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REVIEW 4 major objections 6 minor 59 references

Learning dissection trajectories from expert surgical videos via imitation learning with equivariant diffusion

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read iDPOE, an implicit diffusion policy with equivariant representations, predicts ESD dissection trajectories from expert videos more accurately and with better generalization than prior explicit and implicit methods.

desk verdict Solid empirical paper on a new surgical trajectory task, but the load-bearing conditional sampling equation (Eq. 4) is mathematically unjustified and needs correction or explicit heuristic status. read the letter →

arxiv 2506.04716 v1 pith:GXHQTIBN submitted 2025-06-05 cs.CV

Hongyu Wang , Yonghao Long , Yueyao Chen , Hon-Chi Yip , Markus Scheppach , Philip Wai-Yan Chiu , Yeung Yam , Helen Mei-Ling Meng
show 1 more author
Qi Dou
This is my paper
classification cs.CV
keywords imitationlearningdiffusionpolicyequivariantneuralnetworktrajectorypredictionendoscopicsubmucosaldissectionsurgicalvideoanalysisconditionalsamplingbehaviorcloning
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper introduces iDPOE, an imitation-learning method that predicts the dissection trajectory a surgeon will take during Endoscopic Submucosal Dissection (ESD) from a short clip of expert endoscopic video. The method represents expert behavior as a joint state–action distribution modeled by an unconditional diffusion model, rather than a fixed deterministic mapping, so it can capture the genuine variability of dissection paths. It also builds rotational equivariance into the diffusion network, which the paper argues is what allows the policy to generalize to different endoscopic views. On a dataset of nearly two thousand annotated ESD clips, iDPOE reports lower average displacement, final displacement, and Fréchet distance than behavior cloning, an energy-based implicit policy, and three diffusion-based trajectory predictors, both on clips from the same surgical context and on clips from four unseen cases. If these results hold, the approach is a concrete step toward automated dissection-trajectory guidance for surgical training and intraoperative assistance.

What carries the argument

The central object is the implicit diffusion policy network, a U-Net with residual and attention blocks trained as an unconditional denoising diffusion model over the joint state–action pair $x = (s, a)$, where $s$ is the video-clip state and $a$ is the future dissection trajectory. The paper's key supporting identity is the conditional-sampling factorization in Eq. (4), $p_\theta(x_{t-1} \mid x_t, s^*) = p_\theta(x_{t-1} \mid x_t)\, q(s_t \mid s^*)$, which turns the learned unconditional denoiser into a predictor conditioned on an observed video clip $s^*$ by multiplying the denoising transition by a forward noising kernel from the observed state. Rotational equivariance is embedded by using $C_4$-equivariant convolutional layers in the network, so features transform predictably under discrete image rotations. The machinery's job is to let the same trained model generate synthetic trajectories unconditionally, then steer generation toward a specific video at inference time by diffusing the video state forward alongside the action denoising loop.

What would settle it

Train the same implicit diffusion policy but replace the forward-diffusion guidance with a properly trained conditional denoiser (for example, feeding the video frames as conditioning input or using classifier guidance), then re-run the in-context and out-of-context evaluations; if the product-kernel version in Eq. (4) does not at least match the properly conditioned variant, the reported advantage rests on an unvalidated sampling recipe rather than on the learned policy.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that an implicit policy represented by an unconditional diffusion model, trained to maximize the log-likelihood of the joint state–action distribution of expert demonstrations, predicts ESD dissection trajectories more accurately and with better generalization than explicit regression-based policies and prior implicit or diffusion-based trajectory predictors. The paper reports consistent improvements across all three metrics (ADE, FDE, FD) in both in-the-context and out-of-the-context evaluations, and its error standard deviations are lower as well. Two design choices carry the result: (1) representing the policy implicitly as a joint state–action density, which avoids averaging over the multiple plausible dissection paths that a deterministic behavior-cloning objective would collapse, and (2) conditioning the otherwise unconditional diffusion model at inference time through a forward-diffusion guided sampling loop that diffuses the observed video forward and denoises the action back. Rotational equivariance built into the U-Net backbone is what lets the learned policy transfer across rotated endoscopic scenes.

Load-bearing premise

The load-bearing premise is the conditional-sampling factorization in Eq. (4), which treats conditioning the denoising step on the observed video as a simple multiplication of the learned unconditional denoising transition by a forward noising kernel from the video to the noisy state, an identity the paper states without derivation.

Editorial extensions

If this is right

  • If the reported gains are correct, iDPOE can serve as the basis for real-time dissection-trajectory guidance in ESD, running at roughly 23 FPS on a standard GPU.
  • The implicit diffusion policy can generate synthetic expert dissection trajectories; the paper shows that mixing these synthetic trajectories with real ones improves behavior-cloning training, an affordable data-augmentation route for surgical skill models.
  • Because the method generalizes to four unseen surgical cases in the out-of-the-context test set, it is a candidate for cross-patient and cross-scene deployment without per-case retraining.
  • The equivariant representation is the paper's stated mechanism for improving generalization to geometric symmetries, and its ablation attributes a consistent margin to this component.
  • If the method transfers to other endoscopic procedures, the same implicit-diffusion-with-forward-guidance recipe could become a general tool for procedure-agnostic trajectory prediction.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural next step is to prove or empirically test the identity $p_\theta(x_{t-1} \mid x_t, s^*) = p_\theta(x_{t-1} \mid x_t)\, q(s_t \mid s^*)$, since the paper states it without derivation; if it fails, the guided-sampling recipe could be replaced by a properly derived conditional denoiser and the baseline comparison redone.
  • The $C_4$ rotation group is a coarse discretization of the full planar rotation symmetry of dissection trajectories; extending to finer or continuous equivariance groups could yield further gains on highly varied endoscopic views.
  • Because the implicit policy is trained as an unconditional generator, the same model can act as both predictor and data synthesizer; using its synthetic clips to pretrain downstream models such as phase recognition or tool tracking is a testable extension the paper does not explore.
  • The out-of-the-context evaluation uses four unseen surgical cases; a leave-one-case-out cross-validation over all 40 collected videos would sharpen the generalization claim beyond what the paper reports.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes iDPOE, an implicit diffusion policy with equivariant representations for imitation learning, to predict Endoscopic Submucosal Dissection (ESD) dissection trajectories from expert endoscopic videos. It trains an unconditional DDPM-style model on joint state-action pairs and, at inference, uses a proposed "forward-diffusion guided" conditional sampler (Eq. 4) to inject the observed video. The method is evaluated on a private dataset of 1993 annotated clips from 40 ESD videos against BC, iBC, MID, LED, and SingularTrajectory, with ablations for implicit modeling, guidance, equivariance, synthetic data, and blurred conditions. The authors report consistent improvements in ADE/FDE/FD in both in-the-context and out-of-the-context settings and an inference speed of about 23 FPS.

Significance. If the results hold, this would be the first imitation-learning approach for dissection trajectory prediction and could be practically useful for surgical training and intraoperative guidance. The paper's strengths include a sizeable annotated clinical dataset, an evaluation on previously unseen surgical cases, ablations of the main components, and a computational-complexity analysis. However, the central conditional-sampling equation appears mathematically unsound, the empirical comparison lacks significance testing and baseline tuning details, and the out-of-the-context set is small; these issues place the main claim at risk and require a major revision.

major comments (4)
  1. [§3.4, Eq. (4)] The decomposition pθ(x_{t−1}|x_t,s*) = pθ(x_{t−1}|x_t) q(s_t|s*) is not a valid conditional reverse transition. For fixed x_t and s*, q(s_t|s*) is a scalar that does not depend on x_{t−1}; after normalization over x_{t−1}, the right-hand side is exactly pθ(x_{t−1}|x_t). Thus Eq. (4) does not introduce conditioning on s* in the probabilistic sense, and no derivation is given for the equality. The algorithm described in the text and Figure 3—denoising the action while the state channel is re-supplied as a forward-diffused version of s*—may be a useful heuristic, but it is not justified by Eq. (4). Since this sampler is the mechanism by which video observations are injected at inference, the reported gains over the baselines rest on an unsupported inference step. Please provide a correct derivation (e.g., using a likelihood p(s*|x_t) or an approximate guided-sampling formulation) or explicitly reframe the procedure as a heuristic and validate it against an alternative conditioning scheme.
  2. [§4.4, Table 1] The comparison reports only means and standard deviations with no number of independent runs, confidence intervals, or significance tests. For example, in the out-of-the-context set the FDE advantage of iDPOE over SingularTrajectory is 22.076±1.080 vs 22.996±2.367; with the reported standard deviations this difference is not self-evidently significant. In addition, no hyperparameter search or tuning budget is described for any baseline, so it is unclear whether the comparison is fair. Please add significance testing (or per-clip paired tests and effect sizes) and report the baseline tuning protocol.
  3. [§4.2] The out-of-the-context evaluation is based on only four previously unseen surgical cases (393 clips), and the in-the-context set is described as "consecutive frames selected from the same period in the training data," which suggests it may come from the same cases as training. The claim of generalization to "diverse surgical scenarios" needs a clearer case-level split and more unseen cases, or at least a discussion of the limits imposed by the four-case test set.
  4. [§3.1, Eq. (1)] The claimed equivalence max E[log πθ(a|s)] = max E[log pθ(s,a)] is not generally true: log πθ(a|s) = log pθ(s,a) − log pθ(s), and the state marginal pθ(s) also depends on θ. Unless pθ(s) is held fixed or the objective is explicitly defined as a surrogate, the diffusion training objective is not the behavior-cloning objective. The paper should clarify the exact objective being optimized and why maximizing the joint likelihood yields a valid policy.
minor comments (6)
  1. [§4.4] The text says "As shown in Table. 4.1" but should refer to Table 1; similar table-reference issues occur for Table 2 and Table 3.
  2. [§3.2, Eq. (2)] The norm notation in Eq. (2) is ambiguous: it is unclear whether the loss uses L2 norms or squared L2 norms, and the weighting parameter γ is not described in terms of a schedule or sensitivity analysis.
  3. [§3.5] The implementation section reports a fixed maximum of 200 epochs and a learning rate but does not state how the best checkpoint is selected or whether early stopping is used; please specify this for reproducibility.
  4. [§5.4] The synthetic-data augmentation experiment does not describe how the generated trajectories are filtered or validated for quality, and no significance testing is reported for the BC (synt) and BC (mix) comparisons.
  5. [§4.3] The Fréchet Distance metric is only described as measuring "geometrical similarity" between two temporal sequences; the precise discrete computation for length-6 polylines should be specified.
  6. [§1] The introduction states "To date, no data-driven solutions have been developed to predict dissection trajectories," which is inconsistent with the later disclosure that a preliminary version of this work appeared at MICCAI 2023 and with the cited trajectory-prediction works; the novelty claim should be qualified.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the central claim is an independent empirical comparison against external baselines, and the only self-citation is a non-load-bearing lineage note.

full rationale

The paper's central claim is the empirical result in Table 1, where iDPOE is compared with external baselines (BC, iBC, MID, LED, SingularTrajectory) on an annotated ESD dataset using ADE/FDE/FD. No parameter is fitted to those target metrics, no benchmark is redefined in terms of the method's own output, and the comparison is self-contained against external methods. The training losses in Eqs. (1)-(2) follow standard diffusion-model practice and are cited to external work. The only self-citation is the statement in Section 1 that a preliminary version appeared in MICCAI 2023 [27]; it is a lineage note and is not used to justify any equation, exclude alternatives, or supply a uniqueness theorem. Section 3.4's Eq. (4) is asserted without derivation and, as written, is not a valid conditional reverse transition because q(st|s*) is constant in xt-1; however, that is a correctness/mathematical-validity risk, not a circular reduction, because the observed state s* genuinely enters the sampling loop as the source of the forward-diffused visual input. The synthetic-data augmentation experiment in Section 5.4 uses the model's own samples to train a BC baseline, but that is a separate downstream-utility analysis, not the headline prediction result. Therefore no circular step can be exhibited from the paper's equations or citations.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the DDPM training objective, the unproved conditional sampling factorization in Eq. (4), and the assumption of C4 rotational equivariance. No invented entities such as new particles or forces are introduced. The free parameters are hyperparameters and design choices, not constants fitted to the evaluation metrics.

free parameters (3)
  • gamma (state-action noise weighting) = not reported
    Equation (2) weights action noise versus state noise by gamma in [0,1]; the value is a hand-set hyperparameter that is not justified or swept in the paper.
  • T diffusion steps = not reported
    The number of diffusion steps is central to training and sampling but is not specified in the implementation details.
  • cyclic group C4 order = 4
    Equivariance is implemented only under C4 rotations; the choice is an assumption about the symmetry group of the task, not derived from data.
assumptions (4)
  • standard math DDPM ELBO reduces likelihood maximization to noise prediction (Ho et al., 2020)
    Used to write Eq. (2) as the training objective; assumed valid for high-dimensional state-action pairs.
  • domain assumption Dissection trajectories and video states transform equivariantly under C4 rotations of the image plane
    Section 3.3 assumes planar rotational symmetry; endoscopic scenes have gravity, lesion location, and tool orientation which may break this symmetry. No evidence is given that C4 equivariance matches expert behavior.
  • ad hoc to paper Eq. (4) factorization ptheta(xt-1|xt,s*) = ptheta(xt-1|xt) q(st|s*)
    Section 3.4 asserts this conditional sampling decomposition without proof; q(st|s*) is a forward diffusion kernel, not a conditional distribution over xt-1, so the equality as written is not justified.
  • domain assumption Joint state-action density ptheta(s,a) learned unconditionally can be used to recover the optimal action after forward-diffusion guidance
    Eq. (1) treats maximizing the log joint density as the objective, but inference replaces conditioning with a forward-diffusion heuristic; the connection between the trained objective and the sampling procedure is not formally established.

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Cite this review

Pith. "Pith review of Learning dissection trajectories from expert surgical videos via imitation learning with equivariant diffusion." pith.science (2026). https://pith.science/paper/GXHQTIBN

@misc{pith2026250604716,
  author       = {Pith},
  title        = {Pith review of: Learning dissection trajectories from expert surgical videos via imitation learning with equivariant diffusion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GXHQTIBN}},
  note         = {Machine review of arXiv:2506.04716}
}
read the original abstract

Endoscopic Submucosal Dissection (ESD) is a well-established technique for removing epithelial lesions. Predicting dissection trajectories in ESD videos offers significant potential for enhancing surgical skill training and simplifying the learning process, yet this area remains underexplored. While imitation learning has shown promise in acquiring skills from expert demonstrations, challenges persist in handling uncertain future movements, learning geometric symmetries, and generalizing to diverse surgical scenarios. To address these, we introduce a novel approach: Implicit Diffusion Policy with Equivariant Representations for Imitation Learning (iDPOE). Our method models expert behavior through a joint state action distribution, capturing the stochastic nature of dissection trajectories and enabling robust visual representation learning across various endoscopic views. By incorporating a diffusion model into policy learning, iDPOE ensures efficient training and sampling, leading to more accurate predictions and better generalization. Additionally, we enhance the model's ability to generalize to geometric symmetries by embedding equivariance into the learning process. To address state mismatches, we develop a forward-process guided action inference strategy for conditional sampling. Using an ESD video dataset of nearly 2000 clips, experimental results show that our approach surpasses state-of-the-art methods, both explicit and implicit, in trajectory prediction. To the best of our knowledge, this is the first application of imitation learning to surgical skill development for dissection trajectory prediction.

Figures

Figures reproduced from arXiv: 2506.04716 by the authors.

Figure 1
Figure 1. A graphical abstract of iDPOE. iDPOE predicts dissection trajectories by learn [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. An overview of our approach iDPOE. (a) illustrates the modeling of the implicit [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. The inference process for trajectory prediction with the forward-diffusion guid [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Visualized results of our method under settings of in-the-context and out-of [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: Ablation study for key components of our method. [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 6
Figure 6. Figure 6: Visualization of reverse processes of unconditional/conditional sampling from [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]
Figure 7
Figure 7. Figure 7: Performance versus computational complexity. [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.