{"id":"0cfb8427-3e32-401e-be3a-77c6db798cda","arxiv_id":"2506.18747","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"An energy-reweighted flow-matching loss is shown by construction to target a reweighted distribution, with modest benchmark demonstrations of concept removal.","lead":"ContinualFlow removes content from generative models by reweighting flow-matching training samples with an energy score, so no forget-set samples are needed, only a proxy for what should be suppressed. The theoretical result is a definitional equivalence, and the experiments on 2D, MNIST, and CIFAR-10 are mixed.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper never fixes q0: if q0 is a prior, ERFM targets a reweighted prior rather than retained data; if q0 is the pretrained model's output, the original model must remain available for sampling, so no deployed unlearning occurs.","rationale":"The reader's verdict of REJECT is supported. The strongest_claim (Theorem 4.1) is mathematically correct but nearly tautological: the weight is exactly the density ratio \\tilde q1/q0, so the gradient equivalence follows by construction. The interesting claim is the downstream one—that optimizing this loss unlearns a pretrained generative model. The linchpin is the identity of q0. Algorithm 1 samples both endpoints from q0. For a transport from q0 to \\tilde q1 this is legitimate importance sampling, but it means the target is fully determined by q0 and the energy. There is no step in the algorithm that brings in Dretain or the learned data manifold unless q0 already contains it.\n\nIf q0 is a prior, the target is a reweighted prior, which cannot be the retained image/2D distribution observed in the experiments. If q0 is the original model output distribution, then the final flow is a post-processor of the original model, and the original model must be retained for sampling at inference; this contradicts the goal of erasing its influence and the paper's framing as model patching rather than output suppression. The paper's ambiguity between these readings is not a cosmetic omission: it determines whether the method performs unlearning at all.\n\nThe proposed test would disambiguate. This concern matches the reader's weakest_assumption, which singled out the q0 ambiguity; I therefore agree with the reader's assessment. The absence of code, the classifier-based evaluation, and the acknowledged difficulty of learning faithful energies are secondary; the q0 issue alone is enough to withhold acceptance.","tokens_in":15428,"tokens_out":9523,"duration_ms":101998,"concrete_test":"Run the MNIST even/odd experiment exactly as in Algorithm 1 with q0 set to the standard latent Gaussian (the interpretation permitted by Table 2), train vθ from scratch, and sample by integrating the trained flow from this same Gaussian prior. Compute MMD to Dretain and forget rate against the classifier. If samples do not match even digits, the prior reading of q0 fails, and the paper must instead rely on q0 being the original model's output distribution; then repeat inference with q0 replaced by a Gaussian prior to show the deployed model cannot sample without the original model. Either result settles that q0 must be pinned down before the unlearning claim is meaningful.","verdict_should_be":"REJECT","load_bearing_attack":"Section 4.1 defines the ERFM target as \\tilde q1(x) ∝ q0(x) σ(−λF(x)) and Algorithm 1 samples both endpoints x0, x1 from q0. Two readings are possible and neither supports the central 'sample-free unlearning of a trained generative model' claim.\n\nIf q0 is a fixed base prior (as Table 2 lists 'prior' and Section 2 identifies flows as starting from a tractable p0), then the learned transport is from the prior to a reweighted version of the same prior. This distribution is not the retained data distribution, and there is no mechanism by which class- or region-specific data modes are learned; generation from the prior after training should not reproduce Dretain. The 2D/image successes therefore cannot be explained under this reading.\n\nIf q0 is the original model's output distribution, then the original (un-unlearned) model is required to sample q0 at every generation step after unlearning, because the new flow's initial distribution is q0, not a tractable base. The original model is precisely the object whose influence is supposed to be removed; keeping it as the sampler means privacy is not achieved and the claim of modifying 'a pretrained model' is misleading. The paper never states which q0 is used per experiment, and D.3's description ('base Gaussian via conditional flow, followed by energy-reweighted transformation') is consistent with either reading.\n\nTheorem 4.1 is correct, but it only proves equivalence to CFM toward this reweighted q0; it does not connect that target to Dretain. The missing step—specifying q0 and the post-unlearning sampler—is the load-bearing gap.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces ContinualFlow, a framework for targeted unlearning in generative flow models. The method, Energy-Reweighted Flow Matching (ERFM), samples endpoint pairs (x0, x1) from a source distribution q0 and minimizes a Conditional Flow Matching (CFM) loss weighted by sigma(-lambda F(x1)), where F is a scalar energy function intended to score association with a forget distribution. The authors define a reweighted target q̃1(x) proportional to q0(x) sigma(-lambda F(x)) and prove (Theorem 4.1) that the ERFM gradient equals, up to a positive constant, the CFM gradient toward q̃1. They also derive a classifier-based energy approximation (Proposition B.1), describe a sample-based OT-CFM variant, and report experiments on four 2D benchmarks, MNIST digit removal, and CIFAR-10 class suppression, with metrics including MMD, retention accuracy, forget rate, leakage, and training time.","tokens_in":15727,"tokens_out":6245,"duration_ms":64975,"significance":"If the central claims held, ContinualFlow would offer a principled, sample-free way to remove undesired content from a pretrained generative model without retraining. The paper is clearly written and the formal statements are internally consistent. Credit is due for spelling out the reweighted-target formulation and for attempting to connect loss-level weights to a distributional target. However, Theorem 4.1 is essentially an importance-sampling identity: the target is defined as proportional to q0 times the weight, so the equivalence between the weighted loss and CFM toward the reweighted target holds by construction and does not by itself establish any unlearning property. The unresolved ambiguity about q0, the absence of any prior-art unlearning baseline, the implausible identical fine-tuning rows in Table 3, and the worse-than-retrain forgetting metrics on CIFAR-10 jointly undermine the empirical and conceptual claims. The result, as it stands, does not support the paper's stated contributions.","major_comments":[{"comment":"Theorem 4.1 is correct but tautological. Since q̃1(x1)/q0(x1) is proportional to sigma(-lambda F(x1)) by the definition of q̃1 in Section 4.1, the ERFM objective is exactly the CFM objective with importance-sampling weights, and the claimed equality of gradients is the standard identity for importance-weighted CFM. The theorem therefore does not establish that optimizing the loss removes the forget distribution; it only shows that the loss matches a reweighted target that was chosen in advance. The central theoretical support for the method is an identity, not a substantive statement about unlearning.","section":"Section 4.2, Theorem 4.1"},{"comment":"The paper never fixes the source distribution q0, and the two possible readings both break the central 'sample-free unlearning of a pretrained generative model' claim. Algorithm 1 samples both x0 and x1 from q0. If q0 is a fixed base prior, then the learned flow transports the prior to a reweighted version of that same prior; because a generic Gaussian prior contains no data-specific modes, generation from the resulting model cannot reproduce D_retain, and there is no mechanism by which class- or region-specific modes are learned. If instead q0 is the output distribution of the pretrained model G_theta (as suggested by Section 3.1 and Appendix C), then the original model is required to sample q0 at every training step and at every generation step after unlearning, so the original model is never actually removed from the deployment pipeline. The paper must specify which reading is used in each experiment and explain how sampling is performed after unlearning; without this, the central claim is not well-defined.","section":"Section 4.1, Algorithm 1, Table 2"},{"comment":"The empirical comparison is not sufficient to support the paper's claims. In Table 3, the fine-tuning rows are identical to the retrain rows to at least four decimals for Circles, Checkerboard, Moons, and 6 Gaussians across every metric except training time, which suggests that the fine-tuning baseline is not actually trained or the numbers were copied from the retrain column; as reported, this baseline provides no information. In the 6-Gaussians row, the proposed method is worse than the identical retrain/fine-tuning baseline on every forgetting metric (MMD 0.0370 vs 0.0303, forget rate 0.0302 vs 0.0018, leakage 0.0338 vs 0.0031). In Table 1, the CIFAR-10 forget rate and leakage for Ours (0.1704 and 0.1748) are worse than retrain (0.1127 and 0.1546), directly contradicting the claim of unlearning performance comparable to retraining. No prior-art unlearning method is used as a baseline anywhere.","section":"Section 5, Table 3 and Table 1"},{"comment":"The evaluation protocol may be circular, and this is load-bearing for the reported forget-rate improvements. Retention accuracy, forget rate, and leakage are computed with a pretrained binary classifier (Appendix D), while the energy function F in Section 4.1 is described as a proxy scoring association with the forget distribution. If the same classifier supplies both the training weight sigma(-lambda F(x1)) and the evaluation score, then the forget-rate and leakage numbers are partly a self-fulfilling consequence of optimizing against the evaluator. The paper never states whether the classifier used for evaluation is distinct from the classifier used to define F, nor how the energy function is obtained for MNIST and CIFAR-10 beyond the general description of a proxy.","section":"Appendix D, evaluation metrics"}],"minor_comments":[{"comment":"The sampling description in D.3 ('base Gaussian via conditional flow, followed by energy-reweighted transformation') is ambiguous between a fixed latent Gaussian and the output distribution of the pretrained flow; this ambiguity should be resolved for reproducibility.","section":"Section D.3"},{"comment":"Case 1 (sample-based unlearning with full access) is described in Section 3.1 and revisited in Appendix C, but no experiments or results are reported for it; either add results or explicitly state that Case 1 is only a conceptual setup.","section":"Section 3.1"},{"comment":"Figure 5 contains garbled axis labels consisting of repeated '/uni...' strings; the figure should be regenerated before any resubmission.","section":"Various figures"},{"comment":"The abstract states the method works 'without requiring direct access to the samples to be unlearned,' but Proposition B.1 requires a Bayes-optimal classifier trained to distinguish qf from q0, which in practice requires forget-set samples or labels; the practical requirements for obtaining F should be stated explicitly.","section":"Abstract and Section 3.2"},{"comment":"The reported inference times (e.g., 0.004 ms) appear implausibly small for image-domain generation and the units are inconsistently formatted; please verify the measurements and clearly state the integration-step settings.","section":"Table 3"}],"recommendation":"reject","confidential_remarks":"The identical fine-tuning rows in Table 3 and the absence of any unlearning baseline beyond retrain/fine-tuning warrant careful scrutiny before further consideration. I would also ask the authors to provide code and exact experimental configurations, especially for q0, the energy function, and the classifier used in evaluation. The central conceptual issues around q0 and the tautological nature of Theorem 4.1 are not presentation-level fixes; they affect the validity of the claimed contributions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline: this is a cleanly written paper with a correct but essentially tautological theorem, and a clear gap between the theory and the claimed unlearning capability. If you're looking for a case study in how importance-weighting can masquerade as a new method, this is a useful one — but as a contribution to generative unlearning, the central claim doesn't hold up.\n\nWhat's genuinely new: framing unlearning as reweighting the flow-matching training pairs with a sigmoid energy weight, and showing that this is equivalent to CFM toward a reweighted target. The proof is correct, but it's direct importance sampling: w(x1) is exactly the density ratio tilde q1/q0, so the equivalence holds by construction. The paper does some things well: it's clearly written, notation is consistent, the visualizations of reversible energy guidance on MNIST are nice, and the discussion of composability is a reasonable conceptual point.\n\nThe problems. First, the load-bearing ambiguity: Algorithm 1 samples both x0 and x1 from q0, but the paper never fixes what q0 is. Table 2 lists \"model output or prior.\" If q0 is the base prior, then ERFM learns a transport from prior to reweighted prior — not to retained data — so the 2D and image successes shouldn't happen under that reading. If q0 is the pretrained model's output distribution, you need the original model at generation time, meaning no deployed unlearning occurs. Theorem 4.1 only proves equivalence to CFM toward reweighted q0; nothing connects that target to Dretain. That's the gap. Second, the experiments are weak: only retrain and fine-tuning baselines, no existing unlearning methods; the 2D fine-tuning rows are identical to retrain to four decimals, which suggests fine-tuning isn't actually changing the model; CIFAR-10 results are worse than retrain on forget rate and leakage. Third, the evaluation may reuse the same classifier that defines the energy function, which would make the suppression metrics circular.\n\nNone of this is a takedown. The paper is honest about the difficulty of learning good energy functions, and the theoretical claim is stated accurately. But the central promise — sample-free unlearning without retaining the original model — is not met. I'd recommend desk rejection; if the authors fix the q0 specification and add proper baselines, there might be a workshop-level contribution here.","headline":"A correct but essentially tautological importance-reweighting identity, with an unresolved q0 ambiguity that undermines the central sample-free unlearning claim; clearly written and honest, but not a substantive contribution as it stands.","tokens_in":16311,"tokens_out":3685,"would_cite":false,"duration_ms":32720,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A reweighted flow-matching loss makes generative unlearning possible without the forget samples, using only an energy proxy.","keywords":["machine unlearning","flow matching","energy-based models","generative models","importance weighting","distributional transport","continual learning","soft mass subtraction"],"falsifier":"On a 2D synthetic example, compute the intended target $\\tilde{q}_1(x) \\propto q_0(x)\\,\\sigma(-\\lambda F(x))$ by high-resolution numerical integration, train ContinualFlow, and compare generated samples to that density with maximum mean discrepancy. If the trained flow does not approach its own stated target, the optimization claim fails; if it matches the target but the target excludes the wrong regions, the energy proxy is the component to blame.","tokens_in":15172,"feed_emoji":"🌀","tokens_out":7208,"duration_ms":63695,"temperature":0.7,"pith_summary":"This paper tries to establish that generative unlearning can be done by reweighting a flow-matching objective instead of retraining, fine-tuning, or accessing the forget samples. It proposes ContinualFlow, which multiplies each training sample's velocity-matching loss by a sigmoid weight $\\sigma(-\\lambda F(x_1))$ built from an energy function $F(x)$ that scores how strongly a point belongs to the undesired content. The paper proves that this reweighted loss has the same gradient, up to a positive constant, as conditional flow matching toward the soft mass-subtracted target $\\tilde{q}_1(x) \\propto q_0(x)\\,\\sigma(-\\lambda F(x))$. If correct, a model trained on full data can be steered away from high-energy regions using only an energy proxy and samples from the base distribution, preserving retained-content fidelity. Experiments on 2D benchmarks, MNIST digit removal, and CIFAR-10 latent class suppression show behavior comparable to retraining.","feed_headline":"One reweighting term erases content from a generative flow","feed_subtitle":"ContinualFlow steers a pretrained flow away from high-energy regions, guided only by a proxy for the data to forget.","key_machinery":"The central object is the Energy-Reweighted Flow Matching loss, a conditional flow matching objective in which every displacement sample $(x_0, x_1)$ is weighted by $\\sigma(-\\lambda F(x_1))$, with $\\sigma$ the logistic sigmoid and $\\lambda$ a suppression scale. The energy function $F(x) \\propto -\\log q_f(x)$ acts as a scalar potential that is high where the forget distribution is dense, and the sigmoid weight softly down-weights those regions. The argument runs through the identity $\\tilde{q}_1(x)/q_0(x) \\propto \\sigma(-\\lambda F(x))$, which makes the weighted loss exactly a constant multiple of the CFM loss toward the soft mass-subtracted target $\\tilde{q}_1$. This identity converts unlearning into an importance-sampling reweighting of the standard flow-matching objective, and Algorithm 1 instantiates it by sampling both endpoints from $q_0$ and normalizing the weighted loss by the sum of weights.","core_discovery":"The central claim is Theorem 4.1: for a base distribution $q_0$, a forget energy $F(x) \\propto -\\log q_f(x)$, and $\\lambda > 0$, the Energy-Reweighted Flow Matching loss with weights $\\sigma(-\\lambda F(x_1))$ satisfies $\\nabla_\\theta L_{\\mathrm{ERFM}}(\\theta) = C\\,\\nabla_\\theta L_{\\mathrm{CFM}}^{q_0 \\to \\tilde{q}_1}(\\theta)$ with $C > 0$, where $\\tilde{q}_1 \\propto q_0(x)\\,\\sigma(-\\lambda F(x))$. Because the weight equals the density ratio $\\tilde{q}_1(x_1)/q_0(x_1)$, the result follows from importance sampling: reweighting samples drawn from $q_0$ by the sigmoid replaces the endpoint distribution $q_0$ by the reweighted target $\\tilde{q}_1$. The paper presents this identity as the reason unlearning can be performed without forget samples: the energy acts as a soft mask that lowers the contribution of high-energy trajectories. The same mechanism extends to classifiers, where the Bayes-optimal classifier logit defines $F$, and to reversing the energy to recover previously forgotten content.","pith_inferences":["Because the weight $\\sigma(-\\lambda F(x_1))$ is exactly the density ratio defining $\\tilde{q}_1$, the equivalence in Theorem 4.1 holds by construction; the substantive question shifts to whether $\\tilde{q}_1$, so defined, is the retained distribution the practitioner actually wants.","When the energy is derived from a classifier trained to separate $q_f$ from $q_0$, the effective target depends on $q_0$; if $q_0$ is a fixed Gaussian prior rather than the original model's output distribution, the flow is reweighted toward a reweighted prior, not necessarily the data manifold.","The latent-space image experiments suggest a practical recipe that the paper leaves implicit: train an autoencoder, perform unlearning in the latent space where a semantic classifier is easier to define, then decode, and the same energy-reweighting theorem applies unchanged.","A direct stress test of the framework would be a sequence of concept removals with a time-varying energy, checking whether the flow stays on the retained manifold and whether reversing an earlier energy restores the original behavior."],"forward_implications":["A pretrained flow can be re-targeted to a soft mass-subtracted distribution using only an energy proxy and samples from the base distribution, so forget sets need not be stored or replayed.","The suppression strength is controlled by the scalar $\\lambda$, giving a continuous knob from no forgetting to near-complete erasure of the high-energy region.","Reversing the sign of the energy reorients the learned flow toward the previously suppressed content, so forgotten classes can be restored without sample access.","Because the objective is a reweighted version of standard flow matching, the same training loop and architecture apply to any flow-based generative model.","Composing multiple energy functions is allowed by the construction, making incremental and continual unlearning a sequence of energy updates rather than retraining."],"supporting_citations":[{"why":"Defines flow matching, the generative framework that ContinualFlow extends to unlearning.","marker":"Lipman et al., 2023"},{"why":"Provides the conditional flow matching objective and the optimal transport coupling that Algorithm 1 uses to interpolate between endpoints.","marker":"Tong et al., 2023"},{"why":"Supplies the dynamic optimal transport formulation used to justify building a transport path between empirical distributions without known densities.","marker":"Benamou, 2021"},{"why":"Gives the minibatch optimal transport approximation used when the exact transport plan is too expensive.","marker":"Nguyen et al., 2021"},{"why":"Represents classifier guidance, the inference-time suppression approach the paper contrasts with its training-time reweighting.","marker":"Dhariwal & Nichol, 2021"}],"fun_headline_variants":["One reweight erases content, no data needed","Unlearn in flow matching via energy soft mask","ContinualFlow: soft subtraction without forget samples","Reweight, don't retrain: erasing content from flows"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method depends on trusting that the energy function accurately marks the content to be forgotten and that the base distribution used for sampling is the right starting point; if either is wrong, the flow is steered toward the wrong target.","fun_headline_variants_meta":{"raw":{"variants":["One reweight erases content, no data needed","Unlearn in flow matching via energy soft mask","ContinualFlow: soft subtraction without forget samples","Reweight, don't retrain: erasing content from flows"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000582,"raw_usage":{"total_tokens":2712,"prompt_tokens":891,"completion_tokens":1821,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":507,"completion_tokens_details":{"reasoning_tokens":1757}},"tokens_in":507,"tokens_out":1821,"duration_ms":19037,"temperature":1.0,"reasoning_tokens":1757,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T18:44:49.827518+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a 2D synthetic example, compute the intended target $\\tilde{q}_1(x) \\propto q_0(x)\\,\\sigma(-\\lambda F(x))$ by high-resolution numerical integration, train ContinualFlow, and compare generated samples to that density with maximum mean discrepancy. If the trained flow does not approach its own stated target, the optimization claim fails; if it matches the target but the target excludes the wrong regions, the energy proxy is the component to blame.","supporting_citations":[],"review_version":2}