{"id":"131a5586-7dcd-4f3b-ab41-7a0e0ebc6631","arxiv_id":"2412.15341","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A bilevel training procedure that simultaneously restores a pruned diffusion model's quality and suppresses targeted concepts beats sequential fine-tuning followed by unlearning.","lead":"This paper combines fine-tuning and concept unlearning into one training loop for pruned image-generation models, so a compressed model can be taught to drop an artist's style or unsafe content while keeping overall quality. It matters because pruned diffusion models inherit unwanted behaviors from the original model, and the proposed method suppresses them more effectively than the standard fine-then-forget pipeline.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Algorithm 1's outer gradient in Eq. (14) is independent of the inner-loop variable ϑ, so the lower-level iterations do not influence the outer update and the method reduces to weighted-sum fine-tuning; the claimed bilevel interdependency is not implemented, though the empirical joint-vs-sequential…","rationale":"The reader's weakest_assumption correctly identifies a genuine mismatch between the paper's claimed bilevel framework and the actual algorithm. This is the most load-bearing concern because the abstract, introduction, and Sec. 4 present the bilevel optimization as the central novelty. If the algorithm reduces to a weighted sum of the unlearning and fine-tuning losses, the theoretical contribution is overstated. I independently verified the mathematical point: in Eq. (14), the inner-loop variable ϑ appears only in the term −λLft(ϑ), whose gradient with respect to θpruned is zero. Therefore, the outer update in Algorithm 1 is identical regardless of ϑ, and the K lower iterations have no effect on the trajectory of θpruned. The empirical results may still support the weaker claim that joint weighted training outperforms sequential fine-then-forget on pruned diffusion models, so the paper can remain acceptable as an empirical contribution, but only after the framing is corrected and the code is verified. Secondary concerns, such as lack of error bars and reliance on a single pruning method, do not undermine the core empirical finding as directly. The proposed K=0 experiment would settle the question definitively by demonstrating whether the inner loop is inert. Since the reader already conditioned acceptance on this issue, the verdict should remain CONDITIONAL.","tokens_in":17493,"tokens_out":8435,"duration_ms":71038,"concrete_test":"Run Algorithm 1 with K=0 (skip the inner loop entirely) under identical settings (λ=100, same seed, 20,000 outer iterations) and compare the resulting style-removal metrics, FID, and COCO CLIP to the reported K=20 run. If the results are statistically indistinguishable, the inner loop is inert, confirming that the method reduces to weighted-sum training. As a direct check, symbolically compute ∂Gλ/∂θpruned from Eq. (14) and confirm it has no dependence on ϑ.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing concern is that the implemented Algorithm 1 does not actually realize the bilevel optimization claimed in Sec. 4. In Eq. (14), Gλ(θpruned, ϑ) = E||ϵθ(xt,t,c')−ϵθpruned(xt,t,c)||² + λ[Lft(θpruned) − Lft(ϑ)]. The gradient with respect to θpruned is ∇θpruned E||...||² + λ∇θpruned Lft(θpruned); it contains no term involving ϑ. Consequently, the K lower-level iterations in Algorithm 1 (lines 3-6) do not affect the outer update (line 7), and the double-loop is superfluous. The method is equivalent to single-level gradient descent on the weighted sum L_unlearn + λLft(θpruned), i.e., a weighted multi-task objective. The penalized problem in Eq. (12) is a valid penalty approximation of the constrained problem (Eq. (10)), but it is not a bilevel problem; the cited convergence result (Theorem 2 of [35]) addresses the penalty approximation, not an interdependent bilevel solver. The paper's central methodological claim - a novel bilevel framework that solves the 'circular dependency' between fine-tuning and unlearning - is therefore unsupported. This does not invalidate the empirical comparison: joint weighted training may indeed beat sequential fine-then-forget, as Table 1 suggests. But the contribution should be reframed as joint multi-task fine-tuning, not bilevel optimization.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper addresses the problem of fine-tuning pruned text-to-image diffusion models while suppressing unwanted concepts (e.g., artist styles, NSFW content). The authors propose a \"bilevel\" optimization framework that jointly performs distillation-based fine-tuning and concept unlearning, claiming to resolve the circular dependency between restoring generative quality and removing undesirable content. They evaluate the method on an APTP-pruned Stable Diffusion 2.1 model for artist style erasure and explicit content removal, reporting that their approach outperforms two-stage baselines (distillation followed by ESD, UCE, or ConceptPrune) in both concept suppression metrics and generation quality (FID, CLIP). The paper also quantifies the convergence benefit of adding distillation to pruned diffusion model fine-tuning.","tokens_in":17878,"tokens_out":5212,"duration_ms":46073,"significance":"If the empirical results hold, the paper makes a useful practical contribution: it demonstrates that jointly optimizing fine-tuning and forgetting objectives can be more effective than a sequential fine-then-forget pipeline for pruned diffusion models. The distillation convergence study in Sec. 5.1 is also a valuable addition. However, the central methodological claim of a genuinely interdependent bilevel solver is not supported by the algorithm as written; as implemented, the method reduces to a weighted multi-task objective. The lack of error bars and hyperparameter ablations further weakens the empirical case. With a reframed contribution and stronger evaluation, the underlying observation about joint training would be a solid incremental result for the efficient-diffusion-model deployment community.","major_comments":[{"comment":"The outer gradient with respect to θpruned is independent of the inner-loop variable ϑ. In Eq. (14), Gλ(θpruned, ϑ) contains the term λ[Lft(θpruned) − Lft(ϑ)], and the derivative of −λLft(ϑ) with respect to θpruned is zero. Consequently, the K lower-level iterations in Algorithm 1 (lines 3–6) do not affect the upper-level update (line 7), and the algorithm is equivalent to single-level gradient descent on the weighted sum of the unlearning loss and the fine-tuning loss Lft(θpruned). The statement in the last paragraph of Sec. 4 that the gradient is \"influenced by both the upper-level and lower-level losses\" is therefore inaccurate, and the claimed interdependence that distinguishes the bilevel approach from a two-stage method is not implemented. The penalized problem in Eq. (12) is a valid penalty reformulation of the constrained problem, but it is not a bilevel problem in the sense of Eq. (9); the cited convergence result (Theorem 2 of [35]) applies to the penalty approximation, not to this double-loop algorithm as a bilevel solver. The authors should either modify the algorithm to introduce a genuine coupling (e.g., a hypergradient that depends on the lower-level solution ϑ) or reframe the contribution as joint multi-task fine-tuning rather than bilevel optimization.","section":"Sec. 4, Eq. (14), Algorithm 1"},{"comment":"All reported metrics are point estimates without error bars, confidence intervals, or multiple seeds. The central empirical claim is that the proposed method outperforms two-stage baselines in concept suppression and generation quality. Without any measure of variance, it is impossible to assess whether differences such as the CSD score of 39.04 versus 53.19 in Table 1 are statistically meaningful. The authors should report means and standard deviations over at least three independent runs, or otherwise justify that the evaluation is deterministic and not sensitive to randomness in training or sampling.","section":"Sec. 5.2, Tables 1 and 2"},{"comment":"The method introduces several hyperparameters (λ=100, K=20, upper learning rate 5e−6) that are fixed without a sensitivity study. Since the algorithm is effectively a weighted multi-task objective, the choice of λ directly trades off unlearning strength against fine-tuning fidelity and is likely to be dataset- and concept-dependent. An ablation over λ and K is needed to demonstrate that the reported gains are not an artifact of a single hand-tuned configuration. Additionally, the paper does not report how the total iteration budget is split between lower and upper steps in the comparison, which is important for interpreting the computational cost claim.","section":"Sec. 5.2.1 and Appendix C.1.3"}],"minor_comments":[{"comment":"The paper uses \"bilevel\" and \"double-loop\" interchangeably, but the algorithm as implemented is not a bilevel method; please revise the terminology consistently (e.g., \"joint multi-task fine-tuning\") after addressing the major issue above.","section":"Throughout"},{"comment":"The typo \"hiqh quality\" should be corrected to \"high quality\".","section":"Sec. 5.2.1"},{"comment":"Reference [4] is malformed (\"Zhang et. al. To generate or not? ... ECCV, 2024\") and appears to duplicate reference [59]; it should be completed or removed.","section":"References"},{"comment":"In the prompt \"The Three Dancers by Pablo Picass\", the artist's name is missing the final \"o\"; it should read \"Picasso\".","section":"Appendix C.3, Table 5"},{"comment":"The notation DKL(pθ(x|c′)∥pθCU(x|c)) mixes the anchor condition c′ and the target condition c in an unclear way; consider clarifying which conditional distributions are being compared to avoid confusion.","section":"Eq. (5)"},{"comment":"The caption states that the bilevel method produces \"the optimal solution θ*\", but no optimality guarantee is established for the proposed algorithm; please soften this to \"a solution obtained by the proposed joint method\".","section":"Figure 3 caption"}],"recommendation":"major_revision","confidential_remarks":"The manuscript's central methodological claim of a bilevel solver is not supported by the algorithm as written, and reframing will require rewriting portions of the introduction, method, and experiments. The empirical observation that joint weighted training can beat sequential fine-then-forget is plausible and may be a useful contribution, so I do not recommend rejection. However, the evaluation would be considerably strengthened by error bars, hyperparameter ablations, and a direct comparison of the proposed objective against a simple weighted-sum baseline. I also note that the pruning method APTP is from the same author group; the paper should make the independence of the proposed method from the specific pruning technique more explicit, ideally by including results with at least one additional pruning method."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The empirical comparison is real and probably useful: on a pruned SD 2.1, fine-tuning with a weighted sum of distillation and unlearning losses beats a fine-then-forget pipeline on style erasure and NSFW removal while keeping FID competitive. The framing around it, however, does not survive contact with their own equations: the claimed bilevel interdependency is not implemented. The outer gradient in Eq. (14) contains no term involving the inner variable ϑ, so the K lower iterations in Algorithm 1 do not influence the outer update. The method is a single-level weighted sum of L_unlearn + λ L_finetune. The double loop is superfluous. The citation to Theorem 2 of [35] supports the penalty approximation, not the claimed interdependent solver.\n\nWhat is genuinely new: the observation that distillation transfers unwanted concepts to pruned models is quantified for the first time here, and the joint formulation—even as a weighted sum—is not in the cited literature. The experiments are reasonably careful, with multiple baselines (ESD, UCE, ConceptPrune) and two removal tasks. Tables 1 and 2 consistently show the joint method matching or beating the two-stage pipelines, with better FID and COCO CLIP. That central empirical claim holds up; it is not a fitting artifact.\n\nSoft spots, in order of severity. The bilevel claim is load-bearing for the paper's novelty and it is wrong as implemented; the authors should reframe as joint multi-task fine-tuning. The text in Sec. 4 says the gradient is influenced by both levels, which contradicts their own Eq. (14). There are no error bars anywhere, and the key hyperparameters (λ=100, K=20) are hand-set with no sensitivity analysis. The code link is not verified. Some qualitative language about 'complete erasure' is stronger than the metrics support.\n\nWho benefits: practitioners working on compressed diffusion models who want a cheap way to suppress concepts during fine-tuning. The paper deserves a serious referee, mostly to force the reframing and the ablations. I would not cite it in its current form. Bring it to reading group if you want a case study in the gap between a claimed optimization framework and the code actually run.","headline":"Useful empirical result on joint fine-tuning plus unlearning for pruned diffusion models, but the bilevel framing is not actually implemented in the algorithm.","tokens_in":18359,"tokens_out":2627,"would_cite":false,"duration_ms":22545,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that restoring and sanitizing a pruned diffusion model should be one joint optimization, not two sequential steps, and reports that the joint method removes artist styles more thoroughly while keeping generation quality.","keywords":["diffusion models","model pruning","knowledge distillation","concept unlearning","bilevel optimization","text-to-image generation","safe AI deployment","style erasure"],"falsifier":"Decisive ablation: run the exact algorithm of Sec. 4 and a control in which the inner-loop variable $\\vartheta$ is detached from the outer step (equivalently $K = 0$), keeping everything else fixed; if the Table 1 metrics are statistically indistinguishable, the reported gains come from the weighted joint loss, not from the bilevel coupling. Sweeping $K$ from 1 to 50 and $\\lambda$ from 0 to 100 would show which hyperparameter actually drives the effect.","tokens_in":17277,"feed_emoji":"🎨","tokens_out":11099,"duration_ms":64851,"temperature":0.7,"pith_summary":"Pruned diffusion models are cheap to deploy, but the distillation step that restores their quality also carries over the original model's unwanted behaviors—copyrighted styles and unsafe content—even when those are absent from the fine-tuning data. This paper argues that the standard remedy of first fine-tuning the pruned model and then applying a separate concept-erasure method is suboptimal, because the parameters best for restoration are not the best starting point for forgetting. It proposes instead a single bilevel optimization in which a lower-level loop fine-tunes the pruned model with denoising and distillation losses while an upper-level loop applies concept unlearning. On Stable Diffusion 2.1 pruned to 80% MAC, the method reports lower style similarity, higher erasure scores, and better FID and retention CLIP than the two-stage baselines for removing Monet, Picasso, and Van Gogh, and comparable NSFW removal with better generation quality. If this holds, safe compressed diffusion models can be produced in one training pass rather than two.","feed_headline":"One training pass both restores and sanitizes a pruned diffusion model","feed_subtitle":"On pruned Stable Diffusion 2.1, joint training erases three artist styles while keeping image quality.","key_machinery":"The load-bearing object is the penalized minimax reformulation of the bilevel problem, Eq. (13)--(14): minimize over $\\theta_{\\mathrm{pruned}}$ the sum of the unlearning loss and $\\lambda$ times the difference between the fine-tuning loss at $\\theta_{\\mathrm{pruned}}$ and the fine-tuning loss at an auxiliary variable $\\vartheta$. The lower loop minimizes $L_{\\mathrm{ft}}(\\vartheta)$ for $K$ steps; the upper loop takes a gradient step on $G_\\lambda$ with respect to $\\theta_{\\mathrm{pruned}}$. The paper justifies the reformulation by citing a first-order penalty method that relates stationary points of the penalized problem to those of the original bilevel problem. Concept unlearning itself is written as a distillation objective: minimize the squared error between the denoising prediction conditioned on an anchor concept $c'$ (from the frozen teacher) and the prediction conditioned on the target concept $c$ (from the model being unlearned), following the KL reformulation of concept removal.","core_discovery":"The paper's central claim is that restoring a pruned diffusion model's generative quality and suppressing named concepts should be solved as one optimization, not two. Formally it writes the problem as a bilevel program: the lower level minimizes the fine-tuning loss $L_{\\mathrm{ft}}$ (denoising plus output and feature distillation), and the upper level minimizes the concept-unlearning objective, with the constraint that the unlearned model's fine-tuning loss not exceed the infimum over all fine-tuning parameters. A penalty reformulation converts this to a minimax objective $G_\\lambda$, solved by a double loop in which $K$ lower steps do standard fine-tuning and each upper step applies an ESD-style negative-guidance update. On an APTP-pruned Stable Diffusion 2.1 model at 80% MAC, the method reports CLIP similarity 26.28 versus 29.96 for the best two-stage baseline, CP score 97.6 versus 91.3, CSD 39.04 versus 53.19, FID 22.24 versus 27.86, and COCO CLIP 29.19 versus 28.94, and it also matches or beats two-stage pipelines on adversarial NSFW prompts while keeping lower FID.","pith_inferences":["A careful reading of Algorithm 1 suggests the outer update is a weighted sum of the unlearning loss and the fine-tuning loss, with no term depending on the inner-loop variable $\\vartheta$; if so, the practical contribution is that simultaneous weighted training outperforms sequential training, independent of whether the bilevel equivalence is doing the work.","The same joint fine-tune-and-unlearn recipe could be tested on unpruned or fully quantized diffusion models, where sequential safety fine-tuning is currently standard.","The evaluation protocol used here—CLIP similarity, CP, CSD, FID, and COCO CLIP together—could serve as a benchmark for compressed-model safety, since it separates concept removal from generation-quality retention.","Because the unlearning objective is itself a distillation toward an anchor concept, the bilevel framing may extend to other distillation-based behavior control tasks, such as aligning student models to a safe teacher during compression."],"forward_implications":["Compressed diffusion models can be made safe in the same fine-tuning run that restores their quality, removing the need for a separate erasure stage.","Because the unlearning step is plug-in, swapping the upper-level method (for example, from an ESD-style update to a stronger unlearning method) should improve concept suppression while keeping the joint-training advantage.","The quantified distillation results imply that any pruned model retrained with knowledge distillation should be checked for transfer of undesired concepts, since the distillation objective itself carries style information from the teacher.","In NSFW settings, the method gives a better quality-safety trade-off than two-stage erasure: comparable or better removal on I2P, MMA, and Ring-A-Bell prompts with lower FID and higher COCO CLIP.","The resulting checkpoint remains compatible with further unlearning, so multiple concepts can be removed incrementally."],"supporting_citations":[{"why":"Supplies the APTP prompt-based pruning method and the 80%-MAC pruned Stable Diffusion 2.1 model that all fine-tuning experiments start from.","marker":"[12]"},{"why":"Provides the ESD concept-erasure update used in both the upper-level optimization and the two-stage baseline, and the artist-erasure setup.","marker":"[9]"},{"why":"Provides UCE, a two-stage baseline concept-editing method compared in Tables 1 and 2.","marker":"[10]"},{"why":"Provides ConceptPrune, a training-free two-stage baseline, the CP evaluation metric, and the artist-erasure evaluation protocol.","marker":"[2]"},{"why":"Supplies the first-order penalty-method theorem that the paper invokes to justify replacing the bilevel problem with the penalized minimax objective.","marker":"[35]"},{"why":"Gives the KL-based reformulation of concept unlearning as a denoising-prediction matching objective, which the upper-level loss uses.","marker":"[23]"},{"why":"MS-COCO-2017 is the fine-tuning and evaluation dataset for FID and COCO CLIP retention scores.","marker":"[29]"},{"why":"Supplies the CSD style-similarity score used to measure how thoroughly an artist style is erased.","marker":"[48]"},{"why":"Supplies the CLIP similarity and CP-score embeddings used in the style-removal metrics.","marker":"[38]"}],"fun_headline_variants":["One optimization restores and unlearns pruned diffusion","Pruned diffusion: fine-tune and unlearn in one pass","Joint fine-tuning and unlearning for pruned diffusion","Bilevel trick: restore quality and erase concepts in pruned models","Unified optimization fine-tunes and sanitizes pruned models"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result depends on the premise that the double-loop update genuinely couples the fine-tuning state with the unlearning step; if the outer gradient is independent of the inner-loop solution, the method is a weighted combination of two losses rather than a new two-level solver, and the comparison reduces to 'joint training beats sequential training.'","fun_headline_variants_meta":{"raw":{"variants":["One optimization restores and unlearns pruned diffusion","Pruned diffusion: fine-tune and unlearn in one pass","Joint fine-tuning and unlearning for pruned diffusion","Bilevel trick: restore quality and erase concepts in pruned models","Unified optimization fine-tunes and sanitizes pruned models"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001121,"raw_usage":{"total_tokens":4676,"prompt_tokens":968,"completion_tokens":3708,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":584,"completion_tokens_details":{"reasoning_tokens":3623}},"tokens_in":584,"tokens_out":3708,"duration_ms":19344,"temperature":1.0,"reasoning_tokens":3623,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T11:31:27.031399+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Decisive ablation: run the exact algorithm of Sec. 4 and a control in which the inner-loop variable $\\vartheta$ is detached from the outer step (equivalently $K = 0$), keeping everything else fixed; if the Table 1 metrics are statistically indistinguishable, the reported gains come from the weighted joint loss, not from the bilevel coupling. Sweeping $K$ from 1 to 50 and $\\lambda$ from 0 to 100 would show which hyperparameter actually drives the effect.","supporting_citations":[{"cited_title":"Erasing concepts from diffusion models","cited_arxiv_id":null,"evidence_quote":"Provides the ESD concept-erasure update used in both the upper-level optimization and the two-stage baseline, and the artist-erasure setup."},{"cited_title":"Unified concept editing in dif- fusion models","cited_arxiv_id":null,"evidence_quote":"Provides UCE, a two-stage baseline concept-editing method compared in Tables 1 and 2."},{"cited_title":"First-order penalty methods for bilevel optimization","cited_arxiv_id":null,"evidence_quote":"Supplies the first-order penalty-method theorem that the paper invokes to justify replacing the bilevel problem with the penalized minimax objective."},{"cited_title":"Ablating con- cepts in text-to-image diffusion models","cited_arxiv_id":null,"evidence_quote":"Gives the KL-based reformulation of concept unlearning as a denoising-prediction matching objective, which the upper-level loss uses."},{"cited_title":"Microsoft coco: Common objects in context, 2014","cited_arxiv_id":null,"evidence_quote":"MS-COCO-2017 is the fine-tuning and evaluation dataset for FID and COCO CLIP retention scores."}],"review_version":1}