation of their optimality. Additionally, while the paper mentions making the metric \"learnable and co-optimized with policy synthesis\" as future work, it provides no analysis of how suboptimal metric choices (e.g., misweighted \\(d_{rob}\\) vs. \\(d_{env}\\)) impact performance—especially in tasks with complex state spaces (e.g., high-dimensional vision + multi-joint robot states).", "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)