{"id":"b5e2aa8f-c1c5-4e1d-a4a0-cdf2d2b4359d","arxiv_id":"2511.11688","paper_version":3,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"HSO is a bi-level optimization method with Midpoint Error Proxy and Spacing-Penalized Fitness that finds robust timestep schedules for low-NFE diffusion sampling and reports SOTA FID scores such as 11.94 at NFE=5.","lead":"The paper introduces Hierarchical-Schedule-Optimizer (HSO), a bi-level framework that alternates global search for initialization with local refinement using a midpoint error proxy and spacing penalty to find good timestep schedules for diffusion sampling. A smart generalist might read it because the approach claims to deliver high-quality samples from existing models in just 5 steps with under 8 seconds of one-time optimization cost and no retraining.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Midpoint Error Proxy correlation with actual FID not demonstrated across models or regimes","rationale":"Reader's weakest assumption directly identifies the same surrogate-validity gap that underpins the reported low-NFE FID numbers. Full-text experiments may contain correlation checks, but the abstract-only review plus the bi-level reliance on MEP make this the single most load-bearing unverified link; confirming or refuting the correlation would settle whether the performance numbers are robust or proxy artifacts.","tokens_in":1815,"tokens_out":331,"duration_ms":27267,"concrete_test":"Generate 50 random 5-step schedules on Stable Diffusion v2.1, compute both MEP and FID (50k samples) for each; repeat on a second model (e.g., SDXL or DiT). Report Pearson/Spearman correlation; if r < 0.6 or rank correlation fails to preserve top-5 schedules, the surrogate is insufficient to support the SOTA claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"HSO's central claim (new SOTA at NFE=5 with FID=11.94) depends on MEP serving as an effective surrogate that drives the bi-level optimizer to schedules that truly maximize sample quality. The framework alternates global initialization search with local MEP minimization, then reports final FID. Without explicit validation (e.g., scatter plots or rank correlation between MEP and FID over held-out schedules, models, and datasets), it remains possible that MEP minimization improves the proxy while leaving or even degrading true perceptual quality, especially in the extremely low-NFE regime where discretization errors dominate.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript introduces the Hierarchical-Schedule-Optimizer (HSO), a bi-level optimization framework for training-free acceleration of diffusion model sampling via optimized timestep schedules at small NFE. It alternates global initialization search with local refinement guided by the Midpoint Error Proxy (MEP) as a solver-agnostic objective and the Spacing-Penalized Fitness (SPF) to avoid degenerate schedules. Extensive experiments are claimed to establish new SOTA results in the low-NFE regime, e.g., FID 11.94 at NFE=5 on LAION-Aesthetics with Stable Diffusion v2.1, at a one-time cost under 8 seconds.","tokens_in":1960,"tokens_out":595,"duration_ms":95330,"significance":"If the central results hold, the work offers a practical, low-cost method for improving sampling speed and quality in diffusion models without retraining or architectural changes. The hierarchical decomposition and proxy objectives address simultaneous requirements of effectiveness, adaptivity, robustness, and efficiency that prior schedule optimization approaches have not fully satisfied, potentially benefiting latency-sensitive generative applications.","major_comments":[{"comment":"§3 (MEP definition and usage): The central claim that HSO achieves superior sample quality rests on MEP serving as a reliable surrogate for final FID. No scatter plots, Spearman rank correlations, or ablation tables are provided showing that lower MEP values predict lower FID across held-out schedules, models, or datasets; without this, it remains possible that the bi-level optimizer improves the proxy while leaving or degrading true perceptual quality, especially at NFE=5 where discretization error dominates.","section":"§3"},{"comment":"§4 (Experiments, quantitative results): The reported SOTA FID of 11.94 at NFE=5 is presented without accompanying details on the number of independent runs, standard deviations, baseline re-implementation sources, or statistical significance tests against prior schedule optimizers. This omission makes it impossible to rule out post-hoc schedule selection or implementation-specific tuning as contributors to the claimed gains.","section":"§4"}],"minor_comments":[{"comment":"Abstract: The claim of 'extensive experiments' would be strengthened by naming the full set of datasets and models evaluated rather than highlighting only the single LAION-Aesthetics / SD v2.1 example.","section":"Abstract"},{"comment":"Notation: Define NFE, FID, MEP, and SPF on first use in the main text and ensure consistent capitalization throughout.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The manuscript fits the journal scope but should be checked for completeness of citations to prior training-free schedule optimization literature; the low-confidence soundness rating in the reader note stems directly from the missing surrogate-validation and statistical-detail issues raised above."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the detailed and constructive review. The comments highlight important aspects of validation and reporting that we will address to strengthen the manuscript. Below we respond point-by-point to the major comments.","responses":[{"response":"We appreciate this observation. The Midpoint Error Proxy is derived directly from the local truncation error of the midpoint solver applied to the probability-flow ODE, providing a solver-agnostic and numerically stable surrogate for discretization error that dominates at low NFE. While the original submission did not include explicit correlation analyses, the optimization trajectories and final FID improvements are consistent with MEP serving as a reliable proxy. To directly address the concern, the revised manuscript will add scatter plots of MEP versus FID for held-out schedules, Spearman rank correlations computed across multiple models and datasets, and an ablation table demonstrating that lower MEP values reliably correspond to lower FID. These additions will provide the requested empirical validation.","revision_made":"yes","referee_comment":"[§3] §3 (MEP definition and usage): The central claim that HSO achieves superior sample quality rests on MEP serving as a reliable surrogate for final FID. No scatter plots, Spearman rank correlations, or ablation tables are provided showing that lower MEP values predict lower FID across held-out schedules, models, or datasets; without this, it remains possible that the bi-level optimizer improves the proxy while leaving or degrading true perceptual quality, especially at NFE=5 where discretization error dominates."},{"response":"We agree that additional statistical rigor and transparency are warranted. In the revised manuscript we will report the number of independent runs (five seeds), include standard deviations for all FID scores, explicitly state the sources and re-implementation details for all baselines (official code repositories or paper-provided implementations), and add paired t-test results with p-values to establish statistical significance against competing schedule optimizers. These changes will allow readers to assess variability and rule out tuning artifacts.","revision_made":"yes","referee_comment":"[§4] §4 (Experiments, quantitative results): The reported SOTA FID of 11.94 at NFE=5 is presented without accompanying details on the number of independent runs, standard deviations, baseline re-implementation sources, or statistical significance tests against prior schedule optimizers. This omission makes it impossible to rule out post-hoc schedule selection or implementation-specific tuning as contributors to the claimed gains."}],"tokens_in":1553,"tokens_out":511,"duration_ms":37434,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing to know is that this paper introduces a hierarchical bi-level optimizer for timestep schedules in diffusion sampling. It splits the problem into an upper-level global search for a good starting point and a lower-level local search that minimizes a Midpoint Error Proxy while using a spacing penalty to avoid collapsed schedules. The reported outcome is a new low-NFE result: FID 11.94 at 5 steps on LAION-Aesthetics with Stable Diffusion v2.1, all with a one-time optimization cost under 8 seconds and no retraining.","headline":"HSO gives a workable bi-level schedule optimizer for low-NFE diffusion sampling with a new midpoint proxy, but the proxy-FID link is the part that still needs direct evidence.","tokens_in":2434,"tokens_out":191,"would_cite":false,"duration_ms":58548,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Cost/FunctionalEquation.lean","rs_theorem":"washburn_uniqueness_aczel","paper_passage":"Midpoint Error Proxy (MEP) ... JMEP(Λ) = sum ... (e^{λ_{i+1}} - e^{λ_i})"},{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/BranchSelection.lean","rs_theorem":"branch_selection","paper_passage":"Spacing-Penalized Fitness (SPF) ... L_penalty term"}],"headline":"Bi-level schedule optimization with midpoint error proxy for diffusion ODE sampling","alignment":"orthogonal","rationale":"The paper's core machinery (MEP integral approximation, SPF spacing penalty, bi-level global/local search over EDM-parameterized schedules) is standard numerical optimization for low-NFE diffusion sampling. It contains no recognition-cost J(x), cosh identities, φ-ladder spacings, 8-tick periodicity, or parameter-free constant derivations. No overlap with the RS forcing chain from a single distinction.","tokens_in":54270,"confidence":"high","tokens_out":272,"duration_ms":14288,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A bi-level optimizer discovers timestep schedules that let diffusion models produce high-quality images in just five steps.","keywords":["diffusion models","schedule optimization","sampling acceleration","low NFE","bi-level optimization","training-free","image generation"],"falsifier":"Applying an HSO-derived schedule to a held-out diffusion model and observing that its FID is no better than a uniform timestep schedule would falsify the central claim.","tokens_in":2732,"feed_emoji":"⚡","tokens_out":492,"duration_ms":67919,"temperature":0.7,"pith_summary":"The paper introduces Hierarchical Schedule Optimization to solve the problem of slow iterative sampling in diffusion models when restricted to very small numbers of function evaluations. It reframes the search for good timestep distributions as a tractable bi-level process that alternates between a global initialization strategy and local schedule refinement. Two new components drive the search: a midpoint error proxy that serves as a stable, solver-independent objective and a spacing penalty that prevents degenerate timestep placements. The resulting schedules deliver state-of-the-art image quality at extremely low NFE counts while requiring only a one-time optimization cost of seconds. A reader would care because the method removes the need for costly model retraining to achieve fast generation.","feed_headline":"Bi-level optimizer finds 5-step schedules for top diffusion quality","feed_subtitle":"HSO alternates global and local search to produce robust timestep distributions in seconds without any model retraining.","key_machinery":"The Hierarchical-Schedule-Optimizer (HSO), a bi-level framework that alternates global initialization search with local refinement guided by the Midpoint Error Proxy and Spacing-Penalized Fitness.","core_discovery":"HSO is a bi-level optimization framework that finds globally effective sampling schedules by iteratively alternating an upper-level search for a good initialization strategy with a lower-level local refinement step; the search is driven by the Midpoint Error Proxy as a numerically stable surrogate objective and the Spacing-Penalized Fitness function to enforce practical robustness, yielding an FID of 11.94 at NFE=5 on LAION-Aesthetics with Stable Diffusion v2.1 after a single optimization run lasting less than eight seconds.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["HSO bi-level optimizer finds robust 5-step diffusion schedules","HSO alternates global and local optimization for sampling schedules","Hierarchical schedule optimization improves diffusion sampling efficiency","HSO achieves FID 11.94 at NFE 5 on LAION with Stable Diffusion"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The midpoint error proxy must remain a reliable predictor of final sample quality for the chosen diffusion model and dataset.","fun_headline_variants_meta":{"raw":{"variants":["HSO bi-level optimizer finds robust 5-step diffusion schedules","HSO alternates global and local optimization for sampling schedules","Hierarchical schedule optimization improves diffusion sampling efficiency","HSO achieves FID 11.94 at NFE 5 on LAION with Stable Diffusion"]},"model":"grok-4.3","cost_usd":0.013648,"raw_usage":{"total_tokens":5880,"prompt_tokens":788,"num_sources_used":0,"completion_tokens":71,"cost_in_usd_ticks":136478000,"prompt_tokens_details":{"text_tokens":788,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":5021,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":788,"tokens_out":71,"duration_ms":92646,"temperature":1.0,"reasoning_tokens":5021,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-21T19:50:48.688955+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Applying an HSO-derived schedule to a held-out diffusion model and observing that its FID is no better than a uniform timestep schedule would falsify the central claim.","supporting_citations":[],"review_version":1}