{"id":"bf588f72-5593-43b5-b763-aafcff6d86a1","arxiv_id":"2509.08775","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"JM2D samples diffusion plans and safety-filter corrections jointly using a single importance-sampling-guided diffusion process, improving task success and reducing safety-filter interventions.","lead":"This paper introduces JM2D, a method that jointly samples robot trajectories from a diffusion planner and corrections from a safety filter, so the two modules become mutually compatible without retraining. It matters because robots using generative planners often need safety filters, and current methods either override the planner or sacrifice task performance.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 2's importance-sampling identity holds only for the exact posterior proposal, but Algorithm 2 uses the learned reverse process; the implemented estimator is not the one proven.","rationale":"The reader's weakest-assumption analysis identifies the same load-bearing issue: Theorem 2 assumes the exact posterior p^x_{0|i} for the x-proposal, while Algorithm 2 uses full denoising with the learned reverse model. I agree with that assessment. My stress-test sharpens the concern: the mismatch is not merely an approximation without a bound; the algebraic cancellation in Appendix A.2 is invalid when q_x is the learned reverse process, so the estimator implemented is not the estimator proven. The paper's own ablation (Sec. 6.2, Table 3) demonstrates high sensitivity to clean-sample quality, which is consistent with this theoretical gap. The empirical results are credible and suggest the method can work in practice, but the central theoretical claim needs correction or explicit hedging. This does not move the verdict: the paper should remain CONDITIONAL, requiring either a corrected theorem with a proper error analysis or an explicit reframing of Eq. (7) as a heuristic approximation validated empirically. The limitations section honestly acknowledges that hard constraint satisfaction relies on a backup module, which is compatible with this assessment. No ad hominem is intended; the concern is about the argument, not the authors.","tokens_in":17342,"tokens_out":10495,"duration_ms":77033,"concrete_test":"Re-derive Eq. (7) for the proposal actually used in Algorithm 2, namely q_x equal to the learned reverse process p_θ (I-step full denoising), and compute the true importance weight w(y0) = p0|i(y0|yi) / [p_θ(x0|xi) q^k(k0|ki)]. In a tractable Gaussian or Gaussian-mixture example where both p^x_{0|i} and p_θ are known, implement Algorithm 1 exactly and compare the empirical distribution of its output samples to the target p(x,k) ∝ p_θ(x)p(k)V(x,k). If the weighted score in Eq. (7) with weights w ∝ V p^k0 is biased whenever p_θ differs from p^x_{0|i}, then the theorem does not cover the implemented algorithm; the paper must either amend the theorem and proof or explicitly reframe Eq. (7) as an approximate heuristic with a corresponding error analysis.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central theoretical result, Theorem 2 (Eq. 7), is derived in Appendix A.2 under the proposal q(y0|yi) = p^x_{0|i}(x0|xi) q^k(k0|ki), where p^x_{0|i} is the exact posterior of the model-free data distribution under the forward noising kernel. The proof cancels p^x_{0|i} in the numerator and denominator to obtain importance weights proportional to V(x0,k0) p^k0(k0). However, Algorithm 2 (SAMPLEMC) constructs x-samples by full reverse denoising with the learned model p_θ(x_{τ-1}|x_τ), not by sampling from the exact posterior p^x_{0|i}. For any learned diffusion model these distributions differ, especially at high noise levels. With the actual proposal q_x = p_θ, the importance weight is proportional to V p^k0 times the ratio p^x_{0|i}(x0|xi)/p_θ(x0|xi); this ratio does not cancel and is not accounted for in Eq. (7). Consequently, the Monte Carlo estimator implemented in Algorithm 1 is not the estimator proven in Theorem 2, and the paper provides no error bound or empirical check on the resulting bias. The ablation in Sec. 6.2, Table 3 (u=0,1) shows the method collapses when clean-sample estimates are poor, so the mismatch is not a negligible technicality. This gap directly affects the central claim: the claimed joint sampling from p(x,k) ∝ p_θ(x)p(k)V(x,k) is not guaranteed by the presented theory for the actual algorithm. The missing specification of p(k0) in the experiments is a secondary manifestation of the same under-specification of the estimator.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Joint Model-based Model-free Diffusion (JM2D), a training-free framework that jointly samples a diffusion-planned trajectory x and a model-based optimization output k from a joint distribution p(x,k) proportional to p_theta(x) p(k) V(x,k), where V is an interaction potential encoding compatibility, non-differentiable constraints, and safety objectives. The method estimates the joint score via self-normalized importance sampling with a tractable proposal, so that only evaluations of V on clean samples are needed. The authors prove a joint-score identity under this proposal, show that conditional generation and model-based diffusion arise as special cases, and validate the method in a 2D PointMaze safety-filtering task, a real Franka mug-pickup task, and D3IL-Avoiding constrained-generation tasks, reporting improved safe success and lower intervention rates relative to RAIL, Gibbs sampling, SafeDiffuser, DPCC, and MPD. The paper also includes an ablation showing that the quality of clean-sample estimation is critical to the method's performance.","tokens_in":17704,"tokens_out":6169,"duration_ms":56475,"significance":"If the central claim holds, JM2D is a useful contribution: it provides a principled way to integrate pre-trained diffusion planners with model-based safety modules while handling non-differentiable potentials, and it avoids additional training or privileged gradient information. The paper's strengths include an explicit derivation of the joint score and importance weights, a broad set of experiments including a real-robot demonstration, and an honest ablation that reveals sensitivity to the clean-sample estimator. However, the theoretical result is proven for an exact-posterior proposal that the implemented algorithm does not use, and key experimental components such as the model-based prior and interaction temperature are left unspecified. These issues affect the validity and reproducibility of the central claims, so the paper needs substantial revision before it can be accepted.","major_comments":[{"comment":"Theorem 2 proves the joint-score identity for the proposal q(y0|yi) = p^x_{0|i}(x0|xi) q^k(k0|ki), where p^x_{0|i} is the exact posterior of the forward noising kernel, and the proof in Appendix A.2 relies on cancellation of p^x_{0|i} in the importance-weight ratio. Algorithm 2, however, constructs x-samples by full reverse denoising with the learned model p_theta(x_{tau-1}|x_tau). For a learned diffusion model, p_theta(x0|xi) does not equal p^x_{0|i}(x0|xi), so the importance weight actually used is proportional to V(x0,k0) p^k0(k0) times p^x_{0|i}(x0|xi)/p_theta(x0|xi), and this extra ratio does not cancel in Eq. (7). The implemented estimator is therefore not the estimator proven in Theorem 2, and no error bound, bias analysis, or empirical validation of this approximation is provided. Because Table 3 shows that the method collapses when clean-sample estimates are poor (u=0,1), this gap is load-bearing for the central claim that JM2D samples from p(x,k) proportional to p_theta(x)p(k)V(x,k). I ask the authors to extend the analysis to the learned-proposal case, or to state clearly that Eq. (7) is an approximation and provide evidence that the resulting bias is acceptable in the settings considered.","section":"Sec. 4.2 (Theorem 2), Appendix A.2, Algorithm 2"},{"comment":"Algorithm 1 and Eq. (7) require a model-based prior p^k0(k0) and an interaction temperature lambda in V(x,k) = exp(-J(k|x)/lambda) * 1(g(k|x) <= 0), but the main experiments never state which prior over backup actions was used or which temperature values were chosen for the PointMaze, real-robot, or Avoiding experiments. Table B.1 reports only the diffusion schedules and sample counts. Without these specifications the method is not reproducible, and the reported gains cannot be separated from tuning of lambda or the prior. The paper should report these values and, ideally, a sensitivity analysis over lambda for at least one of the benchmark tasks.","section":"Sec. 5.1, Sec. 6.2, Algorithm 1, Table B.1"},{"comment":"The Introduction states that JM2D yields trajectories that 'satisfy arbitrary, possibly non-differentiable, safety constraints by construction,' but the Remark after Theorem 2 says that infeasible joint samples are postprocessed with a model-based optimization step to guarantee feasibility, and Sec. 7 states that the approach 'cannot strictly enforce constraints' and requires a separate backup module. These statements are contradictory and affect the interpretation of the safety claims in Sec. 5.1, where the phrase 'none of these methods violate safety' is true only because of the external filter. The authors should remove the 'by construction' claim or clearly attribute hard guarantees to the postprocessing module.","section":"Sec. 1, Remark after Theorem 2, Sec. 7"}],"minor_comments":[{"comment":"The headings 'Proof of Definition 2' and 'Proof of Definition 3' refer to Theorem 2 and Corollary 3; please correct the numbering and terminology.","section":"Appendix A.2, A.3"},{"comment":"The caption of Fig. 4 says '80 trials of 5 random seeds' while the setup in Sec. 5.1 states 100 simulations per seed; harmonize these numbers.","section":"Sec. 5.1, Fig. 4"},{"comment":"After Eq. (6), the text says 'q(·|y_i) denotes (5)', but the proposal is defined in Eq. (6); the cross-reference should be corrected.","section":"Sec. 4.2, Eq. (6)"},{"comment":"The denoising update references 'Eq. (6) in [6]' without reproducing the equation; either make the update self-contained or include the full expression in the appendix.","section":"Algorithm 1, line 5"},{"comment":"The table uses inconsistent column labels 'SHor.' and 'THor.' for the same task-horizon metric; use one label consistently.","section":"Table 1"},{"comment":"The real-robot experiment is reported only qualitatively; please include numerical success/safety statistics or explicitly state that the demonstration is qualitative.","section":"Sec. 5.2"}],"recommendation":"major_revision","confidential_remarks":"The core idea is attractive and the empirical work is extensive, but the theory-algorithm mismatch and the missing specification of p(k) and lambda are serious. If the authors can close the gap by either proving the estimator for the learned-proposal case or providing a carefully validated approximation statement, and by disclosing the missing experimental hyperparameters, I would be willing to support acceptance. The special-case result in Corollary 3 should also be framed carefully so that the conditional-generation experiments are not presented as evidence for the joint-sampling mechanism."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Jung et al. propose JM2D, a way to sample jointly from a pretrained diffusion planner and a model-based safety module by importance-weighting an interaction potential. The idea is clean: define p(x,k) ∝ p_θ(x)p(k)V(x,k), then estimate the joint score with Monte Carlo samples of clean (x,k) pairs; the method needs only evaluations of V, not gradients. Conditional generation and model-based diffusion fall out as special cases. On the empirical side, the paper shows real gains over RAIL and Gibbs on PointMaze with a reachability safety filter, and beats DPCC, SafeDiffuser, and MPD on constrained generation. The real-robot mug pick is a nice bonus. The ablation on clean-sample estimation is honest and informative: guidance collapses when you shortcut the denoising, which pins the method's success on the quality of the clean samples.\n\nThe soft spots are real but addressable. The main one is the gap between Theorem 2 and Algorithm 2. The proof uses the exact posterior p^x_{0|i}(x0|xi) as the proposal and cancels it in the importance weight. The implementation samples x0 by full reverse denoising with the learned model p_θ. For an imperfect diffusion model those are different distributions, and the unaccounted ratio p^x_{0|i}/p_θ survives in the weight; no error bound or diagnostic is given. The u=0,1 rows in Table 3 show that when the clean samples are poor, the method degrades to the worst baselines, so the mismatch is not a technicality. That said, the empirical evidence with full denoising is strong, so the fix is to restate the theorem for the actual proposal (or at least discuss the approximation and validate it, e.g., by comparing against exact posterior samples in a toy example).\n\nSecond, the paper leaves λ and p(k) unspecified in the experiments. The model-based prior appears in the weight, so it matters. Also no runtime numbers are reported, and the method is expensive (I(I+1)/2 denoising chains). The limitations section acknowledges the cost but not the missing hyperparameters.\n\nThe derivation is not circular; the special-case reductions to conditional generation and model-based diffusion are correct, and the related work is honestly positioned. I'd describe it as a well-executed method paper with a theory section that overreaches. It is not a desk-reject: the problem is important, the experimental comparison is fair, and the flaws are fixable. A serious referee should engage with it, and I'd expect a revise-and-resubmit.","headline":"JM2D is a promising and well-executed method for aligning diffusion planners with safety filters, but the proof of the score estimator assumes an exact posterior that the implementation replaces with a learned denoiser, and key hyperparameters go unreported.","tokens_in":18214,"tokens_out":5616,"would_cite":true,"duration_ms":379341,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper introduces JM2D, a training-free method that jointly samples a robot plan from a diffusion model and a safety correction from an optimization module, improving task success and reducing safety-filter interventions compared with…","keywords":["diffusion models","robot motion planning","safety filters","constrained generation","importance sampling","joint sampling","model-based optimization","offline reinforcement learning"],"falsifier":"On a synthetic problem where the true joint distribution $p(x,k)$ is known and its score computable, compare the JM2D importance-sampling score estimate, with full denoising, against the true score; if the estimate does not converge to the true score as the number of MC samples grows, the unbiasedness claim behind Theorem 2 is falsified. Alternatively, if a one-step denoising estimate ever matches the performance of full denoising on the D3IL-Avoiding tasks, the paper's claim that clean-sample fidelity is the decisive factor would be contradicted.","tokens_in":17167,"feed_emoji":"🤖","tokens_out":8067,"duration_ms":59233,"temperature":0.7,"pith_summary":"Model-free diffusion planners generate diverse, multimodal trajectories, but they often ignore safety constraints that are best enforced by model-based optimization modules. This paper claims that the usual approach of first sampling a plan and then running a safety filter is wasteful and can fail, because the planner never accounts for what the filter can and cannot correct. The authors propose JM2D, which samples the plan and the safety correction jointly from a distribution weighted by an interaction potential that rewards mutual compatibility, using an importance-sampling score estimate that needs only evaluations of the potential, not gradients. On offline RL and real manipulation tasks, JM2D achieves higher safe success rates and lower intervention rates than sequential safety filters and other constrained-diffusion baselines while preserving hard safety guarantees.","feed_headline":"Joint sampling of plan and safety correction improves robot success","feed_subtitle":"JM2D samples plan and safety backup together, raising task success and cutting interventions without losing hard safety guarantees.","key_machinery":"The load-bearing object is the Monte Carlo joint score estimator of Theorem 2, which rewrites the gradient of the joint noisy log-density as a weighted average of Tweedie scores, with weights proportional to $V(\\hat{x}_0,\\hat{k}_0) p^k(\\hat{k}_0)$. The proposal $q(y_0|y_i)$ is the key design choice: for $x$ it is the exact posterior of the pre-trained diffusion model, approximated in practice by full denoising, and for $k$ it is a Gaussian centered on the noisy value. This estimator is what makes the method gradient-free and applicable to hard, non-differentiable constraints; its accuracy, the paper's ablations show, depends critically on the quality of the clean-sample estimates.","core_discovery":"The central claim is that model-free and model-based modules can be aligned without retraining by sampling from a joint distribution $p(x,k) \\propto p_\\theta(x)p(k)V(x,k)$, where $p_\\theta(x)$ is a pre-trained diffusion planner, $p(k)$ is a prior on the optimization output, and $V$ is an interaction potential encoding compatibility, for example safety and task objective. JM2D implements this as a joint diffusion process over the concatenated variable $[x,k]$, estimating the joint score by self-normalized importance sampling with a proposal that factorizes into the model-free reverse diffusion for $x$ and a Gaussian for $k$. The resulting update uses only evaluations of $V$ on clean samples, so it handles non-differentiable and non-convex objectives. The paper shows empirically that this joint sampling outperforms sequential and Gibbs safety filters and projection- or gradient-based constrained planners, and proves that conditional generation and model-based diffusion are special cases.","pith_inferences":["The estimator effectively performs annealed importance sampling over the interaction potential, so the paper's ablation suggests that better proposals, such as few-step samplers or learned posteriors, could cut compute without losing alignment.","The method's benefit is tied to the planner's multimodality: the authors note performance fades when the learned policy is less multimodal, which implies a testable prediction that the gain over sequential filtering scales with the effective number of modes in the plan distribution.","The paper never specifies the prior $p(k)$ used for the optimization output; a natural extension is to test sensitivity to that prior, since the estimator's weights are proportional to $V p^k$.","The joint-sampling formulation extends by composition of interaction potentials to more than two modules, for example planner, tracking controller, and safety filter, which the authors name as future work."],"forward_implications":["JM2D increases safe success rate and reduces safety-filter interventions compared to sequential filtering (RAIL) and Gibbs sampling, with the gap growing as inference-time obstacles diverge from training data.","The method needs no gradients, so it can steer pre-trained diffusion planners by any black-box objective, including non-convex optimizers, reachability sets, or rule-based checks.","Conditional generation is a special case: with a factorized interaction potential and uniform prior, JM2D decouples into classifier-style guidance for $x$ and model-based diffusion for $k$, unifying those two prior lines of work.","Because joint samples are already aligned with the safety module, running a single post-hoc safety-filter step on infeasible samples still gives strict safety while avoiding the overrides that hurt sequential methods."],"supporting_citations":[{"why":"Defines the diffusion score framework and Tweedie score used in the joint score estimator.","marker":"[1]"},{"why":"Supplies the forward noising and reverse denoising process that JM2D extends to joint variables.","marker":"[2]"},{"why":"The pre-trained model-free planner used in the safety-filter experiments and real-robot deployment.","marker":"[3]"},{"why":"The sequential safety-filter baseline (RAIL) whose decoupled design JM2D replaces and outperforms.","marker":"[10]"},{"why":"The reachability-based safety policy (RTD) used as the model-based optimization module in the robot experiments.","marker":"[37]"},{"why":"The projection-based constrained diffusion planner (DPCC) used as a baseline in the Avoiding benchmark.","marker":"[15]"},{"why":"The per-state projection baseline (SafeDiffuser) that exhibits trap behavior in the comparisons.","marker":"[16]"},{"why":"The gradient-guided diffusion planner (MPD) used as a baseline for constrained generation.","marker":"[5]"},{"why":"Provides the DDIM reverse-process equation used for denoising joint samples in Algorithm 1.","marker":"[38]"},{"why":"The model-based diffusion method whose score form JM2D generalizes and to which it connects via Corollary 3.","marker":"[6]"}],"fun_headline_variants":["JM2D: joint sampling improves robot planning with safety","Sampling plan and safety together boosts task success","Aligning diffusion planners with safety via joint sampling","Joint sampling of plan and safety correction improves success"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes that the internal guesses it makes about fully denoised plans and corrections are accurate; the paper's own ablation shows that when these guesses are cheap and rough, performance collapses to the weakest baselines.","fun_headline_variants_meta":{"raw":{"variants":["JM2D: joint sampling improves robot planning with safety","Sampling plan and safety together boosts task success","Aligning diffusion planners with safety via joint sampling","Joint sampling of plan and safety correction improves success"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000242,"raw_usage":{"total_tokens":1518,"prompt_tokens":933,"completion_tokens":585,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":549,"completion_tokens_details":{"reasoning_tokens":524}},"tokens_in":549,"tokens_out":585,"duration_ms":5643,"temperature":1.0,"reasoning_tokens":524,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:59:43.163869+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a synthetic problem where the true joint distribution $p(x,k)$ is known and its score computable, compare the JM2D importance-sampling score estimate, with full denoising, against the true score; if the estimate does not converge to the true score as the number of MC samples grows, the unbiasedness claim behind Theorem 2 is falsified. Alternatively, if a one-step denoising estimate ever matches the performance of full denoising on the D3IL-Avoiding tasks, the paper's claim that clean-sample fidelity is the decisive factor would be contradicted.","supporting_citations":[{"cited_title":"Kousik, S","cited_arxiv_id":null,"evidence_quote":"The reachability-based safety policy (RTD) used as the model-based optimization module in the robot experiments."}],"review_version":2}