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arxiv: 2606.12365 · v1 · pith:7O37J4DUnew · submitted 2026-06-10 · 💻 cs.RO · cs.AI

Ambient Diffusion Policy: Imitation Learning from Suboptimal Data in Robotics

Adam Wei , Nicholas Pfaff , Thomas Cohn , Arif Kerem Day{\i} , Constantinos Daskalakis , Giannis Daras , Russ Tedrake This is my paper

Pith reviewed 2026-06-27 09:51 UTC · model grok-4.3

classification 💻 cs.RO cs.AI
keywords imitation learningdiffusion policysuboptimal dataroboticsnoise-dependent trainingspectral power lawco-trainingOpen X-Embodiment
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The pith

Ambient Diffusion Policy learns robot behaviors from suboptimal data by restricting its contribution to only high and low diffusion times.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Ambient Diffusion Policy as a method for imitation learning that co-trains on both high-quality and suboptimal robot data. It restricts suboptimal data to high and low diffusion times only, based on the claim that robot action data follows a spectral power law. This power law is said to induce a global-to-local hierarchy and locality properties in the optimal diffusion policy, allowing useful features to be extracted while avoiding harmful ones from the suboptimal samples. The approach is tested on four categories of suboptimal data across six tasks and scales to large heterogeneous collections. If correct, it would make abundant but imperfect demonstration data more usable without extensive filtering.

Core claim

Ambient Diffusion Policy restricts the contribution of suboptimal data during training to only the high and low diffusion times. This restriction is justified by first observing that robot action data exhibits a spectral power law, which induces a global-to-local hierarchy and locality on the optimal Diffusion Policy. The method is shown to extract only useful features from arbitrary suboptimal sources including noisy trajectories, sim-to-real gaps, task mismatches, and large-scale mixtures, outperforming co-training baselines.

What carries the argument

Ambient Diffusion Policy, which adds noise-dependent data usage by restricting suboptimal data to high and low diffusion times to exploit the global-to-local hierarchy and locality induced by the spectral power law in robot action data.

If this is right

  • The method works across noisy trajectories, sim-to-real gaps, task mismatches, and heterogeneous mixtures.
  • It outperforms existing co-training baselines by up to 33 percent when scaled to large datasets like Open X-Embodiment.
  • It increases the utility of suboptimal demonstrations without requiring manual separation of features.
  • It expands the range of data sources that can be used for imitation learning in robotics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same noise-dependent restriction might transfer to diffusion models outside robotics, such as those for planning or generation tasks.
  • The spectral power law observation could motivate similar time-based data weighting in other sequential models.
  • Data collection pipelines might incorporate automatic checks for spectral properties to decide which demonstrations to include at which noise levels.

Load-bearing premise

Robot action data exhibits a spectral power law that creates a global-to-local hierarchy and locality allowing useful features from suboptimal data to be isolated at high and low diffusion times without loss.

What would settle it

Measure whether performance improves, stays the same, or degrades when suboptimal data is allowed at medium diffusion times instead of being restricted; the claim requires that medium times add net harm.

Figures

Figures reproduced from arXiv: 2606.12365 by Adam Wei, Arif Kerem Day{\i}, Constantinos Daskalakis, Giannis Daras, Nicholas Pfaff, Russ Tedrake, Thomas Cohn.

Figure 1
Figure 1. Figure 1: Training Algorithm for Ambient Diffusion Policy. High-quality data can be used during training at all diffusion times. Suboptimal data is restricted to training at low or high diffusion times t ∈ [0, tmax) ∪ (tmin, T]. Task visualizations. We evaluate Ambient Diffusion Policy on four types of action suboptimality, six different tasks, and scale to the Open X-Embodiment (OXE) [1]. Abstract: We propose Ambie… view at source ↗
Figure 2
Figure 2. Figure 2: The spectral power law induces a global-to-local hierarchy in action diffusion. This is analogous to the “coarse-to-fine” hierarchy in image diffusion [60]. (a) t ≥ t2 (global planning): the policy commits to a high-level path through the maze. t < t2 (local refinement): it refines the plan to be collision-free at t1 and smooth at t0. (b) t3: the policy plans to move a block to the right bin. t2: it plans … view at source ↗
Figure 4
Figure 4. Figure 4: The spectral power law makes Gaussian noise act as a high-frequency mask. (a) Noisy trajectory visualizations. (b) PSD analysis for the noisy trajectories in the x-dimension at each diffusion time: the gray regions indicate masked frequencies, which have low SNR. As t increases, adding Gaussian noise destroys the signal in the trajectory, starting from the local (high-frequency) features first. This effect… view at source ↗
Figure 6
Figure 6. Figure 6: The “smoothness vs success rate” Pareto frontier for Ambient (blue) dominates co￾training (red) in both the (a) maze and (b) neural motion planning experiments. This trade-off is controlled by σtmin for Ambient and α for co-training. 7 Controlled Experiments We evaluate Ambient Diffusion Policy on three distribution shifts in robot action data to illustrate its generality: noisy trajectories, sim-to-real g… view at source ↗
Figure 5
Figure 5. Figure 5: GCS (left) vs RRT (right) data. The high-quality GCS [65] trajectories are smoother and shorter than their RRT [66] counterparts. Consider a 2D point robot that must navigate between random start and goal positions in a maze environment (Figure 1a). A policy roll￾out is successful if it reaches an ϵ-ball around the goal within a time limit without collision. We measure a policy’s global understanding of th… view at source ↗
Figure 7
Figure 7. Figure 7: Left: Performance metrics vs σtmax . The logic metric plateaus before σt ∗max = 0.46 and deteriorates rapidly afterwards; the opposite is true for the motion metric. Thus, the policy learns local motion-level features for t ∈ [0, t∗ max) and global logic-level features for t ∈ (t ∗ max, T]. Right: Unlike co-training, Ambient achieves a near-optimal trade-off between logic and motion metrics. 7.4 Task Misma… view at source ↗
Figure 8
Figure 8. Figure 8: Left: success rate of policies finetuned from different base policies. Right: smoothness of finetuned policies in the maze experiment. We compare smoothness instead of success rate since all policies achieved 99.0%+ success rate. 7.5 Finetuning Comparison Finally, we compare against the finetuning baseline. For each experiment, we finetune the best co-trained policy and the best Ambient policy on Dp; imple… view at source ↗
Figure 9
Figure 9. Figure 9: When scaled to OXE, Ambient Diffusion Policy outperforms data filtering and co￾training by up to 15% on table cleaning and 84% on tower building (20 trials per policy). In co-training, St contains all datasets for all t ∈ [0, T]; in Ambient, St depends on each dataset’s tmin and tmax (see Figures 21 and 22). Re-weighting marginally improves the Ambient policies but is not required; in contrast, it is neces… view at source ↗
Figure 10
Figure 10. Figure 10: Ambient is significantly less sensitive to dataset re-weighting than co-training. The Ambient Diffusion Policy performed at most 9% worse without re-weighting. The co-trained poli￾cies were too dangerous to evaluate without re-weighting. 9 Limitations and Future Work Ambient Diffusion Policy does not yet handle distribution shifts in the observation space. We ex￾plore two initial attempts in Appendix J. T… view at source ↗
Figure 11
Figure 11. Figure 11: A visualization of the average PSD for a diverse range of robot datasets; a spectral power law exists in all of them [PITH_FULL_IMAGE:figures/full_fig_p034_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The backward process commits to a global plan at high noise. By σt = 0.878, the global plan in A0 can already be recovered from At with 95% accuracy. Accuracy plateaus afterward. This indicates that the start of the backward process performs global planning [PITH_FULL_IMAGE:figures/full_fig_p035_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Average classifier out￾put for suboptimal samples in the 2D maze dataset (Section 7.1) at different diffusion times. As t increases, pt and qt become harder to distinguish. The dotted line is the threshold 0.5 − τ , which is crossed for tmin = 18. schedule with T = 100 diffusion steps. We apply EMA to the training loop. Sampling is performed online using 10 steps of DDIM [57]. Predicted actions are linear… view at source ↗
Figure 14
Figure 14. Figure 14: Policy rollouts from the same start and goal pairs for different training algorithms. a) The policy trained with data filtering (i.e. GCS-only) has not seen enough data to learn the maze. Its rollouts frequently collide with obstacles. b) The policy trained with RRT-only has memorized the maze, but exhibits non-smoothness. c) The co-trained policy’s behavior is similar to the RRT￾only policy. d) The Ambie… view at source ↗
Figure 15
Figure 15. Figure 15: Maze success rate vs σtmin . For small σtmin , the Ambient Policies are smooth and achieve high success rate (see Figure 6a). As σtmin increases, the RRT data is used less during training, which reduces success rate. Given a start and goal configuration q0, q1 ∈ R 7 , we use BiRRT [88] to produce the suboptimal data. To produce the high-quality data, we first run randomized shortcutting [89] to slightly s… view at source ↗
Figure 16
Figure 16. Figure 16: Figure 6b repeated with best-of-100 evaluation. The overall trends are the same, but the success rates are higher and the gap between the two Pareto frontiers is smaller. The collision-free constraint SDF(q(s)) ≥ 0, ∀s ∈ [0, 1] is applied at 200 points evenly spaced along the trajectory. Collision checking with finer granularity is performed after trajectory opti￾mization to filter trajectories with colli… view at source ↗
Figure 17
Figure 17. Figure 17: Neural motion planning σtmin sweep. (a) For small σtmin , the policies are smoother, which results in fewer accidental collisions and increases success rate. For large σtmin , the RRT data becomes under-utilized, which decreases the success rate. (b) Increasing σtmin improves smooth￾ness. G.3 Sim-and-Real Co-training: Planar Pushing Data Generation: We use the datasets from Wei et al. [12]. Dp contains hu… view at source ↗
Figure 18
Figure 18. Figure 18: Distribution of tmin labels. This histogram shows the distribution of tmin ∈ [0, 100] assigned to each action chunk by the classifier for the sim-and-real experiments. G.4 Task Mismatch: Block Sorting Data Collection: Both datasets were collected using VR teleoperation. Evaluation: On each trial, 1-3 red blocks and 1-3 blue blocks are randomly initialized in a pile between the bins. The time limit is 20s … view at source ↗
Figure 19
Figure 19. Figure 19: Sim-and-real co-training ablations. Eight ablations covering the key design decisions of Ambient Diffusion Policy. See Appendix G.3 for the per-panel analysis. 45 [PITH_FULL_IMAGE:figures/full_fig_p045_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Additional motion-level metrics for the block sorting experiment (Section 7.4). (a) Grasp attempts per block improves as σtmax increases but plateaus after σt ∗max = 0.46. (b) Time per block improves as σtmax increases [PITH_FULL_IMAGE:figures/full_fig_p046_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Table Cleaning: Dataset re-weighting and tmin visualization. These plots show the sampling ratio for Dp (shown in blue) and each dataset in COXE at different diffusion times for the table cleaning task. Left: Co-training uses the same sampling ratio at all diffusion times. Right: The sampling ratio for each dataset varies at each diffusion time. Notably, at intermediate diffusion times, only data from Dp … view at source ↗
Figure 22
Figure 22. Figure 22: Tower Building: Dataset re-weighting and tmin visualization. See [PITH_FULL_IMAGE:figures/full_fig_p049_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Finetuning resulted in no statistically significant change in policy performance on the [PITH_FULL_IMAGE:figures/full_fig_p051_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Algorithms for handling distribution shift in the observation space. Neither approach produced stronger policies on the table cleaning task. (a) Adding Gaussian noise to the observations during training. (b) Classifier-free guidance [94] swept over guidance weights w. 52 [PITH_FULL_IMAGE:figures/full_fig_p052_24.png] view at source ↗
read the original abstract

We propose Ambient Diffusion Policy, a simple and principled method for imitation learning from suboptimal data in robotics. High-quality, task-specific robot data is expensive and time-consuming to collect, while suboptimal datasets with lower-quality or out-of-distribution demonstrations are abundant. Existing methods that co-train on both data sources in robotics often fail to separate the meaningful and the harmful features in the suboptimal samples. In contrast, our method extracts only the useful features by introducing a new axis to co-training in robotics: noise-dependent data usage. Ambient Diffusion Policy restricts the contribution of suboptimal data during training to only the high and low diffusion times. To rigorously justify our approach, we first observe that robot action data exhibits a spectral power law. This induces two important properties on the optimal Diffusion Policy that we exploit: a global-to-local hierarchy and locality. We theoretically formalize this discussion using a simplified model. Our experiments validate Ambient Diffusion Policy on four types of suboptimal action data (noisy trajectories, sim-to-real gap, task mismatch, and large-scale data mixtures) across six tasks. The results show that it effectively learns from arbitrary sources of suboptimal data. Notably, it outperforms existing co-training baselines by up to 33% when scaled to Open X-Embodiment - a large dataset with heterogeneous data quality and unstructured distribution shifts. Overall, Ambient Diffusion Policy increases the utility of suboptimal demonstrations and expands the set of usable data sources in robotics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes Ambient Diffusion Policy, an imitation learning method that co-trains on optimal and suboptimal robotic demonstration data by restricting the suboptimal data's contribution exclusively to high and low diffusion timesteps. This is justified by an observed spectral power law in robot action data that is claimed to induce global-to-local hierarchy and locality properties on the optimal diffusion policy; the approach is formalized via a simplified model in §3 and evaluated on six tasks spanning noisy trajectories, sim-to-real gaps, task mismatch, and large heterogeneous mixtures (including Open X-Embodiment), where it outperforms co-training baselines by up to 33%.

Significance. If the spectral power law and its induced properties hold in the evaluated high-dimensional action spaces, the method would meaningfully expand the set of usable demonstration sources in robotics by mitigating harmful features from suboptimal data without requiring explicit filtering or weighting. The empirical scaling results on heterogeneous real-world datasets provide concrete evidence of practical utility beyond controlled settings.

major comments (2)
  1. [Abstract and §3] Abstract and §3: The central justification for restricting suboptimal data to only high and low diffusion times rests on the claim that the observed spectral power law induces global-to-local hierarchy and locality properties that allow mid-scale features to be safely discarded. The simplified model used for formalization does not appear to include a direct verification that mid-frequency components in real high-dimensional action spaces carry no task-relevant information; this link is load-bearing for the method's correctness and requires either a more rigorous derivation or explicit counterexample analysis.
  2. [Experiments] Experiments (results on Open X-Embodiment and the four suboptimal data types): The reported gains (up to 33%) are presented as evidence that useful features are preserved, but without ablations that isolate the effect of the high/low-time restriction versus other co-training choices, it remains unclear whether the performance stems from the claimed spectral properties or from incidental regularization effects.
minor comments (1)
  1. [Method] Notation for diffusion time thresholds and the exact definition of 'high' and 'low' intervals should be made explicit with equations or pseudocode in the method section to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and detailed review. We address each major comment below with clarifications and commitments to revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3: The central justification for restricting suboptimal data to only high and low diffusion times rests on the claim that the observed spectral power law induces global-to-local hierarchy and locality properties that allow mid-scale features to be safely discarded. The simplified model used for formalization does not appear to include a direct verification that mid-frequency components in real high-dimensional action spaces carry no task-relevant information; this link is load-bearing for the method's correctness and requires either a more rigorous derivation or explicit counterexample analysis.

    Authors: The simplified model in §3 is constructed precisely to capture the observed spectral power law in robot action data and to derive the resulting global-to-local hierarchy and locality properties, thereby showing why mid-scale features from suboptimal data can be excluded at intermediate diffusion times without harming the learned policy. While the model is intentionally simplified to enable closed-form analysis, the empirical spectral observations and task results provide supporting evidence. To strengthen the direct verification in high-dimensional spaces as requested, we will add an explicit counterexample analysis section in the revision, examining mid-frequency components across the evaluated action datasets. revision: partial

  2. Referee: [Experiments] Experiments (results on Open X-Embodiment and the four suboptimal data types): The reported gains (up to 33%) are presented as evidence that useful features are preserved, but without ablations that isolate the effect of the high/low-time restriction versus other co-training choices, it remains unclear whether the performance stems from the claimed spectral properties or from incidental regularization effects.

    Authors: Our experiments compare Ambient Diffusion Policy directly against standard co-training baselines that use the same suboptimal data mixtures without the time-dependent restriction; the performance differential (including the 33% gain on Open X-Embodiment) therefore isolates the contribution of the high/low-time restriction. Nevertheless, to further rule out incidental regularization and to explicitly tie gains to the spectral properties, we will add targeted ablations in the revised manuscript that vary the diffusion-time ranges applied to suboptimal data and compare against alternative regularization strategies. revision: yes

Circularity Check

0 steps flagged

No circularity: method motivated by independent empirical observation of spectral power law and simplified model

full rationale

The paper's central justification begins with an empirical observation ('we first observe that robot action data exhibits a spectral power law') followed by theoretical formalization in a simplified model; this sequence is presented as input to the restriction strategy rather than derived from it. No equations reduce the claimed properties to the method by construction, no parameters are fitted then relabeled as predictions, and no self-citations or uniqueness theorems are invoked as load-bearing. The derivation chain remains self-contained against external data properties.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the spectral power law observation in robot action data and a simplified theoretical model, with potential free parameters in selecting diffusion time thresholds.

free parameters (1)
  • diffusion time thresholds
    The specific high and low diffusion times used to restrict suboptimal data are likely selected or tuned, though not detailed in the abstract.
axioms (1)
  • domain assumption Robot action data exhibits a spectral power law.
    This observation is used to justify the global-to-local hierarchy and locality properties exploited by the method.

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