{"id":"d88682cb-31a1-4dfb-b89d-8eb6b744475d","arxiv_id":"2506.04716","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"An implicit diffusion policy with equivariant representations predicts ESD dissection trajectories from expert videos and beats explicit and implicit baselines on ADE, FDE, and FD.","lead":"This paper trains a diffusion-based imitation learning model to predict where a surgeon's dissection tool will move next in endoscopic videos. The method adds rotation-equivariant representations and a forward-diffusion guided sampling step, and reports better trajectory prediction than several baselines on about 2,000 annotated ESD video clips.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (4) is not a valid conditional reverse transition: multiplying pθ(xt−1|xt) by q(st|s*) cannot condition on s* because the factor is constant in xt−1; the paper's central inference step is unjustified.","rationale":"The reader identified Eq. (4) as the load-bearing assumption, and I agree that it is the weakest point in the paper. The central claim of superior trajectory prediction depends on the forward-diffusion guided inference strategy: the paper explicitly motivates this strategy to correct state mismatches, and the ablation in §5.2 shows that removing guidance degrades performance. However, the paper gives no valid derivation of Eq. (4), and the equation as written cannot define a conditional reverse transition because the multiplying factor is independent of xt−1 and cancels under normalization. This is not a disagreement with the broader empirical results; the comparisons, ablations, and standard deviations are internally consistent. Rather, it means the mechanism behind the reported gains is not established as correct. The appropriate disposition is the same as the reader's: conditional acceptance, requiring either a corrected derivation and validated conditional sampler, or release of code and data to reproduce and test the sampling procedure independently. I therefore do not change the reader's verdict.","tokens_in":14855,"tokens_out":6502,"duration_ms":93762,"concrete_test":"Implement a corrected conditional reverse sampler for the same trained unconditional model: at each reverse step, use reconstruction or classifier guidance with a gradient of log q(s*|xt) or with the Bayes-rule posterior pθ(xt−1|xt,s*) ∝ pθ(xt−1|xt) q(s*|xt−1). Evaluate on the same out-of-context set (393 clips) and compare ADE/FDE against the Eq. (4) procedure and the no-guidance ablation in Fig. 5. If the corrected sampler does not match or beat the reported out-of-context ADE of 15.576, the improvement attributed to Eq. (4) is an artifact of the heuristic and the central mechanism is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central novelty of iDPOE is the forward-diffusion guided conditional sampler in §3.4. Equation (4) claims pθ(xt−1|xt, s*) = pθ(xt−1|xt) q(st|s*). This is not a valid conditional density. For fixed xt and s*, q(st|s*) is a scalar independent of xt−1, so after normalization the factor cancels and the right-hand side is exactly pθ(xt−1|xt). Thus Eq. (4) does not introduce any conditioning on s* beyond the fact that st was replaced by a forward-diffused copy of s*. No derivation is provided, and the decomposition does not follow from the Markov structure of the diffusion process. The ablation in §5.2 shows that the overall procedure changes predictions, but it does not validate Eq. (4) as a conditional transition. A correct conditional sampler would require a likelihood or gradient term coupling s* to the reverse trajectory, such as p(s*|xt) guidance. Because this sampler is the mechanism by which video observations are injected at inference, the reported trajectory-prediction gains rest on an unsupported inference step. This is a correctness risk, not merely a presentation issue.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":15160,"tokens_out":8237,"duration_ms":101911,"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":[{"comment":"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.","section":"§3.4, Eq. (4)"},{"comment":"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.","section":"§4.4, Table 1"},{"comment":"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.","section":"§4.2"},{"comment":"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.","section":"§3.1, Eq. (1)"}],"minor_comments":[{"comment":"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.","section":"§4.4"},{"comment":"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.","section":"§3.2, Eq. (2)"},{"comment":"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.","section":"§3.5"},{"comment":"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.","section":"§5.4"},{"comment":"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.","section":"§4.3"},{"comment":"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.","section":"§1"}],"recommendation":"major_revision","confidential_remarks":"The paper is a substantial extension of the authors' MICCAI 2023 work, and the relationship is disclosed. My main concern is the unsupported Eq. (4); if the authors can supply a derivation or honestly reframe the sampler as a heuristic with deeper empirical validation, and if the comparison is made statistically solid, the paper could become acceptable. The private dataset and clinical motivation are valuable; the lack of data/code release is a limitation but not a blocker for this revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear X,\n\nThe paper reports a clear empirical win on a genuinely new task — ESD dissection trajectory prediction — and the ablations are honest enough to take the method seriously. I'd send it to review, but whoever referees it should pin the authors down on the sampling justification in §3.4 before the method is trusted.\n\nWhat's new: this is the first imitation-learning pipeline for ESD trajectory prediction, combining an implicit diffusion policy with C4-equivariant representations and a forward-diffusion guided inference. The dataset is real surgical video (1993 clips from 40 cases), and the gains over BC, iBC, MID, LED, and SingularTrajectory are consistent across in-context and out-of-context splits. The ablations show each component (implicit modeling, guidance, equivariance) buys something, and the robustness check on blurred frames is a nice extra.\n\nSoft spots. Eq. (4) is not a valid conditional density. q(st|s*) is just a scalar for fixed xt and s*; it doesn't depend on xt−1, so multiplying pθ(xt−1|xt) by it changes nothing once normalized. The algorithm actually described in the text — replacing st with a forward-diffused s* during reverse sampling — is a plausible heuristic, but the paper doesn't derive why that should condition the action trajectory on s*. That gap is load-bearing: it is the mechanism by which video observations enter the prediction. A reviewer should ask for a correct derivation or an explicit statement that this is a heuristic, plus a theoretical or empirical argument for why it works. Also, no significance tests are reported (the standard deviations overlap in some cells), the out-of-context set is only four surgical cases, and the data/code aren't available yet. These are all fixable.\n\nWho it's for: people working on surgical video analysis or trajectory prediction in constrained visual domains. It's not a method paper that will change how diffusion conditioning is done, but it's a solid application study with a suspicious core.\n\nMy recommendation: accept-shaped after major revision. The empirical claim is strong enough that it deserves referee time, but the sampling equation needs to be corrected or downgraded to heuristic status, and the experimental reporting needs significance testing and ideally a larger OOC set.","headline":"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.","tokens_in":15657,"tokens_out":2710,"would_cite":false,"duration_ms":32354,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["imitation learning","diffusion policy","equivariant neural network","trajectory prediction","endoscopic submucosal dissection","surgical video analysis","conditional sampling","behavior cloning"],"falsifier":"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.","tokens_in":14695,"feed_emoji":"🩺","tokens_out":9987,"duration_ms":102413,"temperature":0.7,"pith_summary":"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.","feed_headline":"Diffusion policy beats prior models at predicting dissection paths","feed_subtitle":"Implicit diffusion policy trained on ~2,000 ESD clips predicts tool motion with lower error and better generalization.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"supplies the implicit behavioral-cloning formulation (maximizing the joint state–action density) that iDPOE adopts.","marker":"[23]"},{"why":"gives the denoising diffusion objective the paper adapts for training the implicit policy.","marker":"[49]"},{"why":"the paper's own preliminary version, which establishes the ESD trajectory-prediction task and the annotated dataset.","marker":"[27]"},{"why":"provides the equivariant steerable CNN construction used to embed rotational symmetry in the network.","marker":"[50]"},{"why":"states the equivariant convolution constraint (Eq. 3) that the C4-equivariant layers must satisfy.","marker":"[52]"},{"why":"the MID diffusion-based trajectory predictor that serves as a primary state-of-the-art baseline.","marker":"[57]"},{"why":"the Leapfrog diffusion baseline, whose training instability the paper cites when explaining why it underperforms.","marker":"[58]"},{"why":"the SingularTrajectory diffusion baseline, whose adaptive anchoring the paper says fails in dynamic ESD scenarios.","marker":"[59]"}],"fun_headline_variants":["Diffusion policy predicts surgical dissection paths more accurately","Implicit diffusion model beats SOTA on dissection trajectory prediction","Surgical AI learns dissection from 2000 expert videos","Equivariant diffusion improves dissection trajectory forecasting","AI model predicts dissection paths with lower error"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Diffusion policy predicts surgical dissection paths more accurately","Implicit diffusion model beats SOTA on dissection trajectory prediction","Surgical AI learns dissection from 2000 expert videos","Equivariant diffusion improves dissection trajectory forecasting","AI model predicts dissection paths with lower error"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000609,"raw_usage":{"total_tokens":2858,"prompt_tokens":992,"completion_tokens":1866,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":608,"completion_tokens_details":{"reasoning_tokens":1793}},"tokens_in":608,"tokens_out":1866,"duration_ms":14034,"temperature":1.0,"reasoning_tokens":1793,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T10:34:16.994629+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Florence, C","cited_arxiv_id":null,"evidence_quote":"supplies the implicit behavioral-cloning formulation (maximizing the joint state–action density) that iDPOE adopts."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"the paper's own preliminary version, which establishes the ESD trajectory-prediction task and the annotated dataset."},{"cited_title":"Weiler, G","cited_arxiv_id":null,"evidence_quote":"provides the equivariant steerable CNN construction used to embed rotational symmetry in the network."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"states the equivariant convolution constraint (Eq. 3) that the C4-equivariant layers must satisfy."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"the MID diffusion-based trajectory predictor that serves as a primary state-of-the-art baseline."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"the Leapfrog diffusion baseline, whose training instability the paper cites when explaining why it underperforms."},{"cited_title":"Bae, Y.-J","cited_arxiv_id":null,"evidence_quote":"the SingularTrajectory diffusion baseline, whose adaptive anchoring the paper says fails in dynamic ESD scenarios."}],"review_version":1}