Block-wise Adaptive Caching for Accelerating Diffusion Policy
Authors: Kangye Ji
Yuan Meng
Hanyun Cui
Ye Li
Jianbo Zhou
Shengjia Hua
Lei Chen
Zhi Wang
Venue: ICLR 2026 Poster (2026)
Keywords: Efficient AI
Diffusion Policy
Visuomotor Policy
Robotics
Action Generation
Model Caching.
Primary area: applications to robotics, autonomy, planning
TL;DR: We introduce Block-wise Adaptive Caching, an efficient training-free caching plugin to accelerate Diffusion Policy for triple times.

Abstract: Diffusion Policy has demonstrated strong visuomotor modeling capabilities, but its high computational cost renders it impractical for real-time robotic control.
Despite huge redundancy across repetitive denoising steps, existing diffusion acceleration techniques fail to generalize to Diffusion Policy due to fundamental architectural and data divergences.
In this paper, we propose **B**lock-wise **A**daptive **C**aching (**BAC**), a method to accelerate Diffusion Policy by caching intermediate action features. BAC achieves lossless action generation acceleration by adaptively updating and reusing cached features at the block level, based on a key observation that feature similarities exhibit non-uniform temporal dynamics and distinct block-specific patterns. 
To operationalize this insight, we first design an Adaptive Caching Scheduler to identify optimal update timesteps by maximizing the global feature similarities between cached and skipped features. However, applying this scheduler for each block leads to significant error surges due to the inter-block propagation of caching errors, particularly within Feed-Forward Network (FFN) blocks. To mitigate this issue, we develop the Bubbling Union Algorithm, which truncates these errors by updating the upstream blocks with significant caching errors before downstream FFNs.
As a training-free plugin, BAC is readily integrable with existing transformer-based Diffusion Policy and vision-language-action models.  Extensive experiments on multiple robotic benchmarks demonstrate that BAC achieves up to 3x inference speedup for free. Project page: https://block-wise-adaptive-caching.github.io.

Published as a conference paper at ICLR 2026
BLOCK-WISE ADAPTIVE CACHING FOR ACCELERATING DIFFUSION POLICY
Kangye Ji', Yuan Mengo! Hanyun Cui'; Ye Li', Jianbo Shenjja Hua" Lei Chen', Zhi Wang't TTsinguua Shenzhen International Graduate School, Tsinghua University *Department of Computer Science and Technology, Tsinghua University
ABSTRACT
Diffusion Policy has demonstrated strong visuomotor modeling capabilities, but its high computational cost renders it impractical for real-time robotic control. Despite huge redundancy across repetitive denoising steps, existing diffusion ac- celeration techniques fail to generalize to Diffusion Policy due to fundamental architectural and data divergences. In this paper, we propose Block-wise Adaptive Caching (BAC), a method to accelerate Diffusion Policy by caching intermediate action features. BAC achieves lossless action generation acceleration by adap- tively updating and reusing cached features at the block level, based on key observation that feature similarities exhibit non-uniform temporal dynamics and distinct block-specific patterns. To operationalize this insight, we first design an Adaptive Caching Scheduler to identify optimal update timesteps by maximizing the global feature similarities between cached and skipped features. However, applying this scheduler for each block leads to significant error surges due the inter-block propagation of caching errors, particularly within Feed-Forward Network (FFN) blocks. To mitigate this issue, we develop the Bubbling Union Algorithm, which truncates these errors by updating the upstream blocks with significant caching errors before downstream FFNs. As a training-fire plugin, BAC is readily integrable with existing transformer-base language- action models. Extensive experiments on multiple robotic benchmarks demonstrate that BAC achieves up to 3x inference speedup for free. Project page: fittps:/bblon wise adaptive inppiiiee caching gi githhb..o. io.
Diffusion Policy and vision-
INTRODUCTION
Diffusion Policy has gained substantial attention in robotic control, due to its ability to model action distributions via conditional denoising processes (Chi et al., 2023). Recently, it has also been widely adopted by vision- casioo-languagg-atttio to perform highly dexterous and complex tasks. However, its massive computational burden in the denoising process makes the action frequency unable to satisfy real-time and smooth control. For instance, on 6-DoF robotic arm executing block pick-and-place, 50 diffusion denoising steps at 1 ms per step restrict the action update rate to 10 Hz, well below 30-50 Hz usually needed for smooth real-time control (Shih et al., 2023).
models (Wen et al., 2025; Liu et al., 2025b; Hou et al., 2025)
Despite the aforementioned necessity, the acceleration of Diffusion Policy remains an underexplored field. Cache- based methods have recently gained significant attention in accelerating diffusion models on image- image-generatie generation tasks (Ma et al., 2024b; Wimbauer et al., 2024; Selvaraju et al., 2024; Chen et al., 2024; Zou et al., 2025) and video-generation tasks (Liu et al., 2024; Kahatapitiya et al., 2024; Lv et al., 2024). However, they cannot be directly applied to Diffusion Policy, due to differences in data characteristies and model architectures.
To address this issue, we aim to propose customized feature caching method for Diffusion Policy. We first explore the distinct characteristics of Diffusion Policy models and identify two key observations
1 *Corespooning authors
WWor performed during internship AMI.ab@SICC Tsinghua University

---

Published as a conference paper at ICLR 2026
Self Attention
Cross Alzention
FPN
0
1.0
1.0
0-
1.0
0.8
20-
0.8
Timestep
40-
Timestep
0.6
Tmestop
40
0.6
60
80
0.4
60
0.4
0.4
0.2
0.2
80
80
80
0.0
0.2
0.0
25
Timestep
Timestep
Timestep
(a) Feature similarities across timesteps.
Self Attention
Cross Attention
FFN
1.0
1.0
1.0
Similarity Value
Similarity Value
Similarity Value
0.8
0.8-
8.6
Layor
Layer
Layor
Laysz 0
Layer
Layar
Loyer
0.7
Layor 1
Layer 5
0.0
Layer
Layer
Layer
Layer
Layer 2
Layer
Layer
Layer?
0.6
Layor
Layer
Layer
20
40
6l
6b
60
80
0.5
20
40
60
80
Timesttpp
Timostep
Timestep
(b) Similarity change curves, measured between timestep and t- 10.
Figure I: Temporal and block-wise feature similarity patterns. (a) Similarity matrices of blocks in the third decoder layer. (b) Similarity change curves of different blocks. The feature similarity between consecutive timesteps varies non-uniformly over time and differs across blocks.
in feature similarities: (1) feature similarities across timesteps vary non-uniformly, and (2) different blocks exhibit distinct temporal similarity patterns as shown in Fig. I. Motivated by this observation, propose Block-wise Adaptive Caching (BAC), a training- free method that accelerates transformer- based Diffusion Policy by adaptively updating and reusing cached action features at the block level. BAC integrates Adaptive Caching Scheduler (ACS) to allocate block-specific caching schedules and the Bubbling Union Algorithm (BUA) to truncate inter-block error propagation.
Specifically, the Adaptive Caching Scheduler aims to identify maximize the global feature similarities between cached and skipped features. However, directly searching this set within an exponential search space is unacceptable. To address this challenge, we reformulate the problem as dynamic programming optimization, where the global similarity serves the objective and the block-specific similarity matrix defines the scores. Leveraging the high episode homogeneity within single task, the scheduler computes once before inference, incurring virtually no additional cost.
of cache update timesteps that
While the Adaptive Caching Scheduler effectively determines update timesteps, extending the scheduler to the block level can trigger significant error surges, leading to performance collapse. We examine this problem theoretically and experimentally and attribute this failure to inter-block caching error propagation: FFN blocks introduce the caching errors from upstream blocks during their updates, due to the lack of intermediate normalization. To truncate the error propagation, we propose the Bubbling Union Algorithm, which first selects the upstream blocks with large caching errors and then enforces them to update their cache if downstream FFNs do.
Our main contributions are as follows:
1. We propose Block-wise Adaptive Caching, training-free acceleration method for transformer based Diffusion Policy, which adaptively updates and reuses cached features at the block level.
2. We develop the Adaptive Caching Scheduler that optimally determines cache update timesteps by maximizing the global feature similarity with dynamic programming solver.
2

---

Published as a conference paper at ICLR 2026
3. We design the Bubbling Union Algorithm to further extend the caching schedule to the block level by truncating inter-block caching error propagation, based on the theoretical and empirical analysis of the error surge phenomenon in Diffusion Policy.
4. We conduct extensive robotic experiments to evaluate our method. The results demonstrate that our method efficiently boosts Diffusion Policy by 3x for free.
Uniform Caching
Adaptive Caching
Unified Schedule
Block-wise Schedule
Previous Paradigams
Block-wise Adaptive Caching
Figure 2: Comparison of Block-wise Adaptive Caching and previous caching paradigms.
RELATED WORK
2.1 DIFFUSION POLICY
Diffusion models, initially developed for image generation (Sohl-Dickstein et al., 2015; Ho et al., 2020; Esser al., 2024; Bar-Tal al., 2024), have been adapted for robot policy learning (Martinez- Cantin et al., 2007). Within the Diffusion Policy framework (Chi et al., 2023), both U-Net (Ron- neberger al., 2015) and Diffusion Transformer (DiT) (Peebles & Xie, 2023; Yuan al., 2024; Zhao et al, 2024) denoisers are supported, enabling scalable backbone designs. Recent VIA methods (Bro- han al., 2023; Kim et al., 2024; Wen al., 2024; 2025) increasingly adopt Transformer-based denoisers for stronger expressivity, but the iterative denoising steps induce significant inference latency, motivating acceleration techniques (Xu al., 2025; Song et al., 2025). Detailed discussion provided in Appendix A.2.
2.2 DIFFUSION MODELS CACHING
Despite the success of cache-based methods for diffusion models, their adaptation Diffusion Policy remains underexplored. Existing caching methods primarily target U-Net-based diffusion models (Ma al., 2024b; Wimbauer et al., 2024). For example, DeepCache (Ma et al., 2024b) exploits the temporal redundancy inherent in U-Nets by caching high-level feature representations. Nevertheless, these methods cannot be generalized to transformer backbones. Recently, some methods (Selvaraju et al., 2024; Ma et al., 2024a; Chen et al., 2024; Zou et al., 2025) explore the caching mechanism in transformer- based diffusion models. These methods typically operate at a coarse granularity, with all the blocks sharing uniform caching schedule (Selvaraju et al., 2024; Ma et al., 2024b), i.e., updating the cache at uniform intervals. Despite some works extending this schedule in finer architectural granularity, they either require extra training (Ma et al., 2024a) specifically designed for the patterns of the image generation process (Chen et al., 2024).
BLOCK- WISE ADAPTIVE CACHING
As illustrated in Fig. 3, BAC achieves a finer-grained cache schedule by first applying the Adaptive Caching Scheduler to compute optimal update timesteps for each block and then employing the Bubbling Union Algorithm to truncate inter-block eттor propagation. In this section, we first present the preliminaries in Sec. 3.1. Next, introduce the Adaptive Caching Scheduler in Sec. 3.2. To extend the scheduler to the block level, we analyze the error surge phenomenon in Sec. 3.3 and describe the Bubbling Union Algorithm in Sec. 3.4.
3

---

Published as a conference paper at ICLR 2026
3.1 PRELIMINARIES
Diffusion Policy. Diffusion Policy treats robot visuomotor control as sampling from conditional denoising diffusion model (Chi et al., 2023). At each time step t. we first draw an initial noisy action (K) from standard Gaussian prior and then apply K learned reverse-diffusee steps:
a,
a
(k-1) 1) fo (a
O1d. k),, k K, K
where fo parameterizes the conditional reverse kemel (i.e. the denoiser) and the final sample a, used as the control action.
(0) is
Diffusion Transformer (DiT). The DiT architecture in Diffusion Policy utilizes MLP encode observation embeddings, which are then passed into a transformer-batt -bsee decoder. The decoder consists of L. layers, where each layer contains cross-attention (CA) block that conditions timesteps and observations, a self-attention (SA) block, and a feed-forward network (FFN) block. For given imput h denoising step k, the output of layer is computed by summing the residual outputs of these blocks:
= hg (1-1) + S + C + FFFN
Problem Formulation. To reduce redundant computations across timesteps in the denoising process of diffusion models, cache-based methods reuse intermediate features to skip repeated computations partially. Following existing caching methods (Ma et al., 2024b; Selvaraju al., 2024), adopt update-then-reuse paradigm.
Let b& denote the output of target block step k. A caching mechanism defines a of update steps C (1...., K}. where:
The update step: If k E C. computes by and updates its cached features.
The reuse step: The block reuses the cached feature b which is computed in the most recent update step V'' = min(i E C k}.
Following prior work (Zou al., 2025; Selvaraju et al., 2024; Ma et al., 2024b), construct baseline in which all blocks share unified caching schedule, with a fixed update interval C (e.g.. updating the cache every three timesteps). BAC aims improve upon this baseline by allocating an optimal C* for each block.
3.2 ADAPTIVE CACHING SCHEDULER
Optimization Objective. In this work, we use cosine similarity to measure the similarity be- tween features due to its superior performance in measuring directional consistency between high- dimensional feature vectors. The consecutive similarity calculated as:
b
b b
8 = cos(ba. bx-1)
h = I...,,K,
(3)
b b bbll2
We define the interval similarity between timesteps and ((i.j) Σí Ekmip sk. A larger d(i, j) indicates lower caching errors incurred by reusing the cached feature by over the interval [i,j]. The value function is then:
M Σ m=0
max CL K)
O(C,, Cm+11 1), with co 0, CM+1 = K,
(4)
CC =
where oo and CM+1 boundary conditions representing the start step and the end step of the path.
4

---

Published as a conference paper at ICLR 2026
Adaptive Caching Scheduler
Budget
DP Solver
Optimal Caching Schedule
Nx Block
Temporal features
Similarity matrices
Bubbling Union Algorithm
4.2
Union
Error Score
Top-k k Selection
Block wise Error Propagation
Error Propagation Truncation
Stage1: Select upstream blocks
Stage2: Union from downstream FFN:
Residual Transformer Block
Updated features
Skipped features
Bubbling union
Figure 3: Framework of Block-wise Adaptive Caching (BAC). BAC enables adaptive feature caching by introducing the Adaptive Caching Scheduler, and further supports block-wise scheduling through the Bubbling Union Algorithm.
Optimal Schedule Solver. The combinatorial nature of selecting M update steps from K timesteps renders exhaustive search computationally infeasible for large K. To address this, we design dynamic programming (DP) solver that efficiently computes the optimal cache schedule.
Define DP state DP[m]]] [i] as the maximum cumulative similarity achievable when the m-th cache update occurs at timestep j:
DP[m][j] max Σ (e,, 6-1 11).
==0
The corresponding state transition equation is given by: 1|[6] + ((i,)))
DP(m]]ij] max [DP(m-
(6)
ogi<j
To recover the optimal update schedule C* from the DP table, we introduce pointer matrix: PTR[m]]] arg max (DP(m- 1][i] o(i.))), m 1, .., M, agi<)
1,..., K.
Once both DP table and PTR table are filled, we dertermine the final endpoint as: arg max DP[M]]] 15J5K
(8)
and backtrack from jr to reconstruct the full update schedule:
Ei j", c = [T[[m]][c]]] m m M,
(9)
The solved optimal update step set given by C* {oi <... < c Adaptive Caching Scheduler maximizes the performance efficiency trade-off by computing Ca for each block under the given computation budget.
3.3
THE ERROR SURGE PHENOMENON AND ANALYSIS.
However, purely extending the Adaptive Caching Scheduler to the block level can trigger significant enror surges, particularly within FFN blocks. We provide a detailed analysis of this failure mode in the following section and introduce remedy Bubbling Union Algorithm in Sec. 3.4.
5

---

Published as a conference paper at ICLR 2026
EPKO
FPS
TFN2
7.5
Fearse.r R.0100
Eriver Surge
FFN3
150
1.0
Timestep
PPN
(a)
EPNS
Block-dae Unitted
Slocknnde Unilied
Jpampp
TFSS
2.5
3.5
TENT
10
Timestep 14
Lagerooen
Tirastepp33 31
30
42 99 Timestops
(b)
(d)
(c)
Figure 4: (a) Caching enror of the third FFN block when updated using the block-wise versus unified schedule. (b) Caching error of sub-layers within the third FFN block at update timesteps 14 and 31. (c) Correlation between the caching errors of the seventh and eighth FFN blocks. (d) Update-induced error under varying input error magnitudes, controlled by the scaling factor B. (e) Caching error across all blocks throughout the diffusion process, with white dots indicating update steps. The experiments are conducted on the Square task.
Identifying Error Surge. Extending Adaptive Caching Scheduler to the block level leads to unexpected performance collapse. Our observation uncovers surprising phenomenon: instead of reducing errors, block-wise updates amplify them, resulting in sudden error surges in the FFN blocks, as illustrated in Fig. 4a.
Generally, caching errors arise from either feature reuse or feature update. In the reuse case, the eπго comes from mismatch between cached features and the shifted ground-truth distribution. In the update case, the error results from inaccurate inputs caused by errors from upstream blocks. We observe that error surges often occur during update steps of FFN blocks, where update-induced errors exceed reuse-induced errors, indicating a failure in the update process. We first elucidate how FFN blocks incorporate these upstream errors during updates, then delineate the complete inter-block error propagation process.
Error Propagation in FFN Blocks. To understand how FFN blocks incorporate the upstream errors, we begin by formalizing the error propagation process. Let
FFN(X) =
W (W + b1) + bz.
(10)
Proposition 3.1. Given upstream error 8, we have
A Wout diag(('(U)) (d)(U)) Win (A +(()))
(11)
where
A diag(r) (11
B diag(y) (X x(X)1) - -
(12)
o(X)
do(X)3
To further analyze the correlation between inter-block errors, design a toy experiment where the upstream block (FFN.6) uses only cached activations, while the downstream block (layer.7.FFN) performs full computation. The relationship between the update-induced error and its corresponding upstream error is depicted Fig. 4c, with a Pearson correlation coefficient of r = 0.9894, indicating strong correlation. To isolate the influence of the timestep. fix and factor 3 to control the magnitude of the upstream enror. The result in Fig. 4d also shows a strong positive correlation between upstream and downstream errors, further confirming the effect of inter-block error propagation.

---

Published as a conference paper at ICLR 2026
Inter-block Error Propagation. A complete propagation chain is shown in Fig. 4e. When block updates at timestep when its upstream block does not update and has a larger caching error, an error surge occurs, visually manifested by sudden deepening of block colors without any gradual transition. Although the upstream block updates later, the surging error in the downstream block still persists, indicating the failure of this update.
3.4 BUBBLING UNION ALGORITHM
To truncate inter-block error propagation, we propose simple yet effective algorithm to revise the original scheduler. The core insight of our algorithm that an FFN block updates its cache, its upstream blocks with large emrrs should also update. Therefore, the updated error A can be mitigated due to the suppressed propagated upstream error 8.
Our algorithm consists of two stages:
Stage 1: Selecting Upstream Blocks with Large Caching Errors. To estimate the caching error magnitude for each block j. compute the average of & norm across features over all pairs of denoising timesteps:
K Σ
e = K
(13)
t=lu=1
larger E, indicates that the block has larger reuse-induced errors. We then select the top n blocks with the largest f and denote this block set by U.
Remark 3.1. As discussed in Sec. 3.3, caching error consists of both reuse-induced errors and update-induced errors. We choose not account for the update-induced error of upstream blocks because it occurs less frequently and is difficult to approximate reliably. Moreover, incorporating would require treating all FFN blocks as upstream blocks, which would compromise the overall trade-off between efficiency and precision.
Stage 2: Unioning Update Timesteps of FENs from Downstream to Upstream. Our algorithm
truncates error propagation by enforcing that each upstream block in U updates its cache before its downstream FFN blocks. Concretely, let (uu) denote cache update timesteps set of block u. Let D(u) be the of all FFN blocks downstream of block u. Then for each u U, we update C(u) as:
C(u) = C(u) U U C(v) vED(u)
(14)
EXPERIMENTS
We first outline the experimental setup, covering benchmarks, baselines, implementation details, and metrics in Sec. 4.1. Following that, we evaluate BAC on the real-world and simulation benchmarks in Sec. 4.2 and Sec. 4.3, respectively. Finally, we present an ablation study of BAC in Sec. 4.4.
4.1 EXPERIMENTAL SETUP
Benchmarks. We comprehensively evaluate BAC across standard real-world and simulation bench- marks. For real-world evaluation, we deploy the Diffusion Policy on a Franka Research 3 arm equipped with a UGREEN CM717 RGB camera. The task requires the robot to grasp, pick, and release a soft, deformable bag whose diameter is approximately 80% of the gripper's maximum jaw opening. This setup requires precise temporal coordination to prevent the object from being toppled. For simulation, we utilize DP-T on four robotic manipulation benchmarks: Robomimic in PH/MH data, Push-T. Multimodal Block Pushing, and Kitchen. To test generalization on VLA models, we employ RDT-1B B on the ManiSkill benchmark, focusing on four representative tasks, e.g.. PegInsertionSide, PickCube, and StackCube.
Baselines. We report the result of DP-T Full Precision and utilize the baseline constructed in Sec. 3.1, in which all blocks update and reuse their cache at uniform intervals simultancously. We refer to this baseline Uniform. We migrate the cache update strategy from TeaCache (Liu et al.,
7

---

Published as a conference paper at ICLR 2026
Undiem (9:006
Saacia Basa (N0)
Iaterten
Figure 5: Left: Hardware setup for real-world evaluation. Right: Performance comparisons on inference frequency, end-to-end latency, and success rate.
2025a) and adapt our setting, which serves as another baseline, denoted as TeaCache, We also include DDIM the representative sampling- based method.
Implementation and Metrics. BAC is implemented as a training-free plugin. We set the hy- perparameter 5 for simulation tasks and 3 for real-world experiments. All experiments are conducted on single NVIDIA GeForce RTX 4090D GPU. We report Success Rate (or target coverage for Push-T) as the primary precision metric, alongside FLOPs and Speedup for efficiency. In real-world settings, we additionally measure Inference Frequency (Hz) and End-to-End Latency to quantify practical speedup.
4.2 REALWORLD BENCHMARK
Quantitative Results. As shown in Fig. 5, BAC significantly outperforms all baselines in both success rate and inference frequency. With
and n = 3, BAC achieves a 71% success rate at 39,2 Hz. By adopting more aggressive caching (S 5), BAC reaches peak inference frreuuency of 45.1 Hz while retaining a competitive 63% success rate. In contrast, the standard DDPM with K 100 steps yields only 3% success rate at impractical 7.8 Hz. Even with acceleration techniques such as DDIM with K = 50 or Uniform (S 20), success rates remain limited to 52% and 40%, respectively, due degraded generation quality.
Qualitative Analysis. Fig. illustrates clear behavioral differences across accelcration methods. BAC (S =) 5) achieves both high generation fidelity and low latency, enabling smooth and successful task execution. In comparison, baselines exhibit severe failure modes: DDPM with K 30 triggers premature picking and fails release, while Uniform poses lying outside the robot's kinematic reachability and subsequently releases too early. Moreover, both baselines suffer from high end-to-end latency of up to seconds, primarily caused by severe observation-actoo desynchronization. For DDPM methods, inference alone exceed 900 per action chunk, rendering predictions stale by the time they are executed. This lag induces wandering motions and chunk rollbacks, the controller attempts reach states that longer match the current state and observations.
20 stays still due to generated joint
DDPM
Early pick
No releuse
Uniiform
Stay still
Early velenve
13s
BAC
Pick
Release
Figure 6: Qualitative results of real-world evaluations from different methods.
8

---

Published as a conference paper at ICLR 2026
Table 1:
Results on different benchmarks. We present success rates different checkpoints in the format of (max performance) / (average of last 10 checkpoints), with each averaged across 3 training seeds. The overall average success rate is denoted AVG, with average flops and speedup reported as FLOPs and Speedx, respectively.
Benchmark on Proficient Human (PH) demonstration data.
Success Rate
Method
AVG FLOPs Speed
Lift
Can
Square
Transport
Tool
Push-T
Full Precision
1.00/1.00
0.95/0.97
0.82/0.88
0.78/0.81
0.43/0.53
0.59/0.64
0.76 15.77G
Uniform(fast)
0.99/1.00
0.93/0.96
0.86/0.88
0.78/0.77
0.39/0.50
0.58/0.64
0.79
3.15G
2.69
Unfform(fastest)
0.99/1.00
0.79/0.95
0.73/0.83
0.73/0.78
0.23/0.64
0.57/0.65
0.76
2.72G
3.20
Teacache(fast)
0.99/1.00
0.97/0.95
0.57/0.82
0.79/0.56
0.34/0.23
0.65/0.65
0.71
3.40G
2.23
Teacache(fastest)
1.00/1.00
0.96/0.96
0.67/0.82
0.77/0.52
0.44/0.38
0.63/0.52
0.72
2.78G
3.14
BAC(S = 7)
1.00/1.00
0.90/0.95
0.78/0.87
0.75/0.81
0.36/0.47
0.57/0.61
0.74
2.02G
3.54
BAC(S 10)
1.00/1.00 0.94/0.97 0.82/0.89
0.77/0.82
0.49/0.55
0.59/0.62
0.79 2.66G
3.40
Benchmark Mixed Human (MH) demonstration data.
Success Rate f
Method
AVG FLOPs Speed
Lift
Can
Square
Transport
Full Precision
0.99/1.00
0.92/0.97
0.76/0.79
0.35/0.46
0.76 15.77G
Uniform(fast)
0.99/0.99
0.91/0.96
0.80/0.75
0.24/0.42
0.76
3.15G
2.69
Uniform(fastest)
0.95/1.00
0.65/0.92
0.73/0.78
0.01/0.06
0.64
2.72G
3.20
Teacache(fast)
0.79/0.85
0.97/0.92
0.76/0.66
0.50/0.40
0.73
5,25G
1.41
Teacache(fastest)
0.00/0.02
0.97/0.90
0.26/0.22
0.35/0.31
0.38
2.62G
3.44
BAC(S 7)
0.96/0.99
0.39/0.79
0.56/0.53
0.17/0.41
0.60
2.03G
3.48
BAC(S 10)
0.99/0.98
0.95/0.97
0.77/0.79
0.30/0.46
0.77
2.64G
3.41
Benchmark on multi-stage tasks. For Block-Pushing, px is the frequency of pushing x blocks into the targets. For Kitchen, px is the frequency of interacting with or more objects (c.g. bottom burner..
Success Rate
Method
AVG FLOPs Speed
BP,1
BP,
Kit,1
Kity2
Kitpa
Kitp4
Full Precision
0.98/0.98
0.98/0.96
1.00/1.00
0.98/1.00
0.97/1.00
0.95/0.97
0.98 15.77G
Uniform(fast)
1.00/1.00
0.97/0.97
0.97/1.00
0.93/1.00
0.91/0.99
0.79/0.93
0.96
3.15G
2.85
Uniform((astest)
0.99/0.99
0.95/0.95
0.66/0.89
0.42/0.79
0.29/0.63
0.08/0.34
0.66
2.72G
3.34
Tcasache(fast)
0.33/0.33
0.33/0.49
0.75/0.76
0.24/0.18
0.27/0.13
0.00/0.00
0.52
1.82G
4.42
(fasache(fastest)
0.33/0.33
0.00/0.00
0.75/0.76
0.24/0.18
0.27/0.13
0.00/0.00
0.25
1.80G
4.46
BAC(S 7)
0.99/0.99
0.91/0.93
0.80/0.85
0.61/0.69
0.45/0.57
0.23/0.39
0.69
1.92G
3.78
BAC(S 10)
1.00/0.99
0.97/0.95
1.00/0.99
1.00/0.99
1.00/0.99
0.94/0.97
0.98
2.44G
3.60
4.3 SIMULATION BENCHMARK
Acceleration on Diffusion Policy. We compare BAC against the baselines across multiple simula- tion benchmarks in Table I. We control the computation budget by setting the number of cache update steps S. BAC achieves lossless acceleration with S 10 all the benchmarks, with an average success rate of 0.79, 0.77, 0.98 versus 0.76, 0.76, 0.98 for the full full-precision DP-T, even exhibiting a modest improvement. BAC consistently achieves stable acceleration rates above 3.4x across most of the tasks. Compared with Uniform and Teacache, BAC has two advantages: (1) BAC improves the success significantly the hard tasks such Kitchen,4, where Uniform and Teacache fail to

---

Published as a conference paper at ICLR 2026
1.1
1.0
0.0
0,5
0.2
Origiol
BAC B
BAC 21
Metbod
Tack
(a)
(b)
Figure 7: (a) Performance of BAC RDT-1B. (b) Ablation study BAC.
restore the correct action generation. (2) BAC maintains strong and stable performance in all tasks, demonstrating the reliability of lossless acceleration plugin. We attribute this to the ability of BAC reduce the reuse-induced error by ACS and precisely avoid the update-induced errors by BUA.
Acceleration on VLA. As summarized Fig. 7a, BAC achieves up to 3.55 acceleration with negligible performance drop compared to the original RDT-IB (Liu et al., 2025c) at S 2, while maintaining lossless performance at 1. These results demonstrate that BAC delivers significant speed gains when combined with DPMSolver, providing strong evidence of its robust generalization across Diffusion Policy-based VLA models.
4.4 ABLATION STUDY
Ablation Study Methods. We consider three variants of our caching method. To evaluate the effectiveness of ACS, build Unified ACS, the Adaptive Caching Scheduler is applied solely to the self-attention block in layer 0, which is the very first block in the decoder. The computed update steps are then used by every block. To evaluate the effectiveness BUA, build Block-wise ACS, the scheduler is naively applied to each block, producing a distinct set of update steps for all blocks. Finally, Block-wise ACS BUA, we first compute block-wise update steps Caching Scheduler and then integrate the Bubbling Union Algorithm, yielding our full BAC method. Results of these methods are presented in Fig. 7b.
Adaptive
Effectiveness of ACS. Experiments with the Unified ACS schedule demonstrate clear performance improvement over Uniform. This result confirms the necessity and effectiveness of reducing the reuse-induced error.
Effectiveness of BUA. The performance of Block-wise ACS unexpectedly falls below that of the Unified ACS, empirically substantiating the Error Surge Phenomenon. Integrating BUA into the block-wise schedule recovers full-precision performance across all tasks with the highest score of 0.79, demonstrating the effectiveness the Bubbling Union Algorithm.
CONCLUSION
In this paper, we propose BAC, novel training-free acceleration method for transformer-based Diffusion Policy. BAC minimizes the caching error by adaptively scheduling cache updates through the Adaptive Caching Scheduler. Moreover, we conduct theoretical and empirical analysis on the error surge phenomenon due to inter-block eиror propagation, and propose the Bubbling Union Algorithm to truncate the propagation. Extensive experiments demonstrate that BAC achieves substantial speedups without performance degradation, typically exceeding 3x compared to full computation.
10

---

Published as a conference paper at ICLR 2026
ETHICS STATEMENT
In this work, all experiments are based on publicly available robotic simulation datasets, without involving new human subjects, personal data, or sensitive information. Our method focuses solely on improving computational efficiency and raises no concerns of privacy infringement, discrimination, bias, legal non compllaaee
REPRODUCIBILITY STATEMENT
We have made extensive efforts to ensure reproducibility of our results. All datasets used in this work are publicly available robotic simulation benchmarks (RoboMimic, Push-T, Kitchen, Bllock-Pushing ManiSkill), with details of preprocessing and task setups provided in Appendix A.7. The proposed Block-wise Adaptive Caching (BAC) algorithm is fully described in Section 3, with implementation details and hyperparameters reported in Section 4.1. Complete theoretical assumptions and proofs, including Proposition 3.1, are presented in Appendix A.4. Additional ablation studies, parameter sensitivity analyses, and visualizations are included the supplemental material (Appendix A.7, A.8, A.9, A.12, A.13) to further support reproducibility. The full implementation and instructions will be released on an open-source GitHub repository to enable replication of all experiments.
8 ACKNOWLEDGEMENT
This work is supported by the National Natural Science Foundation China (Grant No. 92467204, 62472249, and 62402264), and the Shenzhen Science and Technology Program (Grant No. JCY10020818101014000 and KIZD202240003100000000
REFERENCES
Omer Bar-Tal, Hila Chefer, and Lumiere: space-time diffusion model for video generation. In SIGGRAPH Asia 2024 Conference Papers, pp. 1-11. Placeholder Publisher, 2024.
Anthony Brohan, Noah Brown, Justice Carbujal, Yevgen Chebotar, Xi Chen, Krzysztof Choromanski, Tianli Ding, Danny Driess, Avinava Dubey, Chelsea Finn, et al. Rt-2: Vision- Vasion-language-actii models transfer web knowledge to robotic control. arXiv preprint arXiv:2307. 2023.
Pengtao Chen, Mingzhu Shen, Peng Ye, Jianjian Cao, Chongjun Tu, Christos-Savver Bouganis, Yiren Zhao, and Tao Chen, 8-dit: A training- free acceleration method tailored for diffusion transformers. arXiv preprint arXiv:2406.011 /25, 2024.
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 International Journal Robotics Research, pp. 02783649241273666 2023.
Hao-Ties TienTTien Lewis Chiang, Zhuo Xu, Zipeng Fu, Mithun George Jacob, Tingnan Zhang, Tsang- Wei Edward Lee, Wenhao Yu. Connor Schenck, David Rendleman, Dhruv Shah, et al. Mobility vla: Multimodal instruction navigation with long-context vlms and topological graphs. arXiv preprint arXiv:2407.07775, 2024. Submitted to Some Conference, unpublished.
Patrick Esser. Sumith Kulal, Andreas Blattmann. Rahim Entezari, Jonas Müller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, et al. Scaling rectified flow transformers for high-resolution image synthesis. In Forty-first international conference machine learning, 2024. Submitted to Some Conference, unpublished.
Pete Florence, Corey Lynch, Andy Zeng, Oscar A Ramirez, Ayzaan Wahid, Laura Downs, Adrian Wong, Johnny Lee, Igor Mordatch, and Jonathan Tompson. Implicit behavioral cloning. In Conference robot learning, pp. 158-168. PMLR, 2022.
Abhishek Gupta, Vikash Kumar, Corey Lynch, Sergey Levine, and Karol Hausman. Relay policy learning: Solving long- hongznorizon tasks via imitation and reinforcement learning. arXiv preprint arXiv: 1910. 1956. 2019.
11

---

Published as a conference paper at ICLR 2026
Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840-688 6851, 2020.
Zhi Hou, Tianyi Zhang, Yuwen Xiong, Hengjun Pu, Chengyang Zhao, Ronglei Tong. Yu Qiao, Jifeng Dai, and Yuntao Chen. Diffusion transformer policy, arXiv preprint arXiv:2410.15959 2024.
Zhi Hou, Tianyi Zhang, Yuwen Xiong, Haonan Duan, Hengjun Pu, Ronglei Tong, Chengyang Zhao, Xizhou Zhu, Yu Qiao, Jifeng Dai, et al. Dita: Scaling diffusion transformer for generalist vision-languagc-actionn policy. arXiv preprint arXiv:2503.19755 2025.
Kumara Kahatapitiya, Haozhe Liu, Sen He, Ding Liu, Menglin Jia, Chenyang Zhang, Michael Ryoo, and Tian Xie. Adaptive caching for faster video generation with diffusion transformers. arXiv preprint arXiv:2411.00000 1.0297,, 2024.
Moo Jin Kim, Karl Pertsch, Siddharth Karamcheti, Ted Xiao, Ashwin Balakrishna, Suraj Nair, Rafael Rafailov, Ethan Foster, Grace Lam, Pannag Sanketi, et al. Openvla: An open-source vision-language-action model. arXiv preprint S1.ii::2006.9244440 2024.
Chengmeng Li, Junjie Wen, Yan Peng, Yaxin Peng, Feifei Feng, and Yichen Zhu, Pointvla: Injecting the 3d world into vision-language-action models. arXiv preprint arXiv:2503.07511 2025.
Feng Liu, Shiwei Zhang, Xiaofeng Wang, Yujie Wei, Haonan Qiu, Yuzhong Zhao, Yingya Zhang, Qixiang Ye, and Fang Wan. Timestep embedding tells: It's time to cache for video diffusion model. arXiv preprint 24 2024.
Feng Liu, Shiwei Zhang, Xiaofeng Wang, Yujie Wei, Haonan Qiu, Yuzhong Zhao, Yingya Zhang, Qixiang Ye, and Fang Wan. Timestep embedding tells: It's time to cache for video diffusion model, 2025a. URL https:// arxii org/ abs/ 2411 11.11.91111 19.08
Jiaming Liu, Hao Chen, Pengju An, Zhuoyang Liu, Renrui Zhang, Chenyang Gu, Xiaoqi Li, Ziyu Guo, Sixiang Chen, Mengzhen Liu, et al. Hybridvla: Collaborative diffusion and autoregression in unified assion-language-acteo action model. arXiv preprint arXiv:2503.106: 2025b.
Songming Liu, Lingxuan Wu, Bangguo Li, Hengkai Tan, Huayu Chen, Zhengyi Wang, Ke Xu, Hang Su, and Jun Zhu, Rdt-1b: a diffusion foundation model for bimanual manipulation, 2025c. URL https:/ /taa:////xxvvvv org/ abs////////// 2210. 07864.
Zhengyao Lv, Chenyang Si, Junhao Song. Zhenyu Yang, Yu Qiao, Ziwei Liu, and Kwan- Yee K Wong. Fastercache: Training-free free video diffusion model acceleration with high quality. arXiv preprint MAXi:22410.1935: 2024.
Xinyin Ma, Gongfan Fang, Michael Bi Mi, and Xinchao Wang. seamnin--to-cchhe Accelerating diffusion transformer via layer caching, Advances in Neural Information Processing Systems, 37: 133282-133304, 2024a.
Xinyin Ma. Gongfan Fang, and Xinchao Wang. Deepcache: Accelerating diffusion models for free. In Proceedings of the IEEF/CVF conference computer vision and pattern recognition, pp- 15762-15772. Placeholder Publisher, 2024b.
Yueen Ma. Zixing Song. Yuzheng Zhuang. Jianye Hao, and Irwin King. A survey vision- lision-language- action models for embodied ai. arXiv preprint arXiv:2405. 1409,, 2024c. Submitted to Some Conference, unpublished.
Ajay Mandlekar, Danfei Xu, Josiah Wong, Soroush Nasiriany, Chen Wang, Rohun Kulkarni, Li Fei- Fei, Silvio Savarese, Yuke Zhu, and Roberto Martín-Martin What matters learning from offline human demonstrations for robot manipulation. In Proceedings of the Conference on Robot Learning (CoRL), 2021.
Ruben Martinez- Martinez-Cantin, Nando de Freitas, Amaud Doucet, and José A Castellanos. Active policy learning for robot planning and exploration under uncertainty. In Robotics: Science and systems, volume 3, pp. 321 128.. Placeholder Publisher, 2007.
12

---

Published as a conference paper at ICLR 2026
William Peebles and Saining Xie. Scalable diffusion models with transformers. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 4195-4205, 2023. Submitted to Some Conference, unpublished.
Olaf Ronneberger, Philipp
Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In Medical image computing and compater-assisted Intervention-MIICAA 2015: 18th international conference, Munich, Germany, October 5-9, 2015, proceedings, part part III 18, pp. 234-241, 2015.
Pratheba Selvaraju, Tianyu Ding, Tianyi Chen, Ilya Zharkov, and Luming Liang. Fora: Fast-forward caching in diffusion transformer acceleration. arXiv preprint arXiv:2407.01425, 2024.
Nur Muhammad Shafiullah, Zichen Cui, Ariuntuya Arty Altanzaya, and Lerrel Pinto. Behavior transformers: Cloning k modes with one stone. Advances in neural information processing systems, 35:22955-22968, 2022.
Andy Shih, Suneel Belkhale, Stefano Ermon, Dorsa Sadigh, and Nima Anari. Parallel sampling of diffusion models. Advances in Neural Information Processing Systems, 36:4263 4276,,4476660000 2023.
Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli. Deep unsupervised learning using nonequilibrium thermodynamics. In International conference on machine learning. pp. 2256-2265 pmlr, Placeholder Publisher, 2015.
Wenxuan Song, Jiayi Chen, Pengxiang Ding, Han Zhao, Wei Zhao, Zhide Zhong, Zongyuan Ge, Jun Ma, and Haoang Li. Accelerating vision-language-action model integrated with action chunking via parallel decoding. arXiv preprini arXiv:2503.023110 2025. Submitted to Some Conference, unpublished.
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention all you need. Advances in neural information processing systems, 30, 2017.
Junjie Wen, Minjie Zhu, Yichen Zhu, Zhibin Tang, Jinming Li, Zhongyi Zhou, Chengmeng Li, Xiaoyu Liu, Yaxin Peng. Chaomin Shen, et al. Diffusion- vla: Scaling robot foundation models via unified diffusion and autoregression. arXiv preprint arXiv:2412.03390 2024. Submitted to Some Conference, unpublished.
Junjie Wen, Yichen Zhu, Jinming Li, Zhibin Tang, Chaomin Shen, and Feifei Feng. Dexvla: Vision-language model with plug-in diffusion expert for general robot control. arXiv preprint arXiv:2502.05885, 2025. Submitted to Some Conference, unpublished.
Felix Wimbauer, Bichen Wu, Edgar Schoenfeld, Xiaoliang Dai, Ji Hou, Zijian He, Artsiom Sanakoyeu, Peizhao Zhang, Sam Tsai, Jonas Kohler, et al. Cache me if you can: Accelerating diffusion models through block caching. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 6211-6220, 2024.
Tian- Yu Xiang, Ao-Qun Jin, Xiao-Hu Zhou, Mei-Jiang Gui, Xiao-Liang Xie, Shi-Qi Liu, Shuang. Yi Wang, Cheng-Bin Duang, Si- Si-Cheng Wang, Zheng Lei, et al. Vla model-expert collaboration for bi-directional manipulation learning. arXiv preprint arXiv:2503.0416. 2025.
Siyu Xu, Yunke Wang, Chenghao Xia, Dihao Zhu, Tao Huang, and Chang Xu. Vla-cache: Towards efficient vision-language-actioo model via adaptive token caching in robotic manipulation. arXiv preprint arXiv:25022.02175 2025. Submitted to Some Conference, unpublished.
Zhihang Yuan, Hanling Zhang, Lu Pu, Xuefei Ning, Linfeng Zhang, Tianchen Zhao, Shengen Yan, Guohao Dai, and Yu Wang. Ditfastattn: Attention compression for diffusion transformer models. Advances in Neural Information Processing Systems, 37:1 19699 2024. Submitted to Some Conference, unpublished.
Wangbo Zhao, Yizeng Han, Jiasheng Tang, Kai Wang, Yibing Song, Gao Huang, Fan Wang, and Yang You. Dynamic diffusion transformer. arXiv preprint arXivv2410.03456. 2024. Submitted to Some Conference, unpublished.
Chang Zou, Xuyang Liu, Ting Liu, Siteng Huang, and Linfeng Zhang. Accelerating diffusion trans- formers with token-wiss wise feature caching. International Conference on Learning Representations (Poster Track), 2025. URL https: wtweeerreeeew.ee/ooouniio..
13

---

Published as a conference paper at ICLR 2026
A APPENDIX / SUPPLEMENTAL MATERIAL
In this supplemental material, we provide declaration of LLMs uses in Appendix A. detailed back- ground on diffusion-based VLA models in Appendix A.2, limitation of our work in Appendix A.3, complete proofs of Proposition 3.1 in Appendix A.4, discussion on cause of error surge phenomenon in Appendix A.5, more details on the benchmark in Appendix A.6, along with additional experiments examining the choice of parameter v in Appendix A.7. We further include ablation studies analyzing different metrics in Appendix A.8, and present more temporal similarity figures in Appendix A.9. Additionally, Appendix A.10 10 contains illustrations demonstrating episode homogeneity within in- dividual tasks, while Appendix A. offers supplementary visualizations supporting Figure 3. In Appendix A.12 and Appendix A.13, we present the update steps obtained under S = 10, = 5, while using cosine as metric via BAC, showing the update steps obtained after employing ACS and BUA, respectively. In Appendix A.14, we provide detailed visualizations and analysis of the cache behavior. We provide large-scale evidence showing that episodes within the same task exhibit strong homogeneity in Appendix A.15. Finally, demonstrate that BAC provides additional speedup even when applied on top of the DDIM baseline in Appendix A.16.
A.1 THE USE OF LARGE LANGUAGE MODELS (LLMs)
In this work, Large Language Models (LLMs) were used solely to polish the language for clarity and readability. No LLMs were employed for idea generation, experimental design, data analysis, or any other part of the research process.
A.2 BACKGROUND ON DIFFUSION BASED VLA MODELS
Diffusion models (Esser al., 2024; Bar-Tal et al., 2024) were originally proposed for image generation (Sohl-Dickstein et al., 2015: Ho et al., 2020) and have been adapted for robot policy learn- ing (Martinez-Cantin et al., 2007). Traditionally, diffusion-based vision-language-action (VLA) (Ma et al., 2024c; Brohan et al., 2023; Kim et al., 2024) methods have depended on U-Net (Ronneberger al., 2015) based denoising backbones borrowed directly from image generation pipelines to model multimodal action distributions and ensure stable training. Within the Diffusion Policy framework (Chi et al., 2023), both U-Net and Diffusion Transformer (DiT) (Peebles & Xie, 2023; Yuan et al., 2024; Zhao et al., 2024) denoisers are supported, enabling exploration of hybrid backbone designs. More recent work has begun to replace U-Net with DiT architectures to improve scalability and expressive power. Diffusion Transformer Policy (Hou et al., 2024) is itself DiT variant within the broader Diffusion Policy framework and uses a large-scale Transformer (Vaswani et al., 2017) as the denoiser in continuous action spaces, conditioned on visual observations and language instructions. The Diffusion- -Vtttssioo--LAAA framework (Wen et al., 2024) unifies autoregressive next-token reasoning with diffusion based action generation into single, scalable framework for fast, interpretable, and gener- alizable visuomotor robot policies. Dcx VLA (Wen et al., 2025) introduces plug-in diffusion expert modules that decouple action generation from the core VLA backbone. However, the iterative denois- ing steps inherent in diffusion models introduce substantial inference latency that poses challenges for figh-freqency VLA tasks requiring real-time responsiveness. Consequently, accelerating the inference procedure of diffusion-based policies through techniques such as caching (Xu et al., 2025; Song et al., 2025) is critical for deploying responsive VLA-driven agents (Chiang et al., 2024; Xiang et al., 2025; Li et al., 2025).
A.3 LIMITATION
The primary limitation of our work arises when the base model's 's accuracy on a given task very low, as our caching strategy may inadvertently amplify this inaccuracy.
A.4 PROOF FOR PROPOSITION 3.1
Assumption A.I.
1. Activation function & is twice continuously differentiable with bounded second derivative
2. LayerNorm variance a (X) amin > O for all valid imputs X
14

---

Published as a conference paper at ICLR 2026
3. Weight matrices satisfy ||ill2 S C1. 2W2 S C2 fixed constants C1, C2 Proposition A.1. Under Assumption 1, input error ò with || S 6, the FFN block outpu enrrr admits the first-order approximation:
FFN + (X) f(6) + 0(16]])
(15)
where the linear response operator [()) is given by:
((6) W2 diag( (U)) Wi (A B)8
(16)
with U (X) + by and operators:
A diag(7) (7) (1 - (1- 111
(17)
o(X)
B diag(7) . (XX) (XX)1)
(18)
(x)
Proof. We analyze the propagation of input error 8:
Let Let = IN(X + 6) - IN(X). Define:
_ m(X), x Ms - p(8), 0f 02 +
The mean of X d given by:
1 1 _ pa
D m(x +))
p
(19)
d
The variance of X + 8 given by:
0/ 2 =|X + - 0 1s)
2
0² + d
(X pu) psl) + O(118113
(20)
Taking the square root and expanding:
(X p1) T
Ao
+ 0118113
(21)
do
For each dimension d:
X; 0: 11 418
X; K3-Ma
AX,
a + Ag
8 μi
[X; H1
02 Ao
(22)
Substituting Ao from Eq. 21 yields
AX
8
M5
(Xi
Σ (Xx -p1) 6x
do3
k=1
d
(6s) 4)
7 (X; n)(X,, 11)
53.
(23)
d
j=1
15

---

Published as a conference paper at ICLR 2026
Eq. 23 implies:
AX diag(?) (1 11
diag(?) (X -1) -11) 8 + 0(16113)
(24)
do3
The error propagates through the first linear layer:
AU - WA- -
(25)
Using Taylor expansion of & at U:
ΦU + AU) ((U) diag()'(U))AU A 0(]AU11)))
diag(d'(U))W, B) + O(1ā)
(26)
Finally, projecting through W2:
((6) = W2 diag(d W3 (A - 6)
(27)
The proof is complete.
A.5 DISCUSSION ON CAUSE OF ERROR SURGE PHENOMENON
Based on Eq. 10, we conducted additional experiments to examine the Frobenius norm distributions of weights across different blocks. In FFN blocks, errors propagate sequentially through a layer normalization, the first linear transformation (Wi), 1), a GELU activation function, and the second linear transformation (W2). In contrast, error propagation in attention blocks involves layer normalization, the query W)), key (WK). and value (Wv) projection matrices, and an output projection matrix that aggregates the multi-hear attention outputs. As illustrated in Fig. 8, we found that the magnitudes of Wi and W₂ are approximately three times larger than those of Wv. This substantial difference in weight magnitudes likely contributes to the observed error surges within FFN blocks. Furthermore, the absence of intermediate normalization steps between the two linear layers FFN blocks may exacerbate error amplification.
A.6 MORE DETAILS ON BENCHMARKS
A.6.1 DATASETS
Pusht-T. This dataset is based on the implicit behavioral cloning benchmark introduced by Florence et al. (Florence et al., 2022), comprising human-collected demonstrations of T-shaped block pushing with top-down RGB observations and 2D end-effector velocity control. Variation added by random initial conditions for T block and end-effector. The task requires exploiting complex and contact-rich object dynamics to push the block precisely, using point contacts. There are two variants: one with RGB image observations and another with 9 2D keypoints obtained from the groundtruth pose of the T block, both with proprioception for endeffector location (Chi et al., 2023).
Block Pushing. This dataset consists of scripted trajectories first presented in Behavior Transformers by Shafiullah al. (Shafiullah et al., 2022). This task tests the policy's s ability to model multimodal action distributions by pushing two blocks into two squares in any order. The demonstration data is generated by scripted oracle with access to groundtruth state info (Chi et al., 2023).
Franka Kitchen. This dataset originates from the Relay Policy Learning framework proposed by Gupta et al. (Gupta et al., 2019), featuring 566 VR tele-operated demonstrations of multi-step manipulation tasks in simulated kitchen using 9-DoF Franka Panda arm. The goal is execute
16

---

Published as a conference paper at ICLR 2026
34-V
140
Uncel
3A-V
Lnvel
CM.V
Lineez
259
CA.
$6.0
$6.0
Nhan Sterhlle
CA-
C1.0
100
Layer tados
Lagus
Lages
Laper
(a) Block pushing
(b) Kitchen
175
Ginel
Lieet
120
Grow?
150
CA.V
150
135
125
180
Layrer tadie
Lugar mmdcs
Layert tedic
(c) Square
(d) Tool
S6.V
Tawel
145
FA.V
Grael
CA.V
1awa2
CA.V
Graa?
SAO
$6-0
San tilee
CNA
Layer
Laper
(c) Transport
(f) Can
Figure 8: Weight Norm
17

---

Published as a conference paper at ICLR 2026
many demonstrated tasks as possible, regardless of order, showcasing both short hoort-h and long-horizon multimodality (Chi et al., 2023).
RoboMimic. This dataset, introduced by Mandlekar et al. (Mandlekar et al., 2021), covers five manipulation tasks. Each task includes four of the tasks additionally offer Mixed- (MH) sets combining proficient and non-proficient operators (9 variants in total). The PH data were recorded by a single operator via the RoboTTurk platform, whereas the MH sets were collected from six different operators using the same system.
Cooficient-Human (PH) teleoperated demonstration set, and
(d)
Figure 9; Visualizations of different tasks. (a) Can (b) Lift (c) Square (d) Transport (e) Tool honl.hang.
Fig. 9 illustrates the five subtasks in the RoboMimic Image dataset. Below we describe each subtask.
Can (Fig. 9a): The robot must grasp cylinder-shaped object and placing it into bin. This subtask tests precise grasp planning and fingertip control under varying object poses (Mandlekar et al., 2021).
Lift (Fig. 9b):
The manipulator picks up heavier, irregularly shaped object (e.g. small box) and raises it to designated height. It evaluates the policy's ability to modulate grip force and maintain stable trajectories (Mandlekar al., 2021).
Square (Fig. 9c): The agent must push or slide object so that its center follows a square- shaped path on the table. This challenges both straight- control and precise cornering maneuvers (Mandlekar al., 2021).
Transport (Fig. 9d): The agent must learn bimanual maneuvers to transfer hammer from a closed container on shelf to the target bin on another shelf. It tests coordinated lifting and translational motion under variable loads (Mandlekar et al., 2021).
Tool Hang (Fig. 9e): The robot arm must learn gigh-precision manipulation behaviors to assemble a frame by inserting hook into narrow base. This requires fine-tuned wrist orientation and insertion accuracy (Mandlekar al., 2021).
A.6.2 PRE-TRAINED CHECKPOINTS
We use the pre-trained checkpoints of di fffffuusiio ti Diffusion Policy (Chi et al., 2023), where checkpoints of image-based tasks stored under link and those of multi-stage tasks are stored under link². Following Diffusion Policy (Chi ct al., 2023), evaluate the success rates of two types of checkpoints: The checkpoints that achieve the maximum performance during training and those stored the last 10 epochs. For robustness, these checkpoints collected in three training seeds.
model provided by
A.7 ADDITIONAL EXPERIMENTS ON Y
In this experiment, aim to
questions: (1) how influences the effectiveness of BUA in mitigating update-induced error? (2) Does the effectiveness of relate to S?
To answer question 1, evaluate all tasks with 3 and cache number S 10. As shown in Table 2, when n = 3, the average success rates for the three task categories were 0.71, 0.77, and 0.97, respectively, which slightly lower than those for
(0.79, 0.77, 0.98) but still significantly
cs..cs.oo / ffusion-pol icy. cs. col uumbi /dt/ htt.bbbaaaaae/aaaaaa//eerreeeeee http://ttaaaeeeeeee///eeeee/s/// mage// Phttps://di ffusion-pol icy. cs. col umbi edu/ /eepeeepperreeeeeeeeeeeeeeeeeeme ow_dim/
18

---

Published as a conference paper at ICLR 2026
better than the Uniform baseline. Increasing further improve performance at the cost of higher computational overhead. Therefore, we choose n = 5 as the default setting, as it achieves lossless performance while maximizing acceleration.
To answer the second question, we investigate the relationship between the hyperparameter n (number of selected upstream blocks) and (cache number) in the context of the effectiveness of BUA in mitigating update-inde induced errors. The experimental results Table demonstrate that the effectiveness of is closely tied to S.
n plays a more important role in mitigating update- errors. For certain difficult tasks, such Tool_ pangph and Transportma, the results for n. 3, 20 (e.g., 0.32/0.53 and 0.29/0.43, respectively) are outperformed by n = 5, S = 10 (e.g.. 0.49/0.55 and 0.30/0. respectively). This indicates that an appropriately tuned plays dominant role in optimizing the effectiveness of BUA for challenging tasks.
Notebly, the effectiveness of n depends on an appropriate S. for fixed n 3, increasing S from to 20 significantly improves the average success rate across tasks with performance collapse, from 0.07 = 5 to 0.80 update-induced errors. Thus, the interplay between n and S suggests that balanced combination, such as 5, S 10, achieves robust performance across diverse tasks.
20, suggesting that a larger number of cache update steps helps to mitigate
Table Effect of the hyperparameter on the mitigation of update-induced induced error across PH, MH and multi-stage settings by BUA (S 10).
Benchmark on Proficient Human (PH) demonstration data.
Success Rate
Method
AVG FLOPs Speed
Lift
Can
Square
Transport
Tool
Push-T
BAC (n
1.00/1.00
0.93/0.96
0.83/0.91
0.81/0.79
0.03/0.07
0.59/0.60 0.71 2.39G
3.21
BAC (n 1.00/1.00
0.94/0.97 0.82/0.89
0.77/0.82
0.49/0.55
0.59/0.62 0.79 2.66G
3.40
Benchmark Mixed Human (MH) demonstration data.
Success Rate
Method
AVG FLOPs Speed x
Lift
Can
Square
Transport
BAC (n 3)
0.97/0.99
0.93/0.97
0.79/0.77
0.21/0.53
0.77 2.48G
3.21
BAC (n 0.99/0.98
0.95/0.97
0.77/0.79
0.30/0.46
0.77
2.64G
3.41
Benchmark on multi stage tasks. For Block Block-Pushing task, pz the frequency of pushing x blocks the targets. For Kitchen task, Pa is frequency interacting with x or more objects (e.g., the bottom burner).
Success Rate
Method
AVG FLOPs Speed
BP
BP,
Kit,a
Kitp2
Kitp3
Kity+
BAC (n 3) 0.99/0.98
0.94/0.93
0.99/1.00 1.00
0.97/0.99
0.95/0.99
0.89/0.97
0.97
2.23G
3.38
BAC (va = 5) 1.00/0.99
0.97/0.95
1.00/0.99
1.00/0.99
1.00/0.99
0.94/0.97
0.98
2.44G
3.60
A.8 ADDITIONAL EXPERIMENTS ON DIFFERENT SIMILARITY METRICS
In this experiment, we evaluate the performance of BAC across all tasks using four similarity metries: Mean Squared Error (MSE), L1-Norm distance (L1), Wasserstein-1 distance (Wa), and Cosine similarity (Cosine), as presented in Table 4. BAC with metric Cosine achieves average success rates of 0.79, 0.77, and 0.98 for PH, MH, and multi-stage tasks, outperforming BAC with metric MSE (0.78, 0.70, 0.98), BAC with metric LI (0.72, 0.67, 0.98), and BAC with metric Wa (0.70, 0.56, 0.81). BAC with metric Cosine excels particularly in MH settings while matching MSE and LI in multi-stage tasks. BAC with metric Wa struggles with complex tasks (e.g., Kitp4: 0.39/0.67), All metrics exhibit similar computational costs, with FL.OPs ranging from 2.40G to 2.73G and speed
19

---

Published as a conference paper at ICLR 2026
Table Benchmark Results across tasks that have performance collapse (Tool hangph. Transportmh Kitchen), all results set n = 3 and S E (5, 7, 20).
Success Rate
Method
AVG FLOPs Speed x
ToolpA
Transma
Kitp1
Kitza
Kitzs
Kitp1
BAC (S- 5)
0.00/0.00
0.26/0.50
0.04/0.07
0.00/0.00
0.00/0.00
0.00/0.00
0.07
1.49G
4.02
BAC (S
0.00/0.01
0.19/0.32
0.82/0.93
0.64/0.79
0.55/0.70
0.33/0.52
0.49
1.90G
3.66
BAC (S 10)
0.03/0.07
0.21/0.53
0.99/1.00
0.97/0.99
0.95/0.99
0.89/0.97
0.72
2,43G
3.34
BAC (S 20)
0.32/0.53
0.29/0.43
1.00/1000
1.00/1.00
1.00/1.00
0.99/0.97
0.80
4.16G
2.53
from 3.07 to 3.42x. Thus, BAC with metric Cosine and BAC with metric MSE demonstrate the most robust performance, with Cosine preferred for noisy data and complex tasks.
Table 4: Benchmark Results across Proficient Human (PH), Mixed Human (MH), and Multi-stage Demonstrations (n = 5, S 10) using MSE, LI, and Wa Metrics.
Benchmark on Proficient Human (PH) demonstration data.
Success Rate f
Method
AVG FLOPs Speed
Lift
Can
Square
Transport
Tool
Push-T
BAC (MSE)
1.00/1.00
0.79/0.79
0.71/0.83
0.75/0.77
0.40/0.55
0.58/0.66
0.78
2.73G
3.21
BAC (LI)
1.00/1.00
0.89/0.95
0.74/0.85
0.71/0.73
0.19/0.33
0,56/0.65
0.72
2.60G
3.19
BAC (Wa)
1.00/1.00
0.37/0.75
0.79/0.87
0.80/0.79
0.37/0.50
0.52/0.61
0.70
2.73G
3.28
BAC (Cosine)
1.00/1.00
0.94/0.97
0.82/0.89
0.77/0.82
0.49/0.55
0.59/0.62
0.79
2.66G
3.40
Benchmark Mixed Human (MH) demonstration data.
Success Rate
Method
AVG FLOPs Speed x
Lift
Can
Square
Transport
BAC (MSE)
1.00/0.99
0.41/0.86
0.75/0.77
0.26/0.50
0.70
2.69G
3.21
BAC (L.1)
0.97/1.00
0.44/0.87
0.71/0.74
0.23/0.43
0.67
2.63G
3.18
BAC (Wa)
0.98/0.99
0.83/0.90
0.09/0.05
0. 0.19/0.45
0.56
2.71G
3.07
BAC (Cosine)
0.99/0.98
0.95/0.97
0.77/0.79
0.30/0.46
0.77
2.64G
3.41
Benchmark on multi-stage tasks. For Block-Pushin Boock-Pushing task, pN is the frequency of pushing x blocks into the largets. For Kitchen task, is the frequency of interacting with x or more objects (e.g., the bottom burner).
Success Rate
1
Method
AVG FLOPs Speed x
BP
BP
Kitp1
Kity2
Kitpa
Kitpa
BAC (MSE)
0.99/0.99
0.95/0.93
1.00/1.00
1.00/1.00
0.99/0.99
0.97/0.93
0.98 2.49G
3.39
BAC (Ll)
0.99/0.99
0.94/0.94
1.00/1.00
1.00/1.00
1.00/1.00
0.93/0.95
0.98
2.40G
3.42
BAC (Wa)
0.99/1.00
0.95/0.95
0.83/0.95
0.66/0.90
0.55/0.85
0.39/0.67
0.81
2.61G
3.08
BAC (Cosine)
1.00/0.99
0.97/0.95
1.00/0.99
1.00/0999
1.00/0.99
0.94/0.97
0.98
2.44G
3.60
20

---

Published as a conference paper at ICLR 2026
A.9 MORE DETAILS ON TEMPORAL SIMILARITIES
We compute cosine similarity between intermediate features of different timesteps to analyze temporal similarity patterns, using the Squareph task as a case study. Fig. 10 provides more details on the temporal similarity patterns of different decoder blocks. The observation that the feature similarity between consecutive timesteps varies uniforiformly over time exists in all the decoder blocks. This suggests the necessity of ACS method.
Self Allention
Cruss Allention
FFN
1.0
1.0
0
1.0
20-
20-
0.8
20
0.8
Timestep
40
0.8
Timestap
0.6
40
0.7
60
60
0.4
60
80
80
0.2
80
0.5
25
Timestep
Timestep
Timestep
(a) Feature similarities across timesteps in the first layer.
Self Attention
Cross Allention
FFN
0
1.0
1.0
1.0
20
0.8
20
0.8
Timestep
Timestep
40
0.6
60
60
60
0.4
80
80
0.2
80
0.2
0.0
Timestep
Timestep
Timeslep
(b) Feature similarities across timesteps in the second layer.
Self Attention
Cross Attention
FPN
1.0
1.0
1.0
0.8
20
0.8
Thmestep
40
Timestep
40
0.6
40
0.6
60
60
0.4
60
0.4
0.4
0.2
80
80
80
0.2
0.2
0.0
25
Timestep
Timestep
Timestep
(c) Feature similaritics across timesteps in the third layer.
Self Attention
Cross Attention
FFN
1.0
1.0
1.0
0.8
Timestep
Timesten ssteppp
40-
0.6
40-
0.6
40
60-
0.4
60
0.4
60
0.2
0.4
30
75
25
30
50
75
Timestep
Timestep
Timestep
(d) Feature similarities across timesteps in the fourth layer.
21

---

Published as a conference paper at ICLR 2026
Self Attention
Cross Attention
FFN
1.0
1.0
20
20
0.8
20
0.8
Timestep
Timestap
40
0.6
40
0.6
0.6
60
60
60
0.4
0.4
80
80
0.4
80
0.2
0.0
25
75
Timestep
Timestep
Timestep
(c) Feature similarities across timesteps in the fifth layer.
Self Attention
Cross Altention
FFN
1.0
1.0
0
1.0
20-
20-
0.8
20
Timestap
40
0.6
40
60-
60
60
0.4
80
80
0.2
80
0.0
25
Timestep
Timestep
Timestep
(f) Feature similarities across timesteps the sixth layer.
Self Allention
Cross Altention
FFN
1.00
1.0
-1.0
20-
0.75
20
0.8
20-
Timestop
Dmeeste
0.5
40
0.50
0.6
40
60
80
0.4
0.00
80
0.2
-0.5
25 Timestop
Timestep
Timestep
(g) Feature similarities across timesteps in the seventh layer.
Self Atteation
Cross Attention
FFN
1.00
1.00
-10
20
20
0.75
20:
0.5
Timestep
40
0.50
Timestter lepp
40
0.50
40
0.25
0.25
0.0
60
60
0.00
0.00
80
-0.25
0.5
0.25
50 Timestep
75
25
Timestep
Timestep
(h) Feature similaritics across timesteps in the eighth layer.
Figure 10: Feature similarities timesteps for different blocks in each decoder layer.
To provide more details on the block-wise temporal similarity pattern, we compute cosine similarities under different intervals of consecutive steps in timestep and earlier timesteps L-k for various values (1, 5, 10, 15, 20). As shown in Fig. 11, different blocks exhibit distinct temporal similarity patterns. Some blocks maintain high similarity across long horizons, indicating few updates, while others show rapid drops in similarity even at short intervals, suggesting more update steps. This suggests the necessity of block-wis schedule.
22

---

Published as a conference paper at ICLR 2026
Solf Attention
Cross Attention
PFN
1.00
Similariy Value
Similarity Value
Simlerily Value
0.8
0.95
0.8
0.6
0.6
Layer 4
Layes
Layer
Layor
Layer's
Layor 5
0.
0.4
Layor
Layer
8-4
Layer's
Layer 6
Layer
Layer
0.2
Layer
Layer
Layer
Layer?
Layor
20
40
80
100
20
40
60
80
100
20
40
60
80
100
Tim esteptep
Timestep
Timestep
(a) Similarity change curves, measured between timestep / and 1-1.
Atbention
1.0
1.0
1.0
Similarity Value
Similarityy Valuee
Similarity Valuue
0.8
0.8
0.6
Layer 0
Layer
Layer 0
Layer
0.4
Layer 0
Layer
Layer
Laver
Layer
Laver
0.4
Layer 2
Layor
Layer
Layer?
0.7
Layer 2
Layor 3
Layer
Layer
0.2
Layer
Layer
Layer
0.01
Timestep
Timestep
Timestep
(b) Similarity change curves, measured between timestep and t-5.
Solf Attention
Cross Attention
FFN
Similarity Value
1.0
Similarity Value
1.0-
Similarity Value
1.0
0.8
0.8
0.6
Layer
Layer
Layer D
Layer
Layor
Layer
0.7-
Layor
Layer
Layer
Layar
Layar
Layor 2
Laysr
Layer 2
Layer
Layer
Layer
Layer
20
40
60
80
20
40
60
80
00.5
20
40
60
80
Timestop
Timestep
Timestep
(c) Similarity change curves, measured between timestep and 1-0
Attantion
Attention
FFN
1.0
1.0
1.00
Similarity Value
Simalleriy Value
0..
Simllarity Value
0.8
0.50
0.8
0.6-
0.25
Laver
Layer
0.7
Layer
Layer
Layer
Layer
Layer
Layer
Layer
Luyse
Layor
0.6
Layer
Layor 6
-0.25
Layar
Layer
Layer
Layur?
Layor
Layer
Layer
Layer
0.2
20
40
60
80
0.5
40
60
20
40
60
80
Timestap
Timestop
Timestep
(d) Similarity change curves, measured between timestep and t- 15.
Selt Attention
Cross Attenttonn
FPN
1.0
1.00-
Similarity Values
Similagity Value
Similazity Value
0.75
0.8
0..8
0.50
0.6
Layer
Layer 4
0.G
Layer O
Layer 6
0.00
Layer
Layer
Layor
Laysr
Layar
Layor
Layer
Layer
Layer
Layer
Layer
-0.25
Layer
Layer
Layse
Laywr?
Layer
Layor 7
Layar
Layer?
20
Timestop
Timestop
Timestop
(e) Similarity change curves, measured between timestep and 2-20.
Figure 11: Block-wise feature similarity between consecutive steps. Each subfigure shows the similarity between features at timestep and (t-k, where h 1, 5, 10, 15, 20) for different blocks.
23

---

Published as a conference paper at ICLR 2026
A.10 MORE DETAILS THE HIGH EPISODE HOMOGENEITY WITHIN INDIVIDUAL TASKS In this section, we present evidence for the high episode homogeneity of an embodied task by highlighting the distinct similarity patterns in action generation tasks versus image generation tasks.
In action generation tasks, shown in Fig. 12, visualize the feature similarity matrices from the same layer of Diffusion Policy, under the same task (Squarepa). across two different scene demos (demo id 1 1001 vs. demo id 20000). Despite changes in settings, the similarity matrices remain strikingly consistent, suggesting a high degree of representational homogeneity across episodes.
In contrast, image generation tasks, as shown in Fig. 13, we visualize the feature similarity matrices from the same layer of DiT-XL/2 (Peebles & Xie, 2023), across two different classes in ImageNet (class label 1r:"ro American robin, Turdus migratorius" vs. class label 800; "slot, one-armed bandit"), The results from both the self-attention and MLP blocks reveal clear differences in feature patterns.
While an image generation task shows obvious differences feature patterns across different classes, an action generation task shows almost no difference across different scene demos within the same task. These observations support the efficiency of our method, specifically in embodied episodes. Benefiting from the high episode homogeneity within individual tasks, our method can be run only once for given task before inference, incurring virtually no additional cost.
Self Attention
Self Attention
1.0
1.0
0.8
0.8
Timestep
Timestep
40
10
0.6
0.6
60
60
0.4
0.4
80
80
0.2
0.2
0
25
50
75
0
25
50
75
Timestep
Timestep
(a) Diffusion Policy demo 11001.
(b) Diffusion Policy demo 20000.
Cross Attention
Cross Attention
1.0
1.0
20
0.8
20
0.8
Timestep
0.6
Timestep
0.6
0.4
0.4
60
60
0.2
0.2
80
80
0.0
0.0
0
25
50
75
0
25
50
75
Timestep
Timestep
(c) Diffusson Policy demo 11001.
(d) Diffusion Policy demo 20000.
FFN
FFN
1.0
1.0
20
0.8
20
0.8
Timestep
Timestep
40
0.6
40
0.6
60
0.4
0.4
0.2
0.2
80
80
0.0
0.0
25
50
24
25
50 Timestep
75
Timestep
(c) Diffusion Policy demo 11001.
(f) Diffusion Policy demo 20000.

---

Published as a conference paper at ICLR 2026
Figure 12: Feature similarities across timesteps in action generation tasks. We visualize similarity matrices of different blocks in the third layer across different scene demos (e.g., demo id 1 11001 vs. demo id 20000).
25

---

Published as a conference paper at ICLR 2026
Self Attention
Self Attention
0
1.0
0
1.0
0.8
50
0.8
Timestep
Timestep
100
0.6
100
0.6
150
0.4
150
0.4
0.2
200
0.2
0.0
200
100
200
Timestep
Timestep
(a) Diffusion Model class label 15,
(b) Diffusion Model class label 800.
MLP
MLP
0
1.0
1.0
50
0.8
50
0.8
Timestep
Timestep
100
0.6
100
0.6
150
0.4
150
0.4
0.2
200
100
200
0
100
200
Timestep
Timestep
(c) Diffusion Model class label 15.
(d) Diffusion Model class label 800.
Figure 13: Feature similarities across timesteps image generation tasks. We visualize similarity matrices of different blocks in the fourteenth layer across different classes (e.g., class label 15 vs. class label 800).
A.11 MORE DETAILS FOR FIG.3
To support findings of the етrоr surge phenomenon, we present comparisons caching errors across different FFN blocks using block-wise schedule versus unified schedule. As shown in Fig. 14, the block-wise schedule leads to error surges in nearly all FFN blocks except the first one, in contrast to the unified schedule. This observation further suggests that caching errors can propagate through downstream FFN blocks.
2.0
25
[84
||115
Rookkwiss
Unired
United
Updatn Step
1.0
Update Step.
0.5
0.0
0.0
Timestep
Timestap
Caching error in the first FFN block.
(b) Caching error the second FFN block.
26

---

Published as a conference paper at ICLR 2026
1.79
1.50
1.00
[|4
Block wise
[8
Block
0.75
Update Stop
Update Step
0.55
0.00
80
100
Timestop
Timestop
(c) Caching error in the third FFN block.
(d) Caching error in the fourth FFN block.
0.8
0.8
0.6
[|..0.6
wiocke
United
0.4
United
0.4
Update Stop
Update
0.2
0.2
0.0
0.0
20
60
100
20
40
80
100
Timestep
Timestep
(e) Caching error the fifth FFN block.
Caching error the sixth FFN block.
14
5-
Block wise
[|]]
Blocks
Unifed
Update Stop
Update Steg
80
100
20
Timestep
Timestep
(g) Caching error in the seventh FFN block.
(h)) Caching error in the eighth FFN block.
Figure 14: Caching error across different FFN blocks using a block-wiss schedule versus unified onc.
Fig. 15 presents block-wise heatmaps of caching error across all blocks throughout the diffusion process, covering diverse set of tasks and two demonstration settings: Proficient Human (PH) and Mixed Human (MH). Each subfigure corresponds to a different task, with color intensity representing the magnitude of caching steps.
each block and timestep, and white dots indicating cache update
These visualizations support our analysis of inter-block error propagation by consistently exhibiting the following key phenomenon: in multiple tasks, blocks occasionally update at steps where their upstream blocks with large caching errors have not yet been updated. This mismatch leads to sudden, sharp increases in error (seen abrupt darkening) in the downstream block, with no smooth transition. Importantly, even after upstream blocks are later updated, the downstream surge in error remains, indicating that the update failed to recover from the propagated upstream error.
27

---

Published as a conference paper at ICLR 2026
FFNLO
FPVO
0.5
FPXI
0.5
FRX11
0.5
0.0
0.0
0.0
2.5
FRX2
FFN2
FFXL
10.25
PPNJ
0.25
0.00
0.5
BRX
FPNA
0.0
0.0
0.0
0..5
FFN.
00.25
FPNS
0.1
FENU
FPN6
0.1
0.0
0.0
2.5
SFR-
0.25
0.25
6.0
0.00
0.00
Timesbeps
Timestepe
Timesteps
(a) Canan
CanyA
(c) Liftmb
FRK
FF5.0
10.25
5PX1
PRX
0.00
0.1
FPN2
FFN2
0.0
a.os
FFX3
FPNL
0.00
0.00
0.0
0.03
FFN
FPN4
FRXS5
10.5
FRNS
0.00
0.0
0.00
F7N6
3PN6
0.00
0.0
o
0.00
FFN3
Timesteja
Timestaje
Timmsstps
(d) Liftph
(e) Push-T,i ph
(f) SquaremA
FFN3
10
FFN.0
0.25
FEX
FRNJ
0.0
FFN2
0.5
0.0
FFN3
FFN
FRY.A
FR14
0.s
0.3
0.0
0:50
FFNS
FPNS
0.5
0.0
FFN.
FFN6
0.5
FPAT
PRN.7
12 50 24 20 30 62 00
32 18
42 69
42
(g) Squareph
(h) Transport
Transportp4:
28

---

Published as a conference paper at ICLR 2026
FFXLO
FPND
0.25
FRK
2.55
FFNL
0.11
0.0
2.5
FFX2
2.5
FPN2
0.0
0.0
FRLS
FRNS
o.ns
0.0
0.00
0.5
FFNN
0.05
0.0
0.00
FRNS
FFNSS
0.05
FENU
FFN
0.05
0.00
FEN7
10
SPNC1
0.05
0.00
Timestegs
Timesteps
Timesteps
(i Tool Tool hangp/
Kitchen
Block Pushing
Figure 15: Caching error across all blocks throughout the diffusion process, with white dots indicating update steps.
12
DETAILS ON UPDATE STEPS COMPUTED BY ACS
Our algorithm employs two-stage paradigm where apply ACS followed by BUA determine the optimal update steps for different blocks the offline stage, and then accelerate Diffusion Policy by updating and reusing the cached features based the prepared update steps in the online stage.
In Tables 5, 6, 7, 8. 9, 10, 11, 12, 13, 14, and 16, we report the update steps after employing ACS 10.
for all blocks across all tasks
29

---

Published as a conference paper at ICLR 2026
Table 5: Update steps for Canph computed by ACS.
Block
Steps
layers.0.SA
0, 9, 18, 30, 49, 69, 82
layers.0.CA
0.18.3..44.57771. 89,
layers.0.FFN
05, 944.1.2...2244444666.9...88
0,4,
63,
layers.I.SA
layers.1.CA
1114,,,,36,4,,60,3,,,. 60, 73,
layers.1.FFN
08,16,,8,,8,,5,66,668,,
layers.2.SA
68,
layers.2.CA
0.9,18,28..8.,51,6,,,,,,
1ayErs.2.FFN
0, 0,1422..3..511622..888889999
layers.3.SA
0.19..0..0.311.22222222.01..
layers.3.CA
0,6,14.25.,3,,49,,222223 75,
layers.3.FFN
68,
layers.4.SA
0.13,25.37.553,6.81....00
layers.4,CA
0,3,9,22,39, 37, 80,
1aFFrs.4.FFN
0, 06.
layers.5.SA
0,6, 22, 42, 63, 80, 83,8,
layers.5.CA
1,4, 43411...9944.001..1190999090
laycrs.5.FFN
0,37, 60, 79, 88,
layers.6.SA
0,37, 89,9998,,,,,,,,,
layers.6.CA
51, 51, 95,
layers.6.FFM FFFN
0,28, 62, 83,,
layers.7.SA
0,29, 79, 93,
layers.7.CA
0, 49, 68, 83, 89, 89,
0, 0,47, layers.7.FFN
81,
Table 6: Update steps for Liftps computed by ACS.
Block
Steps
layers.O.SA
76, 95,
layers.O.CA
0, 60, 70, 75. 80, 93, 0.4,8, 49. 1,4
layers.0.FFN
layers.1.SA
19,
layers.1.CA
34,, 60, 69, 78,92
laFFrs.1.FFN
18,
layers.2.SA
0.2.7.99.31.
layers.2.CA
layers.2.FFN
0,4, 10, 11,
layers.3.SA
0,6, 19, 40, 65, 74,
layers.3.CA
0, 38, 53,
layers.3.FFN
laycrs.4.SA
266.9..40.66.55.5...2.55.58
layers.4.CA
O, 1210,21.222444
layers.4.FFN
68, 79, 115.37..8.799,88,,999...989
laSers.5.SA
65,
laCers.5.CA
layers.5.FFN
74,
layers.6.SA
407, 84.0
layers.6.CA.
0,8, 14,11,,,2.34444,,,......,,
layers.6.FFM FFN
layers.7.SA
0,7, 67, 84, 0,8, 14,
layers.7.CA
layers.7.FFN
0, 15, 40, 54, 69, 79, 86,
30

---

Published as a conference paper at ICLR 2026
Table 7: Update steps for Square,h computed by ACS.
Block
Steps
layers.0.SA
0,3,9, 17, 49, 62, 69, 80, 89
layers.0.CA
03 77, 77,
layers.0.FFN
0,4, 0,4410.21.33,,4555,,,,777.
layers.I.SA
layers.1.CA
138.1,, 80,
layers.1.FFN
layers.2.SA
0.7,16,,7,37744,,66,6,,,
60,
layers.2.CA
1ayErs.2.FFN
0.7.14.31,44555.677798839
layers.3.SA
0144.24.44444.5566,666666
layers.3.CA
066.1..25..66,4,,,996977..9.
layers.3.FFN
0.4.8.15.22.33664476..7777
layers.4.SA
0,6, 26.13,24438.,57.66888888
layers.4,CA
944.1,22,,33566,,0444499,,,
layers.4.FFN
layers.3.SA
9,,1
layers.5.CA
1.5.8.12..88,,,3665522...
1aFCrs.5.FFN
944.5,22.31,44433,44779999
layers.6.SA
layers.6.CA
0,2,9,
2,,,
layers.6.FFN FFN
layers.7.SA
0,43,
layers.7.CA
0,7, 80,
87, 87,
layers.7.FFN
O, 10, 73, 89,
A.13 DETAILS ON UPDATE STEPS COMPUTED BY BUA
In Tables 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 and 28, we report the steps added after employing BUA across all tasks at 10 and k
31

---

Published as a conference paper at ICLR 2026
Table Update steps for Transportph computed by ACS.
Block
Steps
Aayers.O.AA
0,2,10,24,47,58 24,24,47,55 70, 76, 86, 94
layers.0.CA
3.7.15.23.34.52.65, 76, 86,
layers.0.FFV)
0.3.10.21.31.444,666666
76,
layers.1.SA
laCers.1.AA
01.3,2..31448,566657..77.7.
l.FF
1,1.3.7,19,30444,,,,,,,3
layers.2.SA
layers.2.CA
0,14, 40, 52, 66, 83,
layers.2.FFN
02, 69, 62,
layers.3.SA
0717,42, 68, 95,
layers.3.CA
layers.3.FFN
0,43,74.82, 82, 83, 87,,
layers.4.SA
O, 1116,777.8.588..88888..339
layers.4.CA
26,13.30.449.61,8,,916666
lFFFrs..FFFN
07,
layers.5.SA
layers.5.CA
9.7224441.22.6618222999999
laFNrs.5.FFN
63, 4444299.99.6.770888,,99993.1
layers.6.SA
56,
layers.6.CA
0,,,22,4,,,4,,,,,,,,,,,900,
layers.6. FFNN
0, 28, 49, 60, 79, 88, 98,,
layers.7.SA
0, 26, 78, 72,
layers.7.CA
51, 68, 73, 89, 0, 62. 67, 75, 82, 85,91,
layers.7.FFN
Table 9: Update steps for Tong. computed by ACS.
Block
Steps
layers.O.SA
17,99,,7,,444,8,,, 50,
layers.O.CA
0, 44, 68, 76, 84, 92
layers.0.FFN
0,2,5, 10, 40,
laSe
0,, 40,53, 66,
I.CA
0.1,, 84,99
layers.1.FFN
0,2,6, 10,,444.0600 77,8
layers.2.SA
layers.2.CA
1,,
layers.2.FFN
1.3.10.22.31144444,,,.7777
layers.3.SA
19923..31.00,49.60.7779999
layers.3.CA
0.2.1.222.31144445.66,7777
layNrs.3.FFN
0,3, 10,1000,,,,,.
layers.4.SA
layers.4.CA
0, 2,6,14,20,2224466,,2993888
layers.4.FFN
0, 16,
layers.5.SA
19,
layers.5.CA
0, 02277.16..27337..555.....9999
layers.5.FFN
layers.6.SA
0,54, 83, 99.44444..99..29994955..6666
layers.6.CA
66, 1113,77448.6666229994444466
layers.6. F.F
4,, 0.11,44..5.71.3399999959.7
layers.7.SA
layers.7.CA
0.6,43, 66,43,6,811,9000 96443.66.81.900944999.7777
layers.7.FFN
0, 0..0,7447.911.888897559..
32

---

Published as a conference paper at ICLR 2026
Table 10: Update steps for Pusht-T computed by ACS.
Block
Steps
layers.0.SA
0,,.
layers.0.CA
3,, 78, 95
layers.0.FFV)
layers.1.SA
45,
laCers.1.AA
0.1322..31444,44663....6.0
l.FN
0.37..7..3.33447....453
layers.2.SA
64,
layers.2.CA
0,7,18,25,32224444,,,,,,,,
layers.2.FFN
0...19.31.6..5444474.....
layers.3.SA
16.,2644..44466677222339999
layers.3.CA
0.11.20..5,
layers.3.FFN
45,
layers.4.SA
layers.4.CA
4FFF
0,625,39.,11,65,74885911111
layers.5.SA
O, 26.31.544.44,87999144999999
layers.5.CA
16,
laFNrs.5.FFN
17,,17223,45.00,7988899999
layers.6.SA
laCe
0.5.1.221332444...99733322
layers.6.FFF
44,
layers.7.SA
82,
layers.7.CA
layers.7.FFN
0,7,19.31, 45, 66, 91,999947
Table 11: Update steps for Canma computed by ACS.
Block
Steps
layers.O.SA
0, 26,,4,,,, 62, 75, 75,
layers.O.CA
43, 80, 86, 93 1,,4
layers.0.FFN
laSers.1.SA
0,4,10,20.22,424,44700..13,
I.CA
layers.1.FFN
1.,,11,19..30443,,,,633333
layers.2.SA
layers.2.CA
19,
layers.2.FFN
0.3.11.18..4433336..0.0.
layers.3.SA
layers.3.CA
18.11.225.77,,22.33....7777
layCrs.3.FFN
layers.4.SA
layers.4.CA
layers.4.FFN
78, 68,
layers.5.SA
0,11,34, 60, 80, 9.11
layers.5.CA
0, 16619.331.44.57774999995444
layers.5.FFN
0, 0.94469998..88.919339999777
layers.6.SA
00, 99..8..88999922445559966999999
layers.6.CA
0,
93,
layers.6. FFN
0.43,59, 94449999.79988.
layers.7.SA
layers.7.CA
0. 28, 54, 69, 69, 90, 93,99,7779
layErs.7.FFN
0, 70, 73, 80, 80, 96..999999.
33

---

Published as a conference paper at ICLR 2026
Table 12: Update steps for Liftma computed by ACS.
Block
Steps
Mayers.O.AA
23,,,21,33. 69,
layers.O.CA
1,, 49, 60, 71, 80, 87, 94
layers.0.FFF)
37, 53, 65, 79, 88 0,4,8, 28,
layers.1.SA
0,4,8, 31, 79,88
laCers.I.AA
l.FF
0,4,8, 38,
layers.2.SA
layers.2.CA
0,9, 40, 49,
layers.2.FFN
33,,23,,2,43,600,,
layers.3.SA
54,
layers.3.CA
28,
layErs.3.FFN
244,22,40,550 54, 68, 68, 94442,990,94400888883,99,,,0
layers.4.SA
455118,2,,5,,22279,999999
layers.4.CA
0,5,
lFFFrs.4FFFN
0, 0, 58,
layers..SA
52, 83, 0....66........99999999999999999
layers.5.CA
50, 67,
laFNrs.5.FFN
0,33, 7.33,,00.7,,885,,,,9955553..
layers.6.SA
0,34, 9744666....87,91,,99.99999
layers.6.CA
0,9,22,38,57, 89, 99,
layers.6. FFNN
0,,7,51, 89, 99,99,9999
layers.7.SA
80,
layers.7.CA
0, 0,4,21,39,55, 70, 84, 84,
layers.7.FFN
0,43, 63, 68, 75, 82,
Table 13: Update steps for Squaremm computed by ACS.
Block
Steps
layers.O.SA
0,1,3,9,18.31,5111 76, 85
layers.O.CA
0,13,26,41,5 54, 66, 77, 81, 86, 92
layers.0.FFN
0,3,8, 18, 53, 66. 77,88
laSe
1,, 66, 77,87
I.CA
07,19,34447,,58,8888888
layers.1.FFN
14.7,15,.44405006666,77
layers.2.SA
0.9.24.32.99.6..77,77.888
layers.2.CA
28,21,,3,,6,,,,,,2,2222,
60.,
layFrs.2.FFN
25699,2,.4444458.6,,,,,7
layers.3.SA
0,9,28,33,44
layers.3.CA
0,8, 188.15224.444777.6777909099
layCrs.3.FFN
1.3,10.22.444,,888888622..
layers.4.SA
14414.225.44.2227888499.29
layers.4.CA
layers.4.FFN
layers.5.SA
02, 48, 77,
layers.5.CA
16611.226.55.5667449955533
layers.5.FFN
0.44.76..22.86.9991..99997.
layers.6.SA
O. 9.7.887.91.99..4495597779
layers.6.CA
layers.6.FFF FFN
28, 95, 96,
layers.7.SA
layers.7.CA
0.3, 46, 83,91,
46,
layers.7.FFN
0, 72, 77, 95.
34

---

Published as a conference paper at ICLR 2026
Table 14: Update steps for Transportmh computed by ACS.
Block
Steps
Aayers.O.AA
0,2, 7, 18, 30, 48, 70, 80,
layers.0.CA
0.3,5, 10,
93,97
layers.0.FFF)
011.7.18.99.51.61.7...8111
layers.1.SA
laCers.1.CA
l.FN
087.18,29,40 40, 62, 74,86,9
layers.2.SA
18, 46, 58, 70, 78, 70,78,90,6
layers.2.CA
59, 68,
layers.2.FFN
layers.3.SA
layers.3.CA
layErs.3.FFN
layers.4.SA
layers.4.CA
68,
lFFFrs..FFFN
layers.5.SA
layers.5.CA
0.6, 066.15..5..333336,2222.3,3
laFers.5.FFN
88, 88,
layers.6.SA
20,
laCe
layers.6.FFF
10,
layers.7.SA
90, 901,
layers.7.CA
0,1,3, 10, 42..1110..
layers.7.FFN
17,
46, 63, 76,90,
Table 15: Update steps for Block Pushing computed by ACS.
Block
Steps
layers.O.SA
14,2,,4,4,,2,,3,,40,,,
layers.O.CA
41,,7,, 93.
layers.0.FFN
laSe
0,1,7, 20,
laCers.1.CA
04.11222,.22,,8,,228.2224
layers.1.FFN
0,3,7, 26. 20, 76,8,
layers.2.SA
0,3,7, 15, 40, 1,,
laye
0,4,7, 19, 19, 66,
layers.2.FFN
layers.3.SA
115,
layers.3.CA
12..,,,,0..
layCrs.3.FFN
1.5.10.18.26..52771..88
layers.4.SA
04499.6.22..4553371..8..3
layers.4.CA
0.3.9.16.25.336,11.88.....
layers.4.FFN
41,,,,,3
layers.5.SA
0,5,
43.
layers.5.CA
28,. 42,
layers.5.FFN
15.11.277.66.58.11.888.
layers.6.SA
93.99
layers.6.CA
0,3,6. 15,
layers.6. FFN
0,17,38, 53, 64, 93,93
layers.7.SA
layers.7.CA
0.7.44.26..0971....11...3
layers.7.FFN
40, 64, 166440...4.66.833999999999999
35

---

Published as a conference paper at ICLR 2026
Table 16: Update steps for Kitchen computed by ACS.
Block
Steps
layers.O.SA O.SA
0,2,5, 10, 19, 23,,,,,,,4,, 70,83
layers.0.CA
08.
layers.0.FFN
04,
46.8 46,
l..A
layers.1.CA
layers.1.FFN
layers.2.SA
0,4,10,
244.0.119.33.44144472..44
layers.2.CA
0,2,5,8, 12.358..1.199.30411.444
layErs.2.FFN
181,5.10.188
layers.3.SA
0.L.7.18.22:41555..888111
layers.3.CA
0.3.6:00.13.19.33......7.
1FFErs.3.FFN
0,2.5.8.11,18,22,441133,
laSers,4.SA
layers.4.CA
39,,,
4.FF
1.2.5.1..88.2.444.54777
layers.5.SA
0,3.8.15.22,337466667..88
lyCrrs5.CA
13,,3,2,,,2,,,,,,,,,,,,,,,,
layFrs.5.FFN
18,
layers.6.SA
layers.6.CA
1,,,
layers.6.FFF F.F
layers.7.SA
0,2,41, 62, 80, 89, 93, 95,99,97 0,7, 40, 60, 78,
layers.7.CA
1ayErs.7.FFN
0, 0,1,6, 11, 25, 38, 60, 68,
Table 17: Update steps added for Canph after BUA.
Block
Added Steps
layers.0.FFN
6,8, 14, 16, 18, 23, 27, 28, 37, 38, 39, 47, 48
51, 60, 62, 68, 69, 71. 74, 75,
77.
78,
80, 81,
85, 89, 92,
94,
95,
98,
99
1.FErS.5.FFN
28, 47, 62, 69, 74, 77, 80, 81, 86, 89, 93, 95,
97
1.Se
28, 47, 62, 69, 74, 77
layers.6.FFN
47, 69, 74, 77, 81. 86
Table 18: Update steps added for Liftph after BUA.
Block
Added Steps
layers.0.FFN
10, 15, 17,
28,
29,
40,
44, 48, 51,
54, 65, 68. 69, 78,
79,
86,
91.
93, 95, 96.
97, 98, 99
I.SA
14, 15, 17, 18, 27,
29,
31.
40,
44. 48, 49, 51.
54, 57, 68, 69, 74,
79,
86,
91.
95, 96, 97, 93,
98, 99
I.FF
14, 15, 17, 27, 29,
31, 40,
44 48, 49, 51, 57,
68, 69, 74, 78, 86
91, 93, 95, 96, 97, 98, 99
layers.2.FFN
14, 15, 29, 31, 40, 44. 48, 49, 54, 57, 68, 69,
74, 79, 86, 91, 93, 95,
96, 97, 98, 99
layers.3.FFN
15. 37, 40,
44, 48.
54, 69. 74, 86, 91.
95, 96, 98, 99
36

---

Published as a conference paper at ICLR 2026
Table 19: Update steps added for Squareph after BUA.
Block
Added Steps
layers.0.FFN
8, 14, 15, 23, 36, 37, 44, 48, 52, 53, 57. 61, 64, 67, 69, 74, 76, 78, 79, 83, 87, 89, 90,
91, 93. 95, 96, 97. 98
layers.6.FFN
10, 78, 87, 89, 91, 97
layers.7.SA
10, 78, 83, 87, 89, 97
layers.7.CA
10, 52, 78, 83, 89, 91
Table 20: Update steps added for Transportph after BUA.
Block
Added Steps
laFers.0.FFN
1, 12, 14, 16, 19, 28, 29,
30,
34, 36, 43, 49,
52, 60, 62, 63,
67,
69,
70,
75, 78, 79, 92,
74,
82, 84, 85,
88.
90,
93, 94, 95,
96, 97, 98
layers.3.SA
14, 16, 28, 29,
34, 36,
43,
49,
57. 60, 62, 63,
67, 70, 74, 75, 78, 79,
82, 85 87, 88, 92, 93,
96, 98
layers.3.CA
14, 16, 28, 34, 36, 43, 49, 57, 60, 62, 63, 67,
70, 74, 75, 78, 79,
82, 85, 87, 88, 92, 93, 94,
95, 97, 98
layers.3.FFN
14. 16, 28, 29, 34, 36 49, 57, 60. 62, 63, 67,
70, 75, 79, 88
93,
96
layers.4.FFN
14, 28, 29, 36,
49, 60,
62, 63, 67,
70, 75, 79.
82, 85, 88, 95, 96,
98
Table 21: Update steps added for Toolph after BUA.
Block
Added Steps
laFFrs.0.FFN
6, 11, 12, 16, 23, 24,
31,
44,
48,
53,
60, 61, 63, 66, 71, 74,
77,
78,
79, 80, 81, 83,
85. 86. 87, 88, 91. 93,
94.
95,
96 97, 98, 99
I.FN
3, 11, 12. 16, 23,
24, 31.
44, 48 49,
53,
60, 61, 63, 66. 71, 74. 77,
78, 79,
80,
85, 87, 88, 91,
94
96 97,
layers.5.FFN
11, 40, 53, 60, 74, 79,
81, 83,
95, 97,
layers.6.SA
11, 40, 53, 60, 71,
79,
80,
81,
87, 91, 97,
layers.6.CA
11, 40, 53, 60.
71,
74,
79,
80,
81, 83,
95,97,9 99
Table 22: Update steps added for Pusht-T after BUA.
Block
Added Steps
layers.0.FFN
6. 19, 21, 23, 31, 33, 39, 47, 51, 54, 59, 64. 65, 66, 68, 79, 82, 84, 85, 86, 90, 91, 94, 96. 97
1aFFrs.4.FFN
17, 19, 23, 45, 64, 66, 68, 79, 84, 86, 94, 97
1aFErs.5.FFN
19, 31, 64, 66, 74, 84, 86, 94, 97
layers.6.FFN
19, 31. 66, 86, 94, 97
37

---

Published as a conference paper at ICLR 2026
Table 23: Update steps added for Canma after BUA.
Block
Added Steps
layers.0.FFN
2, 3,5, 18, 24, 28, 30, 33, 38, 57, 59, 60, 62, 69, 76, 78. 80, 85, 86, 87, 88, 91, 92,
93, 94, 95, 96, 97, 98, 99
laFers.5.FFN
43, 59, 60, 70, 73, 76, 79, 80, 86, 87, 94, 96,
98
1aSers.6.SA
43, 59, 70, 73, 76, 79, 86, 87, 91, 99
layers.6.FFN
60, 70, 73, 76, 80, 86, 95, 99
Table 24: Update steps added for Liftmm after BUA.
Block
Added Steps
layers.0.FFN
13, 15, 22,
30,
33,
38,
43.
51, 51, 54, 57, 60, 63 68,
75.
78,
82,
83, 85, 89, 90, 92, 93,
94,
95,
96
97,
98, 99
laSe
27, 43, 01,511600000 60, 63, 65,
68,
71,
81, 82,
85, 89, 92, 95,
layers.5.CA
27, 43, 51,
65,
75, 81, 82,
85, 89, 90, 92. 93, 94, 96, 97,
1ayErs.5.FFN
27, 43, 51, 63, 65, 68, 71, 81, 82, 89, 92, 94,
96, 98
Table 25: Update steps added for Squarema after BUA.
Block
Added Steps
layers.0.FFN
1. 6, 7, 9. 10, 15,
20,
21,
24, 28, 34, 41, 23,
44, 49, 50, 58, 68, 69 72.
76 78, 81, 82, 84,
85, 89, 91, 93, 95,
97, 98, 99
1.FF
6, 21, 28, 58, 72. 77, 81, 85, 92, 93, 96, 98
layers.6.SA
6, 21, 28, 58, 72,
81, 85, 92, 96
layers.6.CA
6, 21, 28, 72, 77, 81, 85, 92, 96
Table 26: Update steps added for Transportma after BUA.
Block
Added Steps
layers.O.SA
1. 3. 5, 6. 10, 17, 19, 24
29,
35,
40,
41, 42,
46, 47, 51, 52, 61. 62, 63.
66
68.
71,
74, 76.
78, 81, 86, 88,
92,
93,
95,
96,
97, 98.
99
layers.0.FFN
3, 5, 6, 10, 17, 19, 24, 30, 35, 40, 41, 42, 46
47, 52, 62. 63, 66. 68, 74. 76, 78, 80, 86, 88,
90, 91, 92, 94, 95, 96, 97, 98, 99
laFErs.1.FFN
1, 10. 17, 19. 30, 35, 41, 46
47, 63, 66, 68, 76, 78, 80, 88, 90, 91, 92, 95,
96, 97, 98, 99
1.FF
3, 10. 17, 35, 46, 47, 63, 76, 90,97 97
layers.6.FFN
17, 17,
Table 27: Update steps added for Block Pushing after BUA.
Block
Added Steps
layers.0.FFN
5. 10. 15, 16, 17, 27, 30, 38, 40, 41. 46, 52, 53, 64, 70. 71, 76. 83, 86, 89, 92, 93, 96.
97, 98
layers.6.FFF
16, 40, 76, 96, 98
7.SA
16, 40, 64, 76, 83, 89, 96, 98
layers.7.CA
16, 40. 64, 76, 89, 93, 96. 98
38

---

Published as a conference paper at ICLR 2026
Table 28: Update steps added for Kitchen after BUA.
Block
Added Steps
layers.O.SA
1,3, 6, 11,
18,
25,
27,
38,
46, 47,
55, 57, 59, 60, 68, 72,
78,
79, 84, 87, 88, 91.
92, 95, 96, 98
1aFFrs.0.FFN
1, 6, 8, 10, 11, 18, 27, 29, 41, 43, 47, 54,
55, 60, 68, 72, 78, 79, 87, 88, 91, 92, 95,
96, 98
layers.5.FFN
6, 25, 29, 38, 47, 59, 60, 68, 92, 95, 96, 98
LaFers.6.FFN
6, 11, 25, 38, 60, 68, 88, 95
I.SA
1, 6, 11, 25, 38, 60, 68, 88
39

---

Published as a conference paper at ICLR 2026
A.14 VISUALIZATION OF CACHE BEHAVIOR
We visualize the ground-truth features, the computed and cached features under the BAC schedule, and their absolute differences for each timestep Figures 16 through 25, with cache update steps marked in red. Across all tasks, we observe two consistent phenomena. First, consecutive steps exhibit high feature similarity, confirming that high temporal redundancy makes caching naturally applicable. Second, the difference maps reveal distinct behaviors between reuse and update phases: during cache reuse, the absolute difference remains low, reflecting activation stability. Conversely, cache update steps show significant feature shifts, indicating that updates are effectively capturing necessary changes. Collectively, these visualizations validate the reliability of the BAC cache schedule.
Sap
Soop
Sepp
Sepp
May
May
May
Figure 16: Feature heatmaps for Lift.ph.
40

---

Published as a conference paper at ICLR 2026
Sep
Sep
23
Swe
Figure 17: Feature heatmaps for Can-ph.
41

---

Published as a conference paper at ICLR 2026
5ep
Sv
13
Figure 18: Feature heatmaps for Square_ph.
42

---

Published as a conference paper at ICLR 2026
Rap
May
May
May
Figure 19: Feature heatmaps for Pusht.
43

---

Published as a conference paper at ICLR 2026
Sep
Sep
May
May
May
39
19
Mep
Figure 20: Feature heatmaps for Transport_ph.
44

---

Published as a conference paper at ICLR 2026
0ep
May
Ovp
Figure 21: Feature heatmaps for Tool_hang.
45

---

Published as a conference paper at ICLR 2026
Bay
Rap
Mep
May
Map
May
Figure 22: Feature heatmaps for Lif
46

---

Published as a conference paper at ICLR 2026
Sep
Sep
23
Swe
Figure 23: Feature heatmaps for Can_mh.
47

---

Published as a conference paper at ICLR 2026
Sep
Svp
Figure 24: Feature heatmaps for Square_mh.
48

---

Published as a conference paper at ICLR 2026
May
May
Rap
Rep
Bap
Aap
Figure 25: Feature heatmaps for Transport mh.
A.15 LARGE, DIVERSE EVIDENCE FOR HIGH EPISODE HOMOGENEITY
In this section, we provide both qualitative and quantitative evidence for high episode homo-
0-
1.00
Cosine similarity
geneity.
Episodd index
6
12
0.95
In qualitative experiments, visualize the simi- larity heatmap for the features between episodes in Figures 27 to 32. Specifically, for each task, we regenerate 50 episodes and extract fea- tures from layers across 10 uniformly sam- pled timesteps. We compute a 50 x 50 cosine- similarity matrix across episodes, producing 80 matrices per task, giving comprehensive view on episode hemogeneity across multimodal tra- jectories. Fig. 26 illustrates an example of the computed similarity matrix. Each entry repre- sents the similarity between the features of two independent episodes. To make the visualiza- tion clearer, the range of all maps is restricted to 008, 1.0). These figures clearly demonstrate strong homogeneity across different episodes.
18
24
0.90
30
36
0.85
[) 42
48
0.80
TO
15
u
0
40
45
HNNMM
Episode index
Figure 26: Inter-episode feature similarity for the
Lift task at the FFN block of layer at timestep 99,
In quantitative analysis, we conduct statistics on inter-episode similarities. As shown in Table 29, the average per-matrix mean similarity stays 20096 with 95th-percentile entries 20.99, indicating
49

---

Published as a conference paper at ICLR 2026
the similarity curve is essentially flat. Moreover, find that differences across episodes emerge almost exclusively within the final 5% denoising steps, this indicates that the vast majority of the diffusion process remains highly consistent across episodes, with only minor divergence introduced during the final stage. These results reflect a repeatable property of the denoising dynamics of the model.
loper
Sggr
loper 2
lspa 5
baper 4
bayes 5
laya: 6
layer 7
1tep
step
Mtp
step
stop
stop
step
59ep
10p
step
Figure 27: Inter-episode similarity pattern for Lift.
50

---

Published as a conference paper at ICLR 2026
layer
lager
layer 2
loper 3
Bayer 4
layer 5
layer is
layer
step
step
step
step
stop
stp
stop
step
step
step
Figure 28: Inter-episode similarity pattern for Can.
loper
layer
loper 2
loper
bayer
Tayer 5
lager 6
bayor
Map
Mtp
Mep
step
step
stop
step 66
59ep
H0p
step
Figure 29: Inter-episode similarity pattern for Square.
51

---

Published as a conference paper at ICLR 2026
bapar 0
bayer I
kyy 2
layer 3
layor
1apa
lopar 6
laper
11
22
33
44
<tpp 55
step 65
step 77
58
99
Figure 30: Inter-episode similarity pattern for Pusht.
52

---

Published as a conference paper at ICLR 2026
layer
lager
layer 2
loper 3
Bayer 4
layer 5
layer i
layer
step
step
step
step
stop
stp
stop
step
step
step
Figure 31: Inter-episode similarity pattern for Transport
loper
layer
loper 2
laper 3
bayer
Tayer 5
lager 66
bayor
Mep
Mtp
Mep
step
step
stop
step
s9ep 77
10pp
step
Figure 32: Inter-episode similarity pattern for Tool hang.
53

---

Published as a conference paper at ICLR 2026
Task
AvgMean
MinMean
AvgStd
MaxStd
AvgP05
AvgP95
Can_mh
0.9910
0.8206
0.0061
0.1414
0.9789
0.9980
Lift_mh
0.9767
0.7352
0.0156
0.1625
0.9465
0.9954
Square mh
0.9744
0.6398
0.0268
0.2050
0.9291
0,9949
Transport.mi
0,9981
0,9393
0.0026
0.1017
0,9922
0.9998
Can_ph
0,9925
0.9049
0.0067
0.0769
0.9782
0.9986
Lift.ph
0.9937
0.9254
0.0048
0.0552
0.9839
0.9988
Pusht
0.9285
0.2885
0.0526
0,5010
0.8277
0.9930
Square ph
0,9622
0.6829
0.0333
0.2729
0.8917
0.9936
Tool hang ph
0,9751
0,6957
0.0290
0.4019
0,9195
0.9983
Transport-ph
0.9920
0.8627
0.0085
0.1348
0.9752
0.9991
Table 29: Inter-episode similarity statistics across tasks.
A.16 EVALUATING BAC UNDER DDIM SCHEDULERS
In this section, investigate the performance of BAC when integrated with sampling- based methods, specifically focusing on the DDIM scheduler with a step size of K = 40. We apply BAC on top of DDIM across different update steps (S 3, 10) and report the results in terms of Success Rate and Speedup.
Table 30: Performance of BAC integrated with DDIM (K 40) across various benchmarks. Results are presented as (Success Rate / Speedup).
Benchmark on Proficient Human (PH) demonstration data.
Method
Lift
Can
Square
Transport
Tool Hang
Push-T
DDIM (K = 40)
1.00/1.00
0,95/1.00
0.84/1.00
0.75/1.00
0.47/1.00
0.55/1.00
BAC (S 3, 3)
1.00/3.22
0.56/3.49
0.64/3.67
0.00/3.14
0,00/3.43
0.44/3.15
BAC (S 5, 3)
1.00/2.41
0.95/3.22
0.87/2.85
0.58/2.97
0.30/3.08
0.53/3.23
BAC (S = 10, 3)
1.00/2.32
0.94/2.41
0,86/2.53
0.76/2.33
0,47/2.38
0.55/2.48
Benchmark on Mixed Human (MH) demonstration data.
Method
Lift
Can
Square
Transport
DDIM (K = 40)
0.99/1.00
0.93/1.00
0.74/1.00
0.34/1.00
BAC (S 3, 3)
0.98/3.44
0.54/3.63
0.04/3.71
0.22/3.55
BAC (S 5, 3)
0.98/3.14
0.87/3.23
0.68/3.33
0.30/2.94
BAC (S 10, 3)
0.99/2.29
0.90/2.43
0.75/2.45
0.33/2.20
Benchmark multi-stage tasks. For Block-Pushing, denotes pushing blocks. For Kitchen, Ps denotes interacting with
objects.
Method
Kitchen pl
Kitchen P2
Kitchen ps
Kitchen p4
BP p1
BP p2
DDIM (K = 40)
1,00/1.00
1,00/1.00
1.00/1000
0.96/1.00
0,98/1.00
0,94/1.00
BAC (S 3, = 3)
0.99/3.56
0.99/3.56
0.99/3.56
0.97/3.56
0.94/3.27
0.95/3.43
BAC (S =5,
1.00/2.99
1.00/2.99
1.00/2999
0.99/2.99
0.94/2.95
0.95/3.16
BAC (S 10, 3)
1.00/2.23
1.00/2.23
1.00/2.23
0.97/2.23
0.98/2.23
0.97/2.36
Even when integrated with the faster DDIM scheduler, the BAC algorithm demonstrates significant speedup of 2.2 to 3.5x while maintaining high success rates. This result emphasizes that the efficiency gains provided by BAC are not merely due to reductions in denoising steps, but rather stem from the inherent acceleration capabilities of BAC itself.
54


Reviews:
[{"review_id": "SoSKbc3sFy", "reviewer": "Reviewer_p5ox", "summary": "his paper introduces Block-wise Adaptive Caching (BAC), a training-free acceleration method for transformer-based Diffusion Policy models used in robotic control. Diffusion Policy models are powerful but computationally expensive due to their iterative denoising process. BAC addresses this by adaptively caching intermediate features at the block level, significantly reducing redundant computation without sacrificing performance.\nKey Contributions:\n1.\tBlock-wise Adaptive Caching (BAC): A novel caching strategy that adaptively updates and reuses features at the block level, tailored for Diffusion Policy architectures.\n2.\tAdaptive Caching Scheduler (ACS): Uses dynamic programming to determine the optimal update timesteps for each block, maximizing feature similarity and minimizing caching error.\n3.\tBubbling Union Algorithm (BUA): Mitigates inter-block error propagation, especially in FFN blocks, by enforcing upstream updates when downstream blocks are updated.\n4.\tExtensive Experimental Validation: Demonstrates up to 3.55× speedup with no performance loss across multiple robotic tasks and models, including large-scale vision-language-action (VLA) models like RDT-1B.\n5.\tTraining-Free and Plug-and-Play: BAC is easy to integrate into existing models without retraining or architectural changes.", "questions": "Q1. Practical Performance on Physical Hardware\nThe reported GPU-time improvements in simulation are promising. However, in real-world robotic systems, such gains can diminish due to factors like camera latency, USB bandwidth limitations, or motor jitter. Could the authors provide any empirical timing results—even from a single task on one robot arm—showing the actual wall-clock frequency achieved in a lab setting? This would help validate the practical applicability of the method.\n\nQ2. Comparison with Fewer Denoising Steps\nIn image diffusion models, reducing denoising steps (e.g., from 1000 to 20) is a common acceleration strategy while maintaining acceptable output quality. Could the authors include a comparative analysis—such as a small plot—illustrating performance when using only 15 or 20 steps, both with and without BAC? This would clarify whether the proposed caching mechanism offers advantages beyond simply executing fewer denoising iterations.\n\nQ3. Visualization of Cache Behavior\nAs a visual learner, I would find it greatly helpful to see a figure illustrating the cache's effect—for instance, an attention map or feature heatmap at a step where the cache decided not to update. Such a visualization would intuitively convey the underlying \"similarity\" concept without relying solely on mathematical formulations.\n\nQ4. Hyperparameter Tuning for New Tasks\nThe paper mentions using S = 7 or 10. If a user applies the method to a new robot task, are there practical guidelines—such as \"start with S = 8\"—to avoid extensive hyperparameter search? A brief recommendation in the paper would greatly improve usability.\n\nQ5. Code Accessibility\nThe commitment to open-source the code is appreciated. Would it be possible to share a GitHub link during the rebuttal period—even if kept private temporarily—so that reviewers can examine the license and potentially run a simple local example?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "This paper presents an original contribution by demonstrating that a block-level, training-free caching mechanism can significantly reduce the inference time of Diffusion Policy without compromising accuracy. Its strength lies in a clear problem statement—addressing the well-known 10 Hz to 30 Hz performance gap—and a novel insight: non-uniform temporal similarity across transformer blocks necessitates per-block caching schedules, while upstream errors can propagate and amplify into downstream FFN failures if not properly trapped. The authors support this with a concise error-propagation model and exhaustive simulations, ranging from small control tasks to a 1-B parameter VLA model, consistently achieving a 3× speedup with reproducible artifacts. Although the idea builds upon existing caching concepts, its novel reframing for Diffusion Policy, plug-and-play practicality, and immediate real-time performance gains render this work both high-quality and broadly significant for deploying generative models under strict latency constraints.", "weaknesses": "My primary concern is the absence of physical validation, as all experiments were conducted in simulation. Based on lessons from computer vision, we know that improvements in GPU-FLOPS do not always translate to reduced real-world latency. A brief hardware trace—even for a single arm and task—would help demonstrate that the acceleration persists in the presence of motor noise and timing jitter. I would also appreciate a comparison with standard diffusion acceleration techniques to validate the unique advantage of the proposed robot cache.\n\nThat said, the core idea is intuitive, the evaluation is thorough within the simulation framework, and the commitment to open-source the code is commendable. Should the authors add at least minimal real-robot validation and discuss the cache's robustness under more aggressive quantization or fewer denoising steps, I believe the paper would be of great value to the community.", "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": "67DnsCvIxy", "reviewer": "Reviewer_o36f", "summary": "This paper proposes Block-wise Adaptive Caching (BAC), a training-free method to accelerate Transformer-based Diffusion Policies for real-time robot control. BAC adaptively caches and reuses intermediate block features using a dynamic scheduling algorithm and a bubbling mechanism to prevent error propagation. It achieves up to 3× faster inference without performance loss across multiple robotics benchmarks.", "questions": "In Stage 1 of BUA, the method identifies “high-error” upstream blocks using a global $L_1$ norm (Eq. 13), which measures the average feature variation across all timesteps. However, the “error surge” analyzed in Section 3.3 is a localized event that occurs when an FFN block updates while its upstream block reuses a high-error cache at the same timestep. Why  is a global average metric $l_j$ the right choice for addressing an instantaneous error propagation problem? Wouldn’t a more appropriate measure be the instantaneous cache error at the specific timesteps where the FFN depends on the block?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper proposes a method that achieves a 3× speedup, which is an important step toward making diffusion policies truly practical for real-world robotic control.\n2. The paper offers an analysis of the internal feature dynamics of Diffusion Policy, revealing that feature similarity across timesteps is non-uniform among different Transformer blocks (SA, CA, FFN), which provides a solid foundation for the proposed block-wise adaptive method.\n3.  Another major highlight is the discovery and explanation of the “Error Surge” phenomenon: naive block-level caching causes severe degradation in FFN blocks, and the authors convincingly attribute this to the amplification and propagation of upstream errors due to the absence of LayerNorm. This insight is broadly relevant to all Transformer-based caching approaches.", "weaknesses": "Proposition 3.1 is the paper’s only theoretical contribution, aiming to explain error propagation in the FFN blocks. While the first-order Taylor expansion (Appendix A.4) is directionally correct, it does not provide any quantitative bound, nor does it explain why the SA/CA blocks (which also contain $W_{out}$) do not exhibit the same error surge phenomenon.", "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": "JmFiW05kcr", "reviewer": "Reviewer_N17f", "summary": "The paper introduces Block-wise Adaptive Caching (BAC), a training-free method designed to accelerate inference for transformer-based Diffusion Policy models in robotic control. The method is composed of two primary components: an Adaptive Caching Scheduler (ACS), which employs dynamic programming to compute an optimal, non-uniform schedule of cache update steps for each transformer block by maximizing feature similarity; and a Bubbling Union Algorithm (BUA). The authors identify a novel \"error surge phenomenon,\" where naive block-wise scheduling leads to catastrophic error propagation, particularly in Feed-Forward Network (FFN) blocks. The BUA is proposed as a targeted solution to mitigate this issue by enforcing upstream blocks with high estimated errors to update their caches in synchrony with their downstream FFN counterparts. Through experiments on several robotic manipulation benchmarks, the authors claim that BAC achieves up to a 3x inference speedup with negligible, or even slightly improved, performance compared to the full-precision model.", "questions": "1. The core assumption of \"episode homogeneity\" is foundational to your method but is supported by only two examples. Could you provide a more systematic study across a large, diverse set of episodes and initial random noises for a given task to statistically validate that the feature similarity structure ($s_k$ curve) remains stable? How does your offline schedule contend with the explicitly multimodal, stochastic nature of diffusion policy?\n\n2. Could you provide qualitative video results comparing the behavior of a robot arm controlled by the baseline versus the BAC-accelerated policy? This would help visually verify that the claimed speedup does not introduce detrimental artifacts. Furthermore, do you have plans for or preliminary results from deploying this method on a physical robot to validate its real-world effectiveness and truly substantiate the claims of enabling real-time control?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- While caching in diffusion models is an existing area of research, the primary contribution of this paper—the identification, analysis, and targeted mitigation of the inter-block \"error surge phenomenon\"—is novel and insightful. The proposed Bubbling Union Algorithm (BUA), motivated by this analysis, is an original and simple heuristic for a previously undocumented problem.\n\n- The use of dynamic programming within the Adaptive Caching Scheduler (ACS) to find an optimal schedule under a well-defined objective function (maximizing feature similarity) is a principled and sound approach.\n\n- The authors validate their method across a commendable range of benchmarks (RoboMimic, Push-T, Kitchen, etc.), data sources (PH, MH), and even extend it to a large-scale Vision-Language-Action model (RDT-1B), providing evidence for the potential generalizability of the approach.", "weaknesses": "- Insufficient Evidence for the Core Assumption of Homogeneity: The entire offline-online paradigm of the proposed method hinges on the crucial assumption of \"high episode homogeneity\"—that a cache schedule computed from one trajectory can generalize to others. The evidence provided for this cornerstone assumption is extraordinarily weak, consisting of a visual comparison between only two demonstration instances (demo 11001 vs. 20000) in Appendix A.9. Generalizing a universal property from two samples is scientifically unsound and constitutes anecdotal evidence at best. This fails to adequately address the challenge that the stochastic nature of diffusion models can lead to fundamentally different trajectories (i.e., different action modalities), which may invalidate a statically computed schedule.\n- Absence of Real-World Hardware Experiments: All experiments are conducted in simulation, but the ultimate goal of robotic policy learning is deployment on physical hardware. The paper makes strong claims about enabling \"real-time robotic control\", but without a single real-world experiment, these claims remain unsubstantiated.", "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)